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<h1>Source code for torch.optim.lbfgs</h1><div class="highlight"><pre>
<span></span><span class="kn">import</span> <span class="nn">torch</span>
<span class="kn">from</span> <span class="nn">functools</span> <span class="kn">import</span> <span class="n">reduce</span>
<span class="kn">from</span> <span class="nn">.optimizer</span> <span class="kn">import</span> <span class="n">Optimizer</span>
<span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span><span class="s1">'LBFGS'</span><span class="p">]</span>
<span class="k">def</span> <span class="nf">_cubic_interpolate</span><span class="p">(</span><span class="n">x1</span><span class="p">,</span> <span class="n">f1</span><span class="p">,</span> <span class="n">g1</span><span class="p">,</span> <span class="n">x2</span><span class="p">,</span> <span class="n">f2</span><span class="p">,</span> <span class="n">g2</span><span class="p">,</span> <span class="n">bounds</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="c1"># ported from https://github.com/torch/optim/blob/master/polyinterp.lua</span>
<span class="c1"># Compute bounds of interpolation area</span>
<span class="k">if</span> <span class="n">bounds</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">xmin_bound</span><span class="p">,</span> <span class="n">xmax_bound</span> <span class="o">=</span> <span class="n">bounds</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">xmin_bound</span><span class="p">,</span> <span class="n">xmax_bound</span> <span class="o">=</span> <span class="p">(</span><span class="n">x1</span><span class="p">,</span> <span class="n">x2</span><span class="p">)</span> <span class="k">if</span> <span class="n">x1</span> <span class="o"><=</span> <span class="n">x2</span> <span class="k">else</span> <span class="p">(</span><span class="n">x2</span><span class="p">,</span> <span class="n">x1</span><span class="p">)</span>
<span class="c1"># Code for most common case: cubic interpolation of 2 points</span>
<span class="c1"># w/ function and derivative values for both</span>
<span class="c1"># Solution in this case (where x2 is the farthest point):</span>
<span class="c1"># d1 = g1 + g2 - 3*(f1-f2)/(x1-x2);</span>
<span class="c1"># d2 = sqrt(d1^2 - g1*g2);</span>
<span class="c1"># min_pos = x2 - (x2 - x1)*((g2 + d2 - d1)/(g2 - g1 + 2*d2));</span>
<span class="c1"># t_new = min(max(min_pos,xmin_bound),xmax_bound);</span>
<span class="n">d1</span> <span class="o">=</span> <span class="n">g1</span> <span class="o">+</span> <span class="n">g2</span> <span class="o">-</span> <span class="mi">3</span> <span class="o">*</span> <span class="p">(</span><span class="n">f1</span> <span class="o">-</span> <span class="n">f2</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">x1</span> <span class="o">-</span> <span class="n">x2</span><span class="p">)</span>
<span class="n">d2_square</span> <span class="o">=</span> <span class="n">d1</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="n">g1</span> <span class="o">*</span> <span class="n">g2</span>
<span class="k">if</span> <span class="n">d2_square</span> <span class="o">>=</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">d2</span> <span class="o">=</span> <span class="n">d2_square</span><span class="o">.</span><span class="n">sqrt</span><span class="p">()</span>
<span class="k">if</span> <span class="n">x1</span> <span class="o"><=</span> <span class="n">x2</span><span class="p">:</span>
<span class="n">min_pos</span> <span class="o">=</span> <span class="n">x2</span> <span class="o">-</span> <span class="p">(</span><span class="n">x2</span> <span class="o">-</span> <span class="n">x1</span><span class="p">)</span> <span class="o">*</span> <span class="p">((</span><span class="n">g2</span> <span class="o">+</span> <span class="n">d2</span> <span class="o">-</span> <span class="n">d1</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">g2</span> <span class="o">-</span> <span class="n">g1</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">d2</span><span class="p">))</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">min_pos</span> <span class="o">=</span> <span class="n">x1</span> <span class="o">-</span> <span class="p">(</span><span class="n">x1</span> <span class="o">-</span> <span class="n">x2</span><span class="p">)</span> <span class="o">*</span> <span class="p">((</span><span class="n">g1</span> <span class="o">+</span> <span class="n">d2</span> <span class="o">-</span> <span class="n">d1</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">g1</span> <span class="o">-</span> <span class="n">g2</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">d2</span><span class="p">))</span>
<span class="k">return</span> <span class="nb">min</span><span class="p">(</span><span class="nb">max</span><span class="p">(</span><span class="n">min_pos</span><span class="p">,</span> <span class="n">xmin_bound</span><span class="p">),</span> <span class="n">xmax_bound</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="p">(</span><span class="n">xmin_bound</span> <span class="o">+</span> <span class="n">xmax_bound</span><span class="p">)</span> <span class="o">/</span> <span class="mf">2.</span>
<span class="k">def</span> <span class="nf">_strong_wolfe</span><span class="p">(</span><span class="n">obj_func</span><span class="p">,</span>
<span class="n">x</span><span class="p">,</span>
<span class="n">t</span><span class="p">,</span>
<span class="n">d</span><span class="p">,</span>
<span class="n">f</span><span class="p">,</span>
<span class="n">g</span><span class="p">,</span>
<span class="n">gtd</span><span class="p">,</span>
<span class="n">c1</span><span class="o">=</span><span class="mf">1e-4</span><span class="p">,</span>
<span class="n">c2</span><span class="o">=</span><span class="mf">0.9</span><span class="p">,</span>
<span class="n">tolerance_change</span><span class="o">=</span><span class="mf">1e-9</span><span class="p">,</span>
<span class="n">max_ls</span><span class="o">=</span><span class="mi">25</span><span class="p">):</span>
<span class="c1"># ported from https://github.com/torch/optim/blob/master/lswolfe.lua</span>
<span class="n">d_norm</span> <span class="o">=</span> <span class="n">d</span><span class="o">.</span><span class="n">abs</span><span class="p">()</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
<span class="n">g</span> <span class="o">=</span> <span class="n">g</span><span class="o">.</span><span class="n">clone</span><span class="p">(</span><span class="n">memory_format</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">contiguous_format</span><span class="p">)</span>
<span class="c1"># evaluate objective and gradient using initial step</span>
<span class="n">f_new</span><span class="p">,</span> <span class="n">g_new</span> <span class="o">=</span> <span class="n">obj_func</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">d</span><span class="p">)</span>
