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<h1>Source code for torch.optim.radam</h1><div class="highlight"><pre>
<span></span><span class="kn">import</span> <span class="nn">math</span>
<span class="kn">import</span> <span class="nn">torch</span>
<span class="kn">from</span> <span class="nn">torch</span> <span class="kn">import</span> <span class="n">Tensor</span>
<span class="kn">from</span> <span class="nn">.optimizer</span> <span class="kn">import</span> <span class="p">(</span><span class="n">Optimizer</span><span class="p">,</span> <span class="n">_use_grad_for_differentiable</span><span class="p">,</span> <span class="n">_get_value</span><span class="p">,</span> <span class="n">_dispatch_sqrt</span><span class="p">,</span> <span class="n">_stack_if_compiling</span><span class="p">,</span>
<span class="n">_default_to_fused_or_foreach</span><span class="p">,</span> <span class="n">_differentiable_doc</span><span class="p">,</span> <span class="n">_foreach_doc</span><span class="p">)</span>
<span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">List</span><span class="p">,</span> <span class="n">Optional</span>
<span class="kn">from</span> <span class="nn">torch.utils._foreach_utils</span> <span class="kn">import</span> <span class="n">_group_tensors_by_device_and_dtype</span>
<span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"RAdam"</span><span class="p">,</span> <span class="s2">"radam"</span><span class="p">]</span>
<div class="viewcode-block" id="RAdam"><a class="viewcode-back" href="../../../generated/torch.optim.RAdam.html#torch.optim.RAdam">[docs]</a><span class="k">class</span> <span class="nc">RAdam</span><span class="p">(</span><span class="n">Optimizer</span><span class="p">):</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="mf">1e-3</span><span class="p">,</span>
<span class="n">betas</span><span class="o">=</span><span class="p">(</span><span class="mf">0.9</span><span class="p">,</span> <span class="mf">0.999</span><span class="p">),</span>
<span class="n">eps</span><span class="o">=</span><span class="mf">1e-8</span><span class="p">,</span>
<span class="n">weight_decay</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span>
<span class="o">*</span><span class="p">,</span>
<span class="n">foreach</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="nb">bool</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
<span class="n">differentiable</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span>
<span class="p">):</span>
<span class="k">if</span> <span class="ow">not</span> <span class="mf">0.0</span> <span class="o"><=</span> <span class="n">lr</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">"Invalid learning rate: </span><span class="si">{}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">lr</span><span class="p">))</span>
<span class="k">if</span> <span class="ow">not</span> <span class="mf">0.0</span> <span class="o"><=</span> <span class="n">eps</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">"Invalid epsilon value: </span><span class="si">{}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">eps</span><span class="p">))</span>
<span class="k">if</span> <span class="ow">not</span> <span class="mf">0.0</span> <span class="o"><=</span> <span class="n">betas</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o"><</span> <span class="mf">1.0</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">"Invalid beta parameter at index 0: </span><span class="si">{}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">betas</span><span class="p">[</span><span class="mi">0</span><span class="p">]))</span>
<span class="k">if</span> <span class="ow">not</span> <span class="mf">0.0</span> <span class="o"><=</span> <span class="n">betas</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o"><</span> <span class="mf">1.0</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">"Invalid beta parameter at index 1: </span><span class="si">{}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">betas</span><span class="p">[</span><span class="mi">1</span><span class="p">]))</span>
<span class="k">if</span> <span class="ow">not</span> <span class="mf">0.0</span> <span class="o"><=</span> <span class="n">weight_decay</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">"Invalid weight_decay value: </span><span class="si">{}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">weight_decay</span><span class="p">))</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">betas</span><span class="o">=</span><span class="n">betas</span><span class="p">,</span>
<span class="n">eps</span><span class="o">=</span><span class="n">eps</span><span class="p">,</span>
<span class="n">weight_decay</span><span class="o">=</span><span class="n">weight_decay</span><span class="p">,</span>
<span class="n">foreach</span><span class="o">=</span><span class="n">foreach</span><span class="p">,</span>
<span class="n">differentiable</span><span class="o">=</span><span class="n">differentiable</span><span class="p">,</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">def</span> <span class="nf">__setstate__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">state</span><span class="p">):</span>
<span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">__setstate__</span><span class="p">(</span><span class="n">state</span><span class="p">)</span>