<span class="n">ls_func_evals</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">gtd_new</span> <span class="o">=</span> <span class="n">g_new</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">d</span><span class="p">)</span>
<span class="c1"># bracket an interval containing a point satisfying the Wolfe criteria</span>
<span class="n">t_prev</span><span class="p">,</span> <span class="n">f_prev</span><span class="p">,</span> <span class="n">g_prev</span><span class="p">,</span> <span class="n">gtd_prev</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">,</span> <span class="n">gtd</span>
<span class="n">done</span> <span class="o">=</span> <span class="kc">False</span>
<span class="n">ls_iter</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">while</span> <span class="n">ls_iter</span> <span class="o"><</span> <span class="n">max_ls</span><span class="p">:</span>
<span class="c1"># check conditions</span>
<span class="k">if</span> <span class="n">f_new</span> <span class="o">></span> <span class="p">(</span><span class="n">f</span> <span class="o">+</span> <span class="n">c1</span> <span class="o">*</span> <span class="n">t</span> <span class="o">*</span> <span class="n">gtd</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="n">ls_iter</span> <span class="o">></span> <span class="mi">1</span> <span class="ow">and</span> <span class="n">f_new</span> <span class="o">>=</span> <span class="n">f_prev</span><span class="p">):</span>
<span class="n">bracket</span> <span class="o">=</span> <span class="p">[</span><span class="n">t_prev</span><span class="p">,</span> <span class="n">t</span><span class="p">]</span>
<span class="n">bracket_f</span> <span class="o">=</span> <span class="p">[</span><span class="n">f_prev</span><span class="p">,</span> <span class="n">f_new</span><span class="p">]</span>
<span class="n">bracket_g</span> <span class="o">=</span> <span class="p">[</span><span class="n">g_prev</span><span class="p">,</span> <span class="n">g_new</span><span class="o">.</span><span class="n">clone</span><span class="p">(</span><span class="n">memory_format</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">contiguous_format</span><span class="p">)]</span>
<span class="n">bracket_gtd</span> <span class="o">=</span> <span class="p">[</span><span class="n">gtd_prev</span><span class="p">,</span> <span class="n">gtd_new</span><span class="p">]</span>
<span class="k">break</span>
<span class="k">if</span> <span class="nb">abs</span><span class="p">(</span><span class="n">gtd_new</span><span class="p">)</span> <span class="o"><=</span> <span class="o">-</span><span class="n">c2</span> <span class="o">*</span> <span class="n">gtd</span><span class="p">:</span>
<span class="n">bracket</span> <span class="o">=</span> <span class="p">[</span><span class="n">t</span><span class="p">]</span>
<span class="n">bracket_f</span> <span class="o">=</span> <span class="p">[</span><span class="n">f_new</span><span class="p">]</span>
<span class="n">bracket_g</span> <span class="o">=</span> <span class="p">[</span><span class="n">g_new</span><span class="p">]</span>
<span class="n">done</span> <span class="o">=</span> <span class="kc">True</span>
<span class="k">break</span>
<span class="k">if</span> <span class="n">gtd_new</span> <span class="o">>=</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">bracket</span> <span class="o">=</span> <span class="p">[</span><span class="n">t_prev</span><span class="p">,</span> <span class="n">t</span><span class="p">]</span>
<span class="n">bracket_f</span> <span class="o">=</span> <span class="p">[</span><span class="n">f_prev</span><span class="p">,</span> <span class="n">f_new</span><span class="p">]</span>
<span class="n">bracket_g</span> <span class="o">=</span> <span class="p">[</span><span class="n">g_prev</span><span class="p">,</span> <span class="n">g_new</span><span class="o">.</span><span class="n">clone</span><span class="p">(</span><span class="n">memory_format</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">contiguous_format</span><span class="p">)]</span>
<span class="n">bracket_gtd</span> <span class="o">=</span> <span class="p">[</span><span class="n">gtd_prev</span><span class="p">,</span> <span class="n">gtd_new</span><span class="p">]</span>
<span class="k">break</span>
<span class="c1"># interpolate</span>
<span class="n">min_step</span> <span class="o">=</span> <span class="n">t</span> <span class="o">+</span> <span class="mf">0.01</span> <span class="o">*</span> <span class="p">(</span><span class="n">t</span> <span class="o">-</span> <span class="n">t_prev</span><span class="p">)</span>
<span class="n">max_step</span> <span class="o">=</span> <span class="n">t</span> <span class="o">*</span> <span class="mi">10</span>
<span class="n">tmp</span> <span class="o">=</span> <span class="n">t</span>
<span class="n">t</span> <span class="o">=</span> <span class="n">_cubic_interpolate</span><span class="p">(</span>
<span class="n">t_prev</span><span class="p">,</span>
<span class="n">f_prev</span><span class="p">,</span>
<span class="n">gtd_prev</span><span class="p">,</span>
<span class="n">t</span><span class="p">,</span>
<span class="n">f_new</span><span class="p">,</span>
<span class="n">gtd_new</span><span class="p">,</span>
<span class="n">bounds</span><span class="o">=</span><span class="p">(</span><span class="n">min_step</span><span class="p">,</span> <span class="n">max_step</span><span class="p">))</span>
<span class="c1"># next step</span>
<span class="n">t_prev</span> <span class="o">=</span> <span class="n">tmp</span>
<span class="n">f_prev</span> <span class="o">=</span> <span class="n">f_new</span>
<span class="n">g_prev</span> <span class="o">=</span> <span class="n">g_new</span><span class="o">.</span><span class="n">clone</span><span class="p">(</span><span class="n">memory_format</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">contiguous_format</span><span class="p">)</span>
<span class="n">gtd_prev</span> <span class="o">=</span> <span class="n">gtd_new</span>
<span class="n">f_new</span><span class="p">,</span> <span class="n">g_new</span> <span class="o">=</span> <span class="n">obj_func</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">d</span><span class="p">)</span>
<span class="n">ls_func_evals</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">gtd_new</span> <span class="o">=</span> <span class="n">g_new</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">d</span><span class="p">)</span>
<span class="n">ls_iter</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="c1"># reached max number of iterations?</span>
<span class="k">if</span> <span class="n">ls_iter</span> <span class="o">==</span> <span class="n">max_ls</span><span class="p">:</span>
<span class="n">bracket</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">t</span><span class="p">]</span>
<span class="n">bracket_f</span> <span class="o">=</span> <span class="p">[</span><span class="n">f</span><span class="p">,</span> <span class="n">f_new</span><span class="p">]</span>
<span class="n">bracket_g</span> <span class="o">=</span> <span class="p">[</span><span class="n">g</span><span class="p">,</span> <span class="n">g_new</span><span class="p">]</span>
<span class="c1"># zoom phase: we now have a point satisfying the criteria, or</span>
<span class="c1"># a bracket around it. We refine the bracket until we find the</span>
<span class="c1"># exact point satisfying the criteria</span>
<span class="n">insuf_progress</span> <span class="o">=</span> <span class="kc">False</span>
<span class="c1"># find high and low points in bracket</span>
<span class="n">low_pos</span><span class="p">,</span> <span class="n">high_pos</span> <span class="o">=</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span> <span class="k">if</span> <span class="n">bracket_f</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o"><=</span> <span class="n">bracket_f</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="k">else</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
<span class="k">while</span> <span class="ow">not</span> <span class="n">done</span> <span class="ow">and</span> <span class="n">ls_iter</span> <span class="o"><</span> <span class="n">max_ls</span><span class="p">:</span>
<span class="c1"># line-search bracket is so small</span>
<span class="k">if</span> <span class="nb">abs</span><span class="p">(</span><span class="n">bracket</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">bracket</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">*</span> <span class="n">d_norm</span> <span class="o"><</span> <span class="n">tolerance_change</span><span class="p">:</span>
<span class="k">break</span>
<span class="c1"># compute new trial value</span>
<span class="n">t</span> <span class="o">=</span> <span class="n">_cubic_interpolate</span><span class="p">(</span><span class="n">bracket</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">bracket_f</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">bracket_gtd</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span>
<span class="n">bracket</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">bracket_f</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">bracket_gtd</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
<span class="c1"># test that we are making sufficient progress:</span>
<span class="c1"># in case `t` is so close to boundary, we mark that we are making</span>
<span class="c1"># insufficient progress, and if</span>
<span class="c1"># + we have made insufficient progress in the last step, or</span>
<span class="c1"># + `t` is at one of the boundary,</span>
<span class="c1"># we will move `t` to a position which is `0.1 * len(bracket)`</span>
<span class="c1"># away from the nearest boundary point.</span>
<span class="n">eps</span> <span class="o">=</span> <span class="mf">0.1</span> <span class="o">*</span> <span class="p">(</span><span class="nb">max</span><span class="p">(</span><span class="n">bracket</span><span class="p">)</span> <span class="o">-</span> <span class="nb">min</span><span class="p">(</span><span class="n">bracket</span><span class="p">))</span>
<span class="k">if</span> <span class="nb">min</span><span class="p">(</span><span class="nb">max</span><span class="p">(</span><span class="n">bracket</span><span class="p">)</span> <span class="o">-</span> <span class="n">t</span><span class="p">,</span> <span class="n">t</span> <span class="o">-</span> <span class="nb">min</span><span class="p">(</span><span class="n">bracket</span><span class="p">))</span> <span class="o"><</span> <span class="n">eps</span><span class="p">:</span>
<span class="c1"># interpolation close to boundary</span>
<span class="k">if</span> <span class="n">insuf_progress</span> <span class="ow">or</span> <span class="n">t</span> <span class="o">>=</span> <span class="nb">max</span><span class="p">(</span><span class="n">bracket</span><span class="p">)</span> <span class="ow">or</span> <span class="n">t</span> <span class="o"><=</span> <span class="nb">min</span><span class="p">(</span><span class="n">bracket</span><span class="p">):</span>
<span class="c1"># evaluate at 0.1 away from boundary</span>
<span class="k">if</span> <span class="nb">abs</span><span class="p">(</span><span class="n">t</span> <span class="o">-</span> <span class="nb">max</span><span class="p">(</span><span class="n">bracket</span><span class="p">))</span> <span class="o"><</span> <span class="nb">abs</span><span class="p">(</span><span class="n">t</span> <span class="o">-</span> <span class="nb">min</span><span class="p">(</span><span class="n">bracket</span><span class="p">)):</span>
<span class="n">t</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">bracket</span><span class="p">)</span> <span class="o">-</span> <span class="n">eps</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">t</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">bracket</span><span class="p">)</span> <span class="o">+</span> <span class="n">eps</span>
<span class="n">insuf_progress</span> <span class="o">=</span> <span class="kc">False</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">insuf_progress</span> <span class="o">=</span> <span class="kc">True</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">insuf_progress</span> <span class="o">=</span> <span class="kc">False</span>
<span class="c1"># Evaluate new point</span>
<span class="n">f_new</span><span class="p">,</span> <span class="n">g_new</span> <span class="o">=</span> <span class="n">obj_func</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">d</span><span class="p">)</span>
<span class="n">ls_func_evals</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">gtd_new</span> <span class="o">=</span> <span class="n">g_new</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">d</span><span class="p">)</span>
<span class="n">ls_iter</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">if</span> <span class="n">f_new</span> <span class="o">></span> <span class="p">(</span><span class="n">f</span> <span class="o">+</span> <span class="n">c1</span> <span class="o">*</span> <span class="n">t</span> <span class="o">*</span> <span class="n">gtd</span><span class="p">)</span> <span class="ow">or</span> <span class="n">f_new</span> <span class="o">>=</span> <span class="n">bracket_f</span><span class="p">[</span><span class="n">low_pos</span><span class="p">]:</span>
<span class="c1"># Armijo condition not satisfied or not lower than lowest point</span>
<span class="n">bracket</span><span class="p">[</span><span class="n">high_pos</span><span class="p">]</span> <span class="o">=</span> <span class="n">t</span>
<span class="n">bracket_f</span><span class="p">[</span><span class="n">high_pos</span><span class="p">]</span> <span class="o">=</span> <span class="n">f_new</span>