<span class="k">for</span> <span class="n">group</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">param_groups</span><span class="p">:</span>
<span class="n">group</span><span class="o">.</span><span class="n">setdefault</span><span class="p">(</span><span class="s2">"foreach"</span><span class="p">,</span> <span class="kc">None</span><span class="p">)</span>
<span class="n">group</span><span class="o">.</span><span class="n">setdefault</span><span class="p">(</span><span class="s2">"differentiable"</span><span class="p">,</span> <span class="kc">False</span><span class="p">)</span>
<span class="n">state_values</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">state</span><span class="o">.</span><span class="n">values</span><span class="p">())</span>
<span class="n">step_is_tensor</span> <span class="o">=</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">state_values</span><span class="p">)</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">)</span> <span class="ow">and</span> <span class="n">torch</span><span class="o">.</span><span class="n">is_tensor</span><span class="p">(</span>
<span class="n">state_values</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="s2">"step"</span><span class="p">]</span>
<span class="p">)</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">step_is_tensor</span><span class="p">:</span>
<span class="k">for</span> <span class="n">s</span> <span class="ow">in</span> <span class="n">state_values</span><span class="p">:</span>
<span class="n">s</span><span class="p">[</span><span class="s2">"step"</span><span class="p">]</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">tensor</span><span class="p">(</span><span class="nb">float</span><span class="p">(</span><span class="n">s</span><span class="p">[</span><span class="s2">"step"</span><span class="p">]))</span>
<span class="k">def</span> <span class="nf">_init_group</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">group</span><span class="p">,</span> <span class="n">params_with_grad</span><span class="p">,</span> <span class="n">grads</span><span class="p">,</span> <span class="n">exp_avgs</span><span class="p">,</span> <span class="n">exp_avg_sqs</span><span class="p">,</span> <span class="n">state_steps</span><span class="p">):</span>
<span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">group</span><span class="p">[</span><span class="s2">"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="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">params_with_grad</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">p</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="o">.</span><span class="n">is_sparse</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s2">"RAdam does not support sparse gradients"</span><span class="p">)</span>
<span class="n">grads</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">p</span><span class="o">.</span><span class="n">grad</span><span class="p">)</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="n">p</span><span class="p">]</span>
<span class="c1"># Lazy state initialization</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">state</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">state</span><span class="p">[</span><span class="s2">"step"</span><span class="p">]</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">tensor</span><span class="p">(</span><span class="mf">0.0</span><span class="p">)</span>
<span class="c1"># Exponential moving average of gradient values</span>
<span class="n">state</span><span class="p">[</span><span class="s2">"exp_avg"</span><span class="p">]</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">zeros_like</span><span class="p">(</span>
<span class="n">p</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">preserve_format</span>
<span class="p">)</span>
<span class="c1"># Exponential moving average of squared gradient values</span>
<span class="n">state</span><span class="p">[</span><span class="s2">"exp_avg_sq"</span><span class="p">]</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">zeros_like</span><span class="p">(</span>
<span class="n">p</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">preserve_format</span>
<span class="p">)</span>
<span class="n">exp_avgs</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">state</span><span class="p">[</span><span class="s2">"exp_avg"</span><span class="p">])</span>
<span class="n">exp_avg_sqs</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">state</span><span class="p">[</span><span class="s2">"exp_avg_sq"</span><span class="p">])</span>
<span class="n">state_steps</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">state</span><span class="p">[</span><span class="s2">"step"</span><span class="p">])</span>
<span class="nd">@_use_grad_for_differentiable</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="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="sd">"""Performs a single optimization step.</span>
<span class="sd"> Args:</span>
<span class="sd"> closure (Callable, optional): A closure that reevaluates the model</span>
<span class="sd"> and returns the loss.</span>
<span class="sd"> """</span>
<span class="n">loss</span> <span class="o">=</span> <span class="kc">None</span>
<span class="k">if</span> <span class="n">closure</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</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="n">closure</span><span class="p">()</span>
<span class="k">for</span> <span class="n">group</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">param_groups</span><span class="p">:</span>
<span class="n">params_with_grad</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">grads</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">exp_avgs</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">exp_avg_sqs</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">state_steps</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">beta1</span><span class="p">,</span> <span class="n">beta2</span> <span class="o">=</span> <span class="n">group</span><span class="p">[</span><span class="s2">"betas"</span><span class="p">]</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_init_group</span><span class="p">(</span><span class="n">group</span><span class="p">,</span> <span class="n">params_with_grad</span><span class="p">,</span> <span class="n">grads</span><span class="p">,</span> <span class="n">exp_avgs</span><span class="p">,</span> <span class="n">exp_avg_sqs</span><span class="p">,</span> <span class="n">state_steps</span><span class="p">)</span>
<span class="n">radam</span><span class="p">(</span>
<span class="n">params_with_grad</span><span class="p">,</span>
<span class="n">grads</span><span class="p">,</span>
<span class="n">exp_avgs</span><span class="p">,</span>
<span class="n">exp_avg_sqs</span><span class="p">,</span>
<span class="n">state_steps</span><span class="p">,</span>
<span class="n">beta1</span><span class="o">=</span><span class="n">beta1</span><span class="p">,</span>
<span class="n">beta2</span><span class="o">=</span><span class="n">beta2</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="s2">"lr"</span><span class="p">],</span>
<span class="n">weight_decay</span><span class="o">=</span><span class="n">group</span><span class="p">[</span><span class="s2">"weight_decay"</span><span class="p">],</span>
<span class="n">eps</span><span class="o">=</span><span class="n">group</span><span class="p">[</span><span class="s2">"eps"</span><span class="p">],</span>
<span class="n">foreach</span><span class="o">=</span><span class="n">group</span><span class="p">[</span><span class="s2">"foreach"</span><span class="p">],</span>
<span class="n">differentiable</span><span class="o">=</span><span class="n">group</span><span class="p">[</span><span class="s2">"differentiable"</span><span class="p">],</span>
<span class="p">)</span>
<span class="k">return</span> <span class="n">loss</span></div>
<span class="n">RAdam</span><span class="o">.</span><span class="vm">__doc__</span> <span class="o">=</span> <span class="sa">r</span><span class="s2">"""Implements RAdam algorithm.</span>
<span class="s2"> .. math::</span>
<span class="s2"> \begin</span><span class="si">{aligned}</span><span class="s2"></span>
<span class="s2"> &\rule</span><span class="si">{110mm}{0.4pt}</span><span class="s2"> \\</span>
<span class="s2"> &\textbf</span><span class="si">{input}</span><span class="s2"> : \gamma \text{ (lr)}, \: \beta_1, \beta_2</span>
<span class="s2"> \text{ (betas)}, \: \theta_0 \text{ (params)}, \:f(\theta) \text{ (objective)}, \:</span>
<span class="s2"> \lambda \text{ (weightdecay)}, \\</span>
<span class="s2"> &\hspace</span><span class="si">{13mm}</span><span class="s2"> \epsilon \text{ (epsilon)} \\</span>
<span class="s2"> &\textbf</span><span class="si">{initialize}</span><span class="s2"> : m_0 \leftarrow 0 \text{ ( first moment)},</span>
<span class="s2"> v_0 \leftarrow 0 \text{ ( second moment)}, \\</span>
<span class="s2"> &\hspace</span><span class="si">{18mm}</span><span class="s2"> \rho_{\infty} \leftarrow 2/(1-\beta_2) -1 \\[-1.ex]</span>
<span class="s2"> &\rule</span><span class="si">{110mm}{0.4pt}</span><span class="s2"> \\</span>
<span class="s2"> &\textbf</span><span class="si">{for}</span><span class="s2"> \: t=1 \: \textbf</span><span class="si">{to}</span><span class="s2"> \: \ldots \: \textbf</span><span class="si">{do}</span><span class="s2"> \\</span>
<span class="s2"> &\hspace</span><span class="si">{6mm}</span><span class="s2">g_t \leftarrow \nabla_{\theta} f_t (\theta_{t-1}) \\</span>
<span class="s2"> &\hspace</span><span class="si">{5mm}</span><span class="s2"> \textbf</span><span class="si">{if}</span><span class="s2"> \: \lambda \neq 0 \\</span>
<span class="s2"> &\hspace</span><span class="si">{10mm}</span><span class="s2"> g_t \leftarrow g_t + \lambda \theta_{t-1} \\</span>
<span class="s2"> &\hspace</span><span class="si">{6mm}</span><span class="s2">m_t \leftarrow \beta_1 m_{t-1} + (1 - \beta_1) g_t \\</span>
<span class="s2"> &\hspace</span><span class="si">{6mm}</span><span class="s2">v_t \leftarrow \beta_2 v_{t-1} + (1-\beta_2) g^2_t \\</span>
<span class="s2"> &\hspace</span><span class="si">{6mm}</span><span class="s2">\widehat</span><span class="si">{m_t}</span><span class="s2"> \leftarrow m_t/\big(1-\beta_1^t \big) \\</span>
<span class="s2"> &\hspace</span><span class="si">{6mm}</span><span class="s2">\rho_t \leftarrow \rho_{\infty} -</span>
<span class="s2"> 2 t \beta^t_2 /\big(1-\beta_2^t \big) \\[0.1.ex]</span>