<span class="n">bracket_g</span><span class="p">[</span><span class="n">high_pos</span><span class="p">]</span> <span class="o">=</span> <span class="n">g_new</span><span class="o">.</span><span class="n">clone</span><span class="p">(</span><span class="n">memory_format</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">contiguous_format</span><span class="p">)</span>
<span class="n">bracket_gtd</span><span class="p">[</span><span class="n">high_pos</span><span class="p">]</span> <span class="o">=</span> <span class="n">gtd_new</span>
<span class="n">low_pos</span><span class="p">,</span> <span class="n">high_pos</span> <span class="o">=</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span> <span class="k">if</span> <span class="n">bracket_f</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o"><=</span> <span class="n">bracket_f</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="k">else</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">if</span> <span class="nb">abs</span><span class="p">(</span><span class="n">gtd_new</span><span class="p">)</span> <span class="o"><=</span> <span class="o">-</span><span class="n">c2</span> <span class="o">*</span> <span class="n">gtd</span><span class="p">:</span>
<span class="c1"># Wolfe conditions satisfied</span>
<span class="n">done</span> <span class="o">=</span> <span class="kc">True</span>
<span class="k">elif</span> <span class="n">gtd_new</span> <span class="o">*</span> <span class="p">(</span><span class="n">bracket</span><span class="p">[</span><span class="n">high_pos</span><span class="p">]</span> <span class="o">-</span> <span class="n">bracket</span><span class="p">[</span><span class="n">low_pos</span><span class="p">])</span> <span class="o">>=</span> <span class="mi">0</span><span class="p">:</span>
<span class="c1"># old high becomes new low</span>
<span class="n">bracket</span><span class="p">[</span><span class="n">high_pos</span><span class="p">]</span> <span class="o">=</span> <span class="n">bracket</span><span class="p">[</span><span class="n">low_pos</span><span class="p">]</span>
<span class="n">bracket_f</span><span class="p">[</span><span class="n">high_pos</span><span class="p">]</span> <span class="o">=</span> <span class="n">bracket_f</span><span class="p">[</span><span class="n">low_pos</span><span class="p">]</span>
<span class="n">bracket_g</span><span class="p">[</span><span class="n">high_pos</span><span class="p">]</span> <span class="o">=</span> <span class="n">bracket_g</span><span class="p">[</span><span class="n">low_pos</span><span class="p">]</span>
<span class="n">bracket_gtd</span><span class="p">[</span><span class="n">high_pos</span><span class="p">]</span> <span class="o">=</span> <span class="n">bracket_gtd</span><span class="p">[</span><span class="n">low_pos</span><span class="p">]</span>
<span class="c1"># new point becomes new low</span>
<span class="n">bracket</span><span class="p">[</span><span class="n">low_pos</span><span class="p">]</span> <span class="o">=</span> <span class="n">t</span>
<span class="n">bracket_f</span><span class="p">[</span><span class="n">low_pos</span><span class="p">]</span> <span class="o">=</span> <span class="n">f_new</span>
<span class="n">bracket_g</span><span class="p">[</span><span class="n">low_pos</span><span class="p">]</span> <span class="o">=</span> <span class="n">g_new</span><span class="o">.</span><span class="n">clone</span><span class="p">(</span><span class="n">memory_format</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">contiguous_format</span><span class="p">)</span>
<span class="n">bracket_gtd</span><span class="p">[</span><span class="n">low_pos</span><span class="p">]</span> <span class="o">=</span> <span class="n">gtd_new</span>
<span class="c1"># return stuff</span>
<span class="n">t</span> <span class="o">=</span> <span class="n">bracket</span><span class="p">[</span><span class="n">low_pos</span><span class="p">]</span>
<span class="n">f_new</span> <span class="o">=</span> <span class="n">bracket_f</span><span class="p">[</span><span class="n">low_pos</span><span class="p">]</span>
<span class="n">g_new</span> <span class="o">=</span> <span class="n">bracket_g</span><span class="p">[</span><span class="n">low_pos</span><span class="p">]</span>
<span class="k">return</span> <span class="n">f_new</span><span class="p">,</span> <span class="n">g_new</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">ls_func_evals</span>
<div class="viewcode-block" id="LBFGS"><a class="viewcode-back" href="../../../generated/torch.optim.LBFGS.html#torch.optim.LBFGS">[docs]</a><span class="k">class</span> <span class="nc">LBFGS</span><span class="p">(</span><span class="n">Optimizer</span><span class="p">):</span>
<span class="sd">"""Implements L-BFGS algorithm, heavily inspired by `minFunc</span>
<span class="sd"> <https://www.cs.ubc.ca/~schmidtm/Software/minFunc.html>`_.</span>
<span class="sd"> .. warning::</span>
<span class="sd"> This optimizer doesn't support per-parameter options and parameter</span>
<span class="sd"> groups (there can be only one).</span>
<span class="sd"> .. warning::</span>
<span class="sd"> Right now all parameters have to be on a single device. This will be</span>
<span class="sd"> improved in the future.</span>
<span class="sd"> .. note::</span>
<span class="sd"> This is a very memory intensive optimizer (it requires additional</span>
<span class="sd"> ``param_bytes * (history_size + 1)`` bytes). If it doesn't fit in memory</span>
<span class="sd"> try reducing the history size, or use a different algorithm.</span>
<span class="sd"> Args:</span>
<span class="sd"> lr (float): learning rate (default: 1)</span>
<span class="sd"> max_iter (int): maximal number of iterations per optimization step</span>
<span class="sd"> (default: 20)</span>
<span class="sd"> max_eval (int): maximal number of function evaluations per optimization</span>
<span class="sd"> step (default: max_iter * 1.25).</span>
<span class="sd"> tolerance_grad (float): termination tolerance on first order optimality</span>
<span class="sd"> (default: 1e-5).</span>
<span class="sd"> tolerance_change (float): termination tolerance on function</span>
<span class="sd"> value/parameter changes (default: 1e-9).</span>
<span class="sd"> history_size (int): update history size (default: 100).</span>
<span class="sd"> line_search_fn (str): either 'strong_wolfe' or None (default: None).</span>
<span class="sd"> """</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
<span class="n">params</span><span class="p">,</span>
<span class="n">lr</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
<span class="n">max_iter</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span>
<span class="n">max_eval</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">tolerance_grad</span><span class="o">=</span><span class="mf">1e-7</span><span class="p">,</span>
<span class="n">tolerance_change</span><span class="o">=</span><span class="mf">1e-9</span><span class="p">,</span>
<span class="n">history_size</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span>