<span class="s2"> &\hspace</span><span class="si">{6mm}</span><span class="s2">\textbf</span><span class="si">{if}</span><span class="s2"> \: \rho_t > 5 \\</span>
<span class="s2"> &\hspace</span><span class="si">{12mm}</span><span class="s2"> l_t \leftarrow \frac{\sqrt{ (1-\beta^t_2) }}{ \sqrt</span><span class="si">{v_t}</span><span class="s2"> +\epsilon } \\</span>
<span class="s2"> &\hspace</span><span class="si">{12mm}</span><span class="s2"> r_t \leftarrow</span>
<span class="s2"> \sqrt{\frac{(\rho_t-4)(\rho_t-2)\rho_{\infty}}{(\rho_{\infty}-4)(\rho_{\infty}-2) \rho_t}} \\</span>
<span class="s2"> &\hspace</span><span class="si">{12mm}</span><span class="s2">\theta_t \leftarrow \theta_{t-1} - \gamma \widehat</span><span class="si">{m_t}</span><span class="s2"> r_t l_t \\</span>
<span class="s2"> &\hspace</span><span class="si">{6mm}</span><span class="s2">\textbf</span><span class="si">{else}</span><span class="s2"> \\</span>
<span class="s2"> &\hspace</span><span class="si">{12mm}</span><span class="s2">\theta_t \leftarrow \theta_{t-1} - \gamma \widehat</span><span class="si">{m_t}</span><span class="s2"> \\</span>
<span class="s2"> &\rule</span><span class="si">{110mm}{0.4pt}</span><span class="s2"> \\[-1.ex]</span>
<span class="s2"> &\bf</span><span class="si">{return}</span><span class="s2"> \: \theta_t \\[-1.ex]</span>
<span class="s2"> &\rule</span><span class="si">{110mm}{0.4pt}</span><span class="s2"> \\[-1.ex]</span>
<span class="s2"> \end</span><span class="si">{aligned}</span><span class="s2"></span>
<span class="s2"> For further details regarding the algorithm we refer to `On the variance of the adaptive learning rate and beyond`_.</span>
<span class="s2"> This implementation uses the same weight_decay implementation as Adam (were the weight_decay is applied</span>
<span class="s2"> to the gradient) and not the one from AdamW (were weight_decay is applied to the update). This</span>
<span class="s2"> is different from the `author's implementation`_.</span>
<span class="s2"> """</span> <span class="o">+</span> <span class="sa">r</span><span class="s2">"""</span>
<span class="s2"> Args:</span>
<span class="s2"> params (iterable): iterable of parameters to optimize or dicts defining</span>
<span class="s2"> parameter groups</span>
<span class="s2"> lr (float, optional): learning rate (default: 1e-3)</span>
<span class="s2"> betas (Tuple[float, float], optional): coefficients used for computing</span>
<span class="s2"> running averages of gradient and its square (default: (0.9, 0.999))</span>
<span class="s2"> eps (float, optional): term added to the denominator to improve</span>
<span class="s2"> numerical stability (default: 1e-8)</span>
<span class="s2"> weight_decay (float, optional): weight decay (L2 penalty) (default: 0)</span>
<span class="s2"> </span><span class="si">{foreach}</span><span class="s2"></span>
<span class="s2"> </span><span class="si">{differentiable}</span><span class="s2"></span>
<span class="s2"> .. _On the variance of the adaptive learning rate and beyond:</span>
<span class="s2"> https://arxiv.org/abs/1908.03265</span>
<span class="s2"> .. _author's implementation:</span>
<span class="s2"> https://github.com/LiyuanLucasLiu/RAdam</span>
<span class="s2"> """</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">foreach</span><span class="o">=</span><span class="n">_foreach_doc</span><span class="p">,</span> <span class="n">differentiable</span><span class="o">=</span><span class="n">_differentiable_doc</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">radam</span><span class="p">(</span>
<span class="n">params</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="n">Tensor</span><span class="p">],</span>
<span class="n">grads</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="n">Tensor</span><span class="p">],</span>
<span class="n">exp_avgs</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="n">Tensor</span><span class="p">],</span>
<span class="n">exp_avg_sqs</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="n">Tensor</span><span class="p">],</span>
<span class="n">state_steps</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="n">Tensor</span><span class="p">],</span>
<span class="c1"># kwonly args with defaults are not supported by functions compiled with torchscript issue #70627</span>
<span class="c1"># setting this as kwarg for now as functional API is compiled by torch/distributed/optim</span>
<span class="n">foreach</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="nb">bool</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
<span class="n">differentiable</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span>
<span class="o">*</span><span class="p">,</span>
<span class="n">beta1</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
<span class="n">beta2</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
<span class="n">lr</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
<span class="n">weight_decay</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
<span class="n">eps</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
<span class="p">):</span>
<span class="sa">r</span><span class="sd">"""Functional API that performs RAdam algorithm computation.</span>