<span class="n">line_search_fn</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="k">if</span> <span class="n">max_eval</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">max_eval</span> <span class="o">=</span> <span class="n">max_iter</span> <span class="o">*</span> <span class="mi">5</span> <span class="o">//</span> <span class="mi">4</span>
<span class="n">defaults</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span>
<span class="n">lr</span><span class="o">=</span><span class="n">lr</span><span class="p">,</span>
<span class="n">max_iter</span><span class="o">=</span><span class="n">max_iter</span><span class="p">,</span>
<span class="n">max_eval</span><span class="o">=</span><span class="n">max_eval</span><span class="p">,</span>
<span class="n">tolerance_grad</span><span class="o">=</span><span class="n">tolerance_grad</span><span class="p">,</span>
<span class="n">tolerance_change</span><span class="o">=</span><span class="n">tolerance_change</span><span class="p">,</span>
<span class="n">history_size</span><span class="o">=</span><span class="n">history_size</span><span class="p">,</span>
<span class="n">line_search_fn</span><span class="o">=</span><span class="n">line_search_fn</span><span class="p">)</span>
<span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">params</span><span class="p">,</span> <span class="n">defaults</span><span class="p">)</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">param_groups</span><span class="p">)</span> <span class="o">!=</span> <span class="mi">1</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">"LBFGS doesn't support per-parameter options "</span>
<span class="s2">"(parameter groups)"</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_params</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">param_groups</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="s1">'params'</span><span class="p">]</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_numel_cache</span> <span class="o">=</span> <span class="kc">None</span>
<span class="k">def</span> <span class="nf">_numel</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_numel_cache</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_numel_cache</span> <span class="o">=</span> <span class="n">reduce</span><span class="p">(</span><span class="k">lambda</span> <span class="n">total</span><span class="p">,</span> <span class="n">p</span><span class="p">:</span> <span class="n">total</span> <span class="o">+</span> <span class="n">p</span><span class="o">.</span><span class="n">numel</span><span class="p">(),</span> <span class="bp">self</span><span class="o">.</span><span class="n">_params</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_numel_cache</span>
<span class="k">def</span> <span class="nf">_gather_flat_grad</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="n">views</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_params</span><span class="p">:</span>
<span class="k">if</span> <span class="n">p</span><span class="o">.</span><span class="n">grad</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">view</span> <span class="o">=</span> <span class="n">p</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">p</span><span class="o">.</span><span class="n">numel</span><span class="p">())</span><span class="o">.</span><span class="n">zero_</span><span class="p">()</span>
<span class="k">elif</span> <span class="n">p</span><span class="o">.</span><span class="n">grad</span><span class="o">.</span><span class="n">is_sparse</span><span class="p">:</span>
<span class="n">view</span> <span class="o">=</span> <span class="n">p</span><span class="o">.</span><span class="n">grad</span><span class="o">.</span><span class="n">to_dense</span><span class="p">()</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">view</span> <span class="o">=</span> <span class="n">p</span><span class="o">.</span><span class="n">grad</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="n">views</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">view</span><span class="p">)</span>
<span class="k">return</span> <span class="n">torch</span><span class="o">.</span><span class="n">cat</span><span class="p">(</span><span class="n">views</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">_add_grad</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">step_size</span><span class="p">,</span> <span class="n">update</span><span class="p">):</span>
<span class="n">offset</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_params</span><span class="p">:</span>
<span class="n">numel</span> <span class="o">=</span> <span class="n">p</span><span class="o">.</span><span class="n">numel</span><span class="p">()</span>
<span class="c1"># view as to avoid deprecated pointwise semantics</span>
<span class="n">p</span><span class="o">.</span><span class="n">add_</span><span class="p">(</span><span class="n">update</span><span class="p">[</span><span class="n">offset</span><span class="p">:</span><span class="n">offset</span> <span class="o">+</span> <span class="n">numel</span><span class="p">]</span><span class="o">.</span><span class="n">view_as</span><span class="p">(</span><span class="n">p</span><span class="p">),</span> <span class="n">alpha</span><span class="o">=</span><span class="n">step_size</span><span class="p">)</span>
<span class="n">offset</span> <span class="o">+=</span> <span class="n">numel</span>
<span class="k">assert</span> <span class="n">offset</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">_numel</span><span class="p">()</span>
<span class="k">def</span> <span class="nf">_clone_param</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="k">return</span> <span class="p">[</span><span class="n">p</span><span class="o">.</span><span class="n">clone</span><span class="p">(</span><span class="n">memory_format</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">contiguous_format</span><span class="p">)</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_params</span><span class="p">]</span>
<span class="k">def</span> <span class="nf">_set_param</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">params_data</span><span class="p">):</span>
<span class="k">for</span> <span class="n">p</span><span class="p">,</span> <span class="n">pdata</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_params</span><span class="p">,</span> <span class="n">params_data</span><span class="p">):</span>
<span class="n">p</span><span class="o">.</span><span class="n">copy_</span><span class="p">(</span><span class="n">pdata</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">_directional_evaluate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">closure</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">d</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_add_grad</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">d</span><span class="p">)</span>
<span class="n">loss</span> <span class="o">=</span> <span class="nb">float</span><span class="p">(</span><span class="n">closure</span><span class="p">())</span>
<span class="n">flat_grad</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_gather_flat_grad</span><span class="p">()</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_set_param</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="k">return</span> <span class="n">loss</span><span class="p">,</span> <span class="n">flat_grad</span>
<div class="viewcode-block" id="LBFGS.step"><a class="viewcode-back" href="../../../generated/torch.optim.LBFGS.html#torch.optim.LBFGS.step">[docs]</a> <span class="nd">@torch</span><span class="o">.</span><span class="n">no_grad</span><span class="p">()</span>
<span class="k">def</span> <span class="nf">step</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">closure</span><span class="p">):</span>
<span class="sd">"""Performs a single optimization step.</span>
<span class="sd"> Args:</span>
<span class="sd"> closure (Callable): A closure that reevaluates the model</span>
<span class="sd"> and returns the loss.</span>
<span class="sd"> """</span>
<span class="k">assert</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">param_groups</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span>
<span class="c1"># Make sure the closure is always called with grad enabled</span>
<span class="n">closure</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">enable_grad</span><span class="p">()(</span><span class="n">closure</span><span class="p">)</span>
<span class="n">group</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">param_groups</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">lr</span> <span class="o">=</span> <span class="n">group</span><span class="p">[</span><span class="s1">'lr'</span><span class="p">]</span>
<span class="n">max_iter</span> <span class="o">=</span> <span class="n">group</span><span class="p">[</span><span class="s1">'max_iter'</span><span class="p">]</span>
<span class="n">max_eval</span> <span class="o">=</span> <span class="n">group</span><span class="p">[</span><span class="s1">'max_eval'</span><span class="p">]</span>
<span class="n">tolerance_grad</span> <span class="o">=</span> <span class="n">group</span><span class="p">[</span><span class="s1">'tolerance_grad'</span><span class="p">]</span>
<span class="n">tolerance_change</span> <span class="o">=</span> <span class="n">group</span><span class="p">[</span><span class="s1">'tolerance_change'</span><span class="p">]</span>
<span class="n">line_search_fn</span> <span class="o">=</span> <span class="n">group</span><span class="p">[</span><span class="s1">'line_search_fn'</span><span class="p">]</span>
<span class="n">history_size</span> <span class="o">=</span> <span class="n">group</span><span class="p">[</span><span class="s1">'history_size'</span><span class="p">]</span>
<span class="c1"># NOTE: LBFGS has only global state, but we register it as state for</span>
<span class="c1"># the first param, because this helps with casting in load_state_dict</span>
<span class="n">state</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">state</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">_params</span><span class="p">[</span><span class="mi">0</span><span class="p">]]</span>
<span class="n">state</span><span class="o">.</span><span class="n">setdefault</span><span class="p">(</span><span class="s1">'func_evals'</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
<span class="n">state</span><span class="o">.</span><span class="n">setdefault</span><span class="p">(</span><span class="s1">'n_iter'</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
<span class="c1"># evaluate initial f(x) and df/dx</span>
<span class="n">orig_loss</span> <span class="o">=</span> <span class="n">closure</span><span class="p">()</span>
<span class="n">loss</span> <span class="o">=</span> <span class="nb">float</span><span class="p">(</span><span class="n">orig_loss</span><span class="p">)</span>
<span class="n">current_evals</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">state</span><span class="p">[</span><span class="s1">'func_evals'</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">flat_grad</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_gather_flat_grad</span><span class="p">()</span>
<span class="n">opt_cond</span> <span class="o">=</span> <span class="n">flat_grad</span><span class="o">.</span><span class="n">abs</span><span class="p">()</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="o"><=</span> <span class="n">tolerance_grad</span>
<span class="c1"># optimal condition</span>
<span class="k">if</span> <span class="n">opt_cond</span><span class="p">:</span>
<span class="k">return</span> <span class="n">orig_loss</span>
<span class="c1"># tensors cached in state (for tracing)</span>
<span class="n">d</span> <span class="o">=</span> <span class="n">state</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'d'</span><span class="p">)</span>
<span class="n">t</span> <span class="o">=</span> <span class="n">state</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'t'</span><span class="p">)</span>
<span class="n">old_dirs</span> <span class="o">=</span> <span class="n">state</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'old_dirs'</span><span class="p">)</span>
<span class="n">old_stps</span> <span class="o">=</span> <span class="n">state</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'old_stps'</span><span class="p">)</span>
<span class="n">ro</span> <span class="o">=</span> <span class="n">state</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'ro'</span><span class="p">)</span>
<span class="n">H_diag</span> <span class="o">=</span> <span class="n">state</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'H_diag'</span><span class="p">)</span>
<span class="n">prev_flat_grad</span> <span class="o">=</span> <span class="n">state</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'prev_flat_grad'</span><span class="p">)</span>
<span class="n">prev_loss</span> <span class="o">=</span> <span class="n">state</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'prev_loss'</span><span class="p">)</span>
<span class="n">n_iter</span> <span class="o">=</span> <span class="mi">0</span>
<span class="c1"># optimize for a max of max_iter iterations</span>
<span class="k">while</span> <span class="n">n_iter</span> <span class="o"><</span> <span class="n">max_iter</span><span class="p">:</span>
<span class="c1"># keep track of nb of iterations</span>
<span class="n">n_iter</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">state</span><span class="p">[</span><span class="s1">'n_iter'</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="c1">############################################################</span>
<span class="c1"># compute gradient descent direction</span>
<span class="c1">############################################################</span>