<span class="sd"> See :class:`~torch.optim.RAdam` for details.</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="ow">not</span> <span class="nb">all</span><span class="p">(</span><span class="nb">isinstance</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">)</span> <span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">state_steps</span><span class="p">):</span>
<span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span>
<span class="s2">"API has changed, `state_steps` argument must contain a list of singleton tensors"</span>
<span class="p">)</span>
<span class="k">if</span> <span class="n">foreach</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">_</span><span class="p">,</span> <span class="n">foreach</span> <span class="o">=</span> <span class="n">_default_to_fused_or_foreach</span><span class="p">(</span><span class="n">params</span><span class="p">,</span> <span class="n">differentiable</span><span class="p">,</span> <span class="n">use_fused</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="k">if</span> <span class="n">foreach</span> <span class="ow">and</span> <span class="n">torch</span><span class="o">.</span><span class="n">jit</span><span class="o">.</span><span class="n">is_scripting</span><span class="p">():</span>
<span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s2">"torch.jit.script not supported with foreach optimizers"</span><span class="p">)</span>
<span class="k">if</span> <span class="n">foreach</span> <span class="ow">and</span> <span class="ow">not</span> <span class="n">torch</span><span class="o">.</span><span class="n">jit</span><span class="o">.</span><span class="n">is_scripting</span><span class="p">():</span>
<span class="n">func</span> <span class="o">=</span> <span class="n">_multi_tensor_radam</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">func</span> <span class="o">=</span> <span class="n">_single_tensor_radam</span>
<span class="n">func</span><span class="p">(</span>
<span class="n">params</span><span class="p">,</span>
<span class="n">grads</span><span class="p">,</span>
<span class="n">exp_avgs</span><span class="p">,</span>
<span class="n">exp_avg_sqs</span><span class="p">,</span>
<span class="n">state_steps</span><span class="p">,</span>
<span class="n">beta1</span><span class="o">=</span><span class="n">beta1</span><span class="p">,</span>
<span class="n">beta2</span><span class="o">=</span><span class="n">beta2</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">weight_decay</span><span class="o">=</span><span class="n">weight_decay</span><span class="p">,</span>
<span class="n">eps</span><span class="o">=</span><span class="n">eps</span><span class="p">,</span>
<span class="n">differentiable</span><span class="o">=</span><span class="n">differentiable</span><span class="p">,</span>
<span class="p">)</span>
<span class="k">def</span> <span class="nf">_single_tensor_radam</span><span class="p">(</span>
<span class="n">params</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="n">Tensor</span><span class="p">],</span>
<span class="n">grads</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="n">Tensor</span><span class="p">],</span>
<span class="n">exp_avgs</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="n">Tensor</span><span class="p">],</span>
<span class="n">exp_avg_sqs</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="n">Tensor</span><span class="p">],</span>
<span class="n">state_steps</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="n">Tensor</span><span class="p">],</span>
<span class="o">*</span><span class="p">,</span>
<span class="n">beta1</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
<span class="n">beta2</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
<span class="n">lr</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
<span class="n">weight_decay</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
<span class="n">eps</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
<span class="n">differentiable</span><span class="p">:</span> <span class="nb">bool</span><span class="p">,</span>
<span class="p">):</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">param</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">params</span><span class="p">):</span>
<span class="n">grad</span> <span class="o">=</span> <span class="n">grads</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<span class="n">exp_avg</span> <span class="o">=</span> <span class="n">exp_avgs</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<span class="n">exp_avg_sq</span> <span class="o">=</span> <span class="n">exp_avg_sqs</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<span class="n">step_t</span> <span class="o">=</span> <span class="n">state_steps</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<span class="c1"># update step</span>
<span class="n">step_t</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">step</span> <span class="o">=</span> <span class="n">_get_value</span><span class="p">(</span><span class="n">step_t</span><span class="p">)</span>
<span class="n">bias_correction1</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">beta1</span> <span class="o">**</span> <span class="n">step</span>
<span class="n">bias_correction2</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">beta2</span> <span class="o">**</span> <span class="n">step</span>