<span class="k">if</span> <span class="n">state</span><span class="p">[</span><span class="s1">'n_iter'</span><span class="p">]</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="n">d</span> <span class="o">=</span> <span class="n">flat_grad</span><span class="o">.</span><span class="n">neg</span><span class="p">()</span>
<span class="n">old_dirs</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">old_stps</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">ro</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">H_diag</span> <span class="o">=</span> <span class="mi">1</span>
<span class="k">else</span><span class="p">:</span>
<span class="c1"># do lbfgs update (update memory)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">flat_grad</span><span class="o">.</span><span class="n">sub</span><span class="p">(</span><span class="n">prev_flat_grad</span><span class="p">)</span>
<span class="n">s</span> <span class="o">=</span> <span class="n">d</span><span class="o">.</span><span class="n">mul</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
<span class="n">ys</span> <span class="o">=</span> <span class="n">y</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">s</span><span class="p">)</span> <span class="c1"># y*s</span>
<span class="k">if</span> <span class="n">ys</span> <span class="o">></span> <span class="mf">1e-10</span><span class="p">:</span>
<span class="c1"># updating memory</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">old_dirs</span><span class="p">)</span> <span class="o">==</span> <span class="n">history_size</span><span class="p">:</span>
<span class="c1"># shift history by one (limited-memory)</span>
<span class="n">old_dirs</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="n">old_stps</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="n">ro</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="c1"># store new direction/step</span>
<span class="n">old_dirs</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
<span class="n">old_stps</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
<span class="n">ro</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mf">1.</span> <span class="o">/</span> <span class="n">ys</span><span class="p">)</span>
<span class="c1"># update scale of initial Hessian approximation</span>
<span class="n">H_diag</span> <span class="o">=</span> <span class="n">ys</span> <span class="o">/</span> <span class="n">y</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">y</span><span class="p">)</span> <span class="c1"># (y*y)</span>
<span class="c1"># compute the approximate (L-BFGS) inverse Hessian</span>
<span class="c1"># multiplied by the gradient</span>
<span class="n">num_old</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">old_dirs</span><span class="p">)</span>
<span class="k">if</span> <span class="s1">'al'</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">state</span><span class="p">:</span>
<span class="n">state</span><span class="p">[</span><span class="s1">'al'</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="kc">None</span><span class="p">]</span> <span class="o">*</span> <span class="n">history_size</span>
<span class="n">al</span> <span class="o">=</span> <span class="n">state</span><span class="p">[</span><span class="s1">'al'</span><span class="p">]</span>
<span class="c1"># iteration in L-BFGS loop collapsed to use just one buffer</span>
<span class="n">q</span> <span class="o">=</span> <span class="n">flat_grad</span><span class="o">.</span><span class="n">neg</span><span class="p">()</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">num_old</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
<span class="n">al</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">old_stps</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">q</span><span class="p">)</span> <span class="o">*</span> <span class="n">ro</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<span class="n">q</span><span class="o">.</span><span class="n">add_</span><span class="p">(</span><span class="n">old_dirs</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">alpha</span><span class="o">=-</span><span class="n">al</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
<span class="c1"># multiply by initial Hessian</span>
<span class="c1"># r/d is the final direction</span>
<span class="n">d</span> <span class="o">=</span> <span class="n">r</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">mul</span><span class="p">(</span><span class="n">q</span><span class="p">,</span> <span class="n">H_diag</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">num_old</span><span class="p">):</span>
<span class="n">be_i</span> <span class="o">=</span> <span class="n">old_dirs</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">r</span><span class="p">)</span> <span class="o">*</span> <span class="n">ro</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<span class="n">r</span><span class="o">.</span><span class="n">add_</span><span class="p">(</span><span class="n">old_stps</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">alpha</span><span class="o">=</span><span class="n">al</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">-</span> <span class="n">be_i</span><span class="p">)</span>
<span class="k">if</span> <span class="n">prev_flat_grad</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">prev_flat_grad</span> <span class="o">=</span> <span class="n">flat_grad</span><span class="o">.</span><span class="n">clone</span><span class="p">(</span><span class="n">memory_format</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">contiguous_format</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">prev_flat_grad</span><span class="o">.</span><span class="n">copy_</span><span class="p">(</span><span class="n">flat_grad</span><span class="p">)</span>
<span class="n">prev_loss</span> <span class="o">=</span> <span class="n">loss</span>
<span class="c1">############################################################</span>
<span class="c1"># compute step length</span>
<span class="c1">############################################################</span>
<span class="c1"># reset initial guess for step size</span>
<span class="k">if</span> <span class="n">state</span><span class="p">[</span><span class="s1">'n_iter'</span><span class="p">]</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="n">t</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">1.</span> <span class="o">/</span> <span class="n">flat_grad</span><span class="o">.</span><span class="n">abs</span><span class="p">()</span><span class="o">.</span><span class="n">sum</span><span class="p">())</span> <span class="o">*</span> <span class="n">lr</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">t</span> <span class="o">=</span> <span class="n">lr</span>
<span class="c1"># directional derivative</span>