<span class="k">if</span> <span class="n">weight_decay</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">grad</span> <span class="o">=</span> <span class="n">grad</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">param</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="n">weight_decay</span><span class="p">)</span>
<span class="c1"># Decay the first and second moment running average coefficient</span>
<span class="n">exp_avg</span><span class="o">.</span><span class="n">mul_</span><span class="p">(</span><span class="n">beta1</span><span class="p">)</span><span class="o">.</span><span class="n">add_</span><span class="p">(</span><span class="n">grad</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mi">1</span> <span class="o">-</span> <span class="n">beta1</span><span class="p">)</span>
<span class="n">exp_avg_sq</span><span class="o">.</span><span class="n">mul_</span><span class="p">(</span><span class="n">beta2</span><span class="p">)</span><span class="o">.</span><span class="n">addcmul_</span><span class="p">(</span><span class="n">grad</span><span class="p">,</span> <span class="n">grad</span><span class="p">,</span> <span class="n">value</span><span class="o">=</span><span class="mi">1</span> <span class="o">-</span> <span class="n">beta2</span><span class="p">)</span>
<span class="c1"># correcting bias for the first moving moment</span>
<span class="n">bias_corrected_exp_avg</span> <span class="o">=</span> <span class="n">exp_avg</span> <span class="o">/</span> <span class="n">bias_correction1</span>
<span class="c1"># maximum length of the approximated SMA</span>
<span class="n">rho_inf</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">beta2</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>
<span class="c1"># compute the length of the approximated SMA</span>
<span class="n">rho_t</span> <span class="o">=</span> <span class="n">rho_inf</span> <span class="o">-</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">step</span> <span class="o">*</span> <span class="p">(</span><span class="n">beta2</span> <span class="o">**</span> <span class="n">step</span><span class="p">)</span> <span class="o">/</span> <span class="n">bias_correction2</span>
<span class="k">if</span> <span class="n">rho_t</span> <span class="o">></span> <span class="mf">5.0</span><span class="p">:</span>
<span class="c1"># Compute the variance rectification term and update parameters accordingly</span>
<span class="n">rect</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span>
<span class="p">(</span><span class="n">rho_t</span> <span class="o">-</span> <span class="mi">4</span><span class="p">)</span>
<span class="o">*</span> <span class="p">(</span><span class="n">rho_t</span> <span class="o">-</span> <span class="mi">2</span><span class="p">)</span>
<span class="o">*</span> <span class="n">rho_inf</span>
<span class="o">/</span> <span class="p">((</span><span class="n">rho_inf</span> <span class="o">-</span> <span class="mi">4</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">rho_inf</span> <span class="o">-</span> <span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">rho_t</span><span class="p">)</span>
<span class="p">)</span>
<span class="n">exp_avg_sq_sqrt</span> <span class="o">=</span> <span class="n">exp_avg_sq</span><span class="o">.</span><span class="n">sqrt</span><span class="p">()</span>
<span class="k">if</span> <span class="n">differentiable</span><span class="p">:</span>
<span class="n">exp_avg_sq_sqrt</span> <span class="o">=</span> <span class="n">exp_avg_sq_sqrt</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">eps</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">exp_avg_sq_sqrt</span> <span class="o">=</span> <span class="n">exp_avg_sq_sqrt</span><span class="o">.</span><span class="n">add_</span><span class="p">(</span><span class="n">eps</span><span class="p">)</span>
<span class="n">adaptive_lr</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">bias_correction2</span><span class="p">)</span> <span class="o">/</span> <span class="n">exp_avg_sq_sqrt</span>
<span class="n">param</span><span class="o">.</span><span class="n">add_</span><span class="p">(</span><span class="n">bias_corrected_exp_avg</span> <span class="o">*</span> <span class="n">lr</span> <span class="o">*</span> <span class="n">adaptive_lr</span> <span class="o">*</span> <span class="n">rect</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=-</span><span class="mf">1.0</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">param</span><span class="o">.</span><span class="n">add_</span><span class="p">(</span><span class="n">bias_corrected_exp_avg</span> <span class="o">*</span> <span class="n">lr</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=-</span><span class="mf">1.0</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">_multi_tensor_radam</span><span class="p">(</span>
<span class="n">params</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="n">Tensor</span><span class="p">],</span>
<span class="n">grads</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="n">Tensor</span><span class="p">],</span>
<span class="n">exp_avgs</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="n">Tensor</span><span class="p">],</span>
<span class="n">exp_avg_sqs</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="n">Tensor</span><span class="p">],</span>
<span class="n">state_steps</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="n">Tensor</span><span class="p">],</span>