<span class="n">gtd</span> <span class="o">=</span> <span class="n">flat_grad</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">d</span><span class="p">)</span> <span class="c1"># g * d</span>
<span class="c1"># directional derivative is below tolerance</span>
<span class="k">if</span> <span class="n">gtd</span> <span class="o">></span> <span class="o">-</span><span class="n">tolerance_change</span><span class="p">:</span>
<span class="k">break</span>
<span class="c1"># optional line search: user function</span>
<span class="n">ls_func_evals</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">if</span> <span class="n">line_search_fn</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="c1"># perform line search, using user function</span>
<span class="k">if</span> <span class="n">line_search_fn</span> <span class="o">!=</span> <span class="s2">"strong_wolfe"</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s2">"only 'strong_wolfe' is supported"</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">x_init</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_clone_param</span><span class="p">()</span>
<span class="k">def</span> <span class="nf">obj_func</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">d</span><span class="p">):</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_directional_evaluate</span><span class="p">(</span><span class="n">closure</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">d</span><span class="p">)</span>
<span class="n">loss</span><span class="p">,</span> <span class="n">flat_grad</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">ls_func_evals</span> <span class="o">=</span> <span class="n">_strong_wolfe</span><span class="p">(</span>
<span class="n">obj_func</span><span class="p">,</span> <span class="n">x_init</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">d</span><span class="p">,</span> <span class="n">loss</span><span class="p">,</span> <span class="n">flat_grad</span><span class="p">,</span> <span class="n">gtd</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_add_grad</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">d</span><span class="p">)</span>
<span class="n">opt_cond</span> <span class="o">=</span> <span class="n">flat_grad</span><span class="o">.</span><span class="n">abs</span><span class="p">()</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="o"><=</span> <span class="n">tolerance_grad</span>
<span class="k">else</span><span class="p">:</span>
<span class="c1"># no line search, simply move with fixed-step</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_add_grad</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">d</span><span class="p">)</span>
<span class="k">if</span> <span class="n">n_iter</span> <span class="o">!=</span> <span class="n">max_iter</span><span class="p">:</span>
<span class="c1"># re-evaluate function only if not in last iteration</span>
<span class="c1"># the reason we do this: in a stochastic setting,</span>
<span class="c1"># no use to re-evaluate that function here</span>
<span class="k">with</span> <span class="n">torch</span><span class="o">.</span><span class="n">enable_grad</span><span class="p">():</span>
<span class="n">loss</span> <span class="o">=</span> <span class="nb">float</span><span class="p">(</span><span class="n">closure</span><span class="p">())</span>
<span class="n">flat_grad</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_gather_flat_grad</span><span class="p">()</span>
<span class="n">opt_cond</span> <span class="o">=</span> <span class="n">flat_grad</span><span class="o">.</span><span class="n">abs</span><span class="p">()</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="o"><=</span> <span class="n">tolerance_grad</span>
<span class="n">ls_func_evals</span> <span class="o">=</span> <span class="mi">1</span>
<span class="c1"># update func eval</span>
<span class="n">current_evals</span> <span class="o">+=</span> <span class="n">ls_func_evals</span>
<span class="n">state</span><span class="p">[</span><span class="s1">'func_evals'</span><span class="p">]</span> <span class="o">+=</span> <span class="n">ls_func_evals</span>
<span class="c1">############################################################</span>
<span class="c1"># check conditions</span>
<span class="c1">############################################################</span>
<span class="k">if</span> <span class="n">n_iter</span> <span class="o">==</span> <span class="n">max_iter</span><span class="p">:</span>
<span class="k">break</span>
<span class="k">if</span> <span class="n">current_evals</span> <span class="o">>=</span> <span class="n">max_eval</span><span class="p">:</span>
<span class="k">break</span>
<span class="c1"># optimal condition</span>
<span class="k">if</span> <span class="n">opt_cond</span><span class="p">:</span>
<span class="k">break</span>
<span class="c1"># lack of progress</span>
<span class="k">if</span> <span class="n">d</span><span class="o">.</span><span class="n">mul</span><span class="p">(</span><span class="n">t</span><span class="p">)</span><span class="o">.</span><span class="n">abs</span><span class="p">()</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="o"><=</span> <span class="n">tolerance_change</span><span class="p">:</span>
<span class="k">break</span>
<span class="k">if</span> <span class="nb">abs</span><span class="p">(</span><span class="n">loss</span> <span class="o">-</span> <span class="n">prev_loss</span><span class="p">)</span> <span class="o"><</span> <span class="n">tolerance_change</span><span class="p">:</span>
<span class="k">break</span>
<span class="n">state</span><span class="p">[</span><span class="s1">'d'</span><span class="p">]</span> <span class="o">=</span> <span class="n">d</span>
<span class="n">state</span><span class="p">[</span><span class="s1">'t'</span><span class="p">]</span> <span class="o">=</span> <span class="n">t</span>
<span class="n">state</span><span class="p">[</span><span class="s1">'old_dirs'</span><span class="p">]</span> <span class="o">=</span> <span class="n">old_dirs</span>
<span class="n">state</span><span class="p">[</span><span class="s1">'old_stps'</span><span class="p">]</span> <span class="o">=</span> <span class="n">old_stps</span>
<span class="n">state</span><span class="p">[</span><span class="s1">'ro'</span><span class="p">]</span> <span class="o">=</span> <span class="n">ro</span>
<span class="n">state</span><span class="p">[</span><span class="s1">'H_diag'</span><span class="p">]</span> <span class="o">=</span> <span class="n">H_diag</span>
<span class="n">state</span><span class="p">[</span><span class="s1">'prev_flat_grad'</span><span class="p">]</span> <span class="o">=</span> <span class="n">prev_flat_grad</span>
<span class="n">state</span><span class="p">[</span><span class="s1">'prev_loss'</span><span class="p">]</span> <span class="o">=</span> <span class="n">prev_loss</span>
<span class="k">return</span> <span class="n">orig_loss</span></div></div>
</pre></div>
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