<span class="o">*</span><span class="p">,</span>
<span class="n">beta1</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
<span class="n">beta2</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
<span class="n">lr</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
<span class="n">weight_decay</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
<span class="n">eps</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
<span class="n">differentiable</span><span class="p">:</span> <span class="nb">bool</span><span class="p">,</span>
<span class="p">):</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">params</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="k">return</span>
<span class="k">assert</span> <span class="ow">not</span> <span class="n">differentiable</span><span class="p">,</span> <span class="s2">"_foreach ops don't support autograd"</span>
<span class="n">grouped_tensors</span> <span class="o">=</span> <span class="n">_group_tensors_by_device_and_dtype</span><span class="p">([</span><span class="n">params</span><span class="p">,</span> <span class="n">grads</span><span class="p">,</span> <span class="n">exp_avgs</span><span class="p">,</span> <span class="n">exp_avg_sqs</span><span class="p">,</span> <span class="n">state_steps</span><span class="p">])</span>
<span class="k">for</span> <span class="n">grouped_params</span><span class="p">,</span> <span class="n">grouped_grads</span><span class="p">,</span> <span class="n">grouped_exp_avgs</span><span class="p">,</span> <span class="n">grouped_exp_avg_sqs</span><span class="p">,</span> <span class="n">grouped_state_steps</span> <span class="ow">in</span> <span class="n">grouped_tensors</span><span class="o">.</span><span class="n">values</span><span class="p">():</span>
<span class="c1"># Update steps</span>
<span class="n">torch</span><span class="o">.</span><span class="n">_foreach_add_</span><span class="p">(</span><span class="n">grouped_state_steps</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="c1"># maximum length of the approximated SMA</span>
<span class="n">rho_inf</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">beta2</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>
<span class="c1"># compute the length of the approximated SMA</span>
<span class="n">rho_t_list</span> <span class="o">=</span> <span class="p">[</span><span class="n">rho_inf</span> <span class="o">-</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">_get_value</span><span class="p">(</span><span class="n">step</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">beta2</span> <span class="o">**</span> <span class="n">_get_value</span><span class="p">(</span><span class="n">step</span><span class="p">))</span> <span class="o">/</span>
<span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">beta2</span> <span class="o">**</span> <span class="n">_get_value</span><span class="p">(</span><span class="n">step</span><span class="p">))</span> <span class="k">for</span> <span class="n">step</span> <span class="ow">in</span> <span class="n">grouped_state_steps</span><span class="p">]</span>
<span class="n">bias_correction1</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span> <span class="o">-</span> <span class="n">beta1</span> <span class="o">**</span> <span class="n">_get_value</span><span class="p">(</span><span class="n">step</span><span class="p">)</span> <span class="k">for</span> <span class="n">step</span> <span class="ow">in</span> <span class="n">grouped_state_steps</span><span class="p">]</span>
<span class="n">bias_correction2</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span> <span class="o">-</span> <span class="n">beta2</span> <span class="o">**</span> <span class="n">_get_value</span><span class="p">(</span><span class="n">step</span><span class="p">)</span> <span class="k">for</span> <span class="n">step</span> <span class="ow">in</span> <span class="n">grouped_state_steps</span><span class="p">]</span>
<span class="k">if</span> <span class="n">weight_decay</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">grouped_grads</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">_foreach_add</span><span class="p">(</span><span class="n">grouped_grads</span><span class="p">,</span> <span class="n">grouped_params</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="n">weight_decay</span><span class="p">)</span>
<span class="c1"># Decay the first and second moment running average coefficient</span>
<span class="n">torch</span><span class="o">.</span><span class="n">_foreach_mul_</span><span class="p">(</span><span class="n">grouped_exp_avgs</span><span class="p">,</span> <span class="n">beta1</span><span class="p">)</span>
<span class="n">torch</span><span class="o">.</span><span class="n">_foreach_add_</span><span class="p">(</span><span class="n">grouped_exp_avgs</span><span class="p">,</span> <span class="n">grouped_grads</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mi">1</span> <span class="o">-</span> <span class="n">beta1</span><span class="p">)</span>
<span class="n">torch</span><span class="o">.</span><span class="n">_foreach_mul_</span><span class="p">(</span><span class="n">grouped_exp_avg_sqs</span><span class="p">,</span> <span class="n">beta2</span><span class="p">)</span>
<span class="n">torch</span><span class="o">.</span><span class="n">_foreach_addcmul_</span><span class="p">(</span><span class="n">grouped_exp_avg_sqs</span><span class="p">,</span> <span class="n">grouped_grads</span><span class="p">,</span> <span class="n">grouped_grads</span><span class="p">,</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">beta2</span><span class="p">)</span>
<span class="n">rect</span> <span class="o">=</span> <span class="p">[</span>
<span class="n">_dispatch_sqrt</span><span class="p">(</span>
<span class="p">(</span><span class="n">rho_t</span> <span class="o">-</span> <span class="mi">4</span><span class="p">)</span>
<span class="o">*</span> <span class="p">(</span><span class="n">rho_t</span> <span class="o">-</span> <span class="mi">2</span><span class="p">)</span>
<span class="o">*</span> <span class="n">rho_inf</span>
<span class="o">/</span> <span class="p">((</span><span class="n">rho_inf</span> <span class="o">-</span> <span class="mi">4</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">rho_inf</span> <span class="o">-</span> <span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">rho_t</span><span class="p">)</span>
<span class="p">)</span>
<span class="k">if</span> <span class="n">rho_t</span> <span class="o">></span> <span class="mi">5</span>
<span class="k">else</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">rho_t</span> <span class="ow">in</span> <span class="n">rho_t_list</span>
<span class="p">]</span>
<span class="n">unrectified</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span> <span class="k">if</span> <span class="n">rect</span> <span class="o">></span> <span class="mi">0</span> <span class="k">else</span> <span class="mf">1.0</span> <span class="k">for</span> <span class="n">rect</span> <span class="ow">in</span> <span class="n">rect</span><span class="p">]</span>
<span class="n">exp_avg_sq_sqrt</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">_foreach_sqrt</span><span class="p">(</span><span class="n">grouped_exp_avg_sqs</span><span class="p">)</span>
<span class="n">torch</span><span class="o">.</span><span class="n">_foreach_add_</span><span class="p">(</span><span class="n">exp_avg_sq_sqrt</span><span class="p">,</span> <span class="n">eps</span><span class="p">)</span>
<span class="n">bias_correction_sqrt</span> <span class="o">=</span> <span class="p">[</span><span class="n">_dispatch_sqrt</span><span class="p">(</span><span class="n">bc</span><span class="p">)</span> <span class="k">for</span> <span class="n">bc</span> <span class="ow">in</span> <span class="n">bias_correction2</span><span class="p">]</span>
<span class="n">denom</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">_foreach_div</span><span class="p">(</span><span class="n">exp_avg_sq_sqrt</span><span class="p">,</span> <span class="n">bias_correction_sqrt</span><span class="p">)</span>
<span class="n">step_size</span> <span class="o">=</span> <span class="n">_stack_if_compiling</span><span class="p">([(</span><span class="n">lr</span> <span class="o">*</span> <span class="n">rect</span> <span class="o">/</span> <span class="n">bc</span><span class="p">)</span> <span class="o">*</span> <span class="o">-</span><span class="mi">1</span> <span class="k">for</span> <span class="n">rect</span><span class="p">,</span> <span class="n">bc</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">rect</span><span class="p">,</span> <span class="n">bias_correction1</span><span class="p">)])</span>
<span class="n">torch</span><span class="o">.</span><span class="n">_foreach_addcdiv_</span><span class="p">(</span><span class="n">grouped_params</span><span class="p">,</span> <span class="n">grouped_exp_avgs</span><span class="p">,</span> <span class="n">denom</span><span class="p">,</span> <span class="n">step_size</span><span class="p">)</span>
<span class="n">denom</span> <span class="o">=</span> <span class="p">[</span><span class="n">torch</span><span class="o">.</span><span class="n">ones_like</span><span class="p">(</span><span class="n">exp_av</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">preserve_format</span><span class="p">)</span> <span class="k">for</span> <span class="n">exp_av</span> <span class="ow">in</span> <span class="n">grouped_exp_avgs</span><span class="p">]</span>
<span class="n">step_size</span> <span class="o">=</span> <span class="n">_stack_if_compiling</span><span class="p">([(</span><span class="n">lr</span> <span class="o">*</span> <span class="n">rect</span> <span class="o">/</span> <span class="n">bc</span><span class="p">)</span> <span class="o">*</span> <span class="o">-</span><span class="mi">1</span> <span class="k">for</span> <span class="n">rect</span><span class="p">,</span> <span class="n">bc</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">unrectified</span><span class="p">,</span> <span class="n">bias_correction1</span><span class="p">)])</span>
<span class="n">torch</span><span class="o">.</span><span class="n">_foreach_addcdiv_</span><span class="p">(</span><span class="n">grouped_params</span><span class="p">,</span> <span class="n">grouped_exp_avgs</span><span class="p">,</span> <span class="n">denom</span><span class="p">,</span> <span class="n">step_size</span><span class="p">)</span>
</pre></div>
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