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<!DOCTYPE html>
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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="k">import</span> <span class="n">reduce</span>
<span class="kn">from</span> <span class="nn">.optimizer</span> <span class="k">import</span> <span class="n">Optimizer</span>
<div class="viewcode-block" id="LBFGS"><a class="viewcode-back" href="../../../optim.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.</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"> Arguments:</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 value/parameter</span>
<span class="sd"> changes (default: 1e-9).</span>
<span class="sd"> history_size (int): update history size (default: 100).</span>
<span class="sd"> """</span>
<span class="k">def</span> <span class="nf">__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="mi">1</span><span class="n">e</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="n">tolerance_change</span><span class="o">=</span><span class="mi">1</span><span class="n">e</span><span class="o">-</span><span class="mi">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="n">LBFGS</span><span class="p">,</span> <span class="bp">self</span><span class="p">)</span><span class="o">.</span><span class="n">__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">data</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">data</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">data</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">data</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">data</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="n">p</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">add_</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="p">:</span><span class="n">offset</span> <span class="o">+</span> <span class="n">numel</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>
<div class="viewcode-block" id="LBFGS.step"><a class="viewcode-back" href="../../../optim.html#torch.optim.LBFGS.step">[docs]</a> <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"> Arguments:</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="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="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="s1">'global_state'</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="n">orig_loss</span><span class="o">.</span><span class="n">data</span><span class="p">[</span><span class="mi">0</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">abs_grad_sum</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="k">if</span> <span class="n">abs_grad_sum</span> <span class="o"><=</span> <span class="n">tolerance_grad</span><span class="p">:</span>
<span class="k">return</span> <span class="n">loss</span>
<span class="c1"># variables 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">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">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="mi">1</span><span class="n">e</span><span class="o">-</span><span class="mi">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="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">s</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">y</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">'ro'</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">'ro'</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">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">ro</span> <span class="o">=</span> <span class="n">state</span><span class="p">[</span><span class="s1">'ro'</span><span class="p">]</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="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">ro</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="mf">1.</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">old_dirs</span><span class="p">[</span><span class="n">i</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_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">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="o">-</span><span class="n">al</span><span class="p">[</span><span class="n">i</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="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_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">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">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="n">old_dirs</span><span class="p">[</span><span class="n">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="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">abs_grad_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"># 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">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s2">"line search function is not supported yet"</span><span class="p">)</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="n">loss</span> <span class="o">=</span> <span class="n">closure</span><span class="p">()</span><span class="o">.</span><span class="n">data</span><span class="p">[</span><span class="mi">0</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">abs_grad_sum</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="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="k">if</span> <span class="n">abs_grad_sum</span> <span class="o"><=</span> <span class="n">tolerance_grad</span><span class="p">:</span>
<span class="k">break</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="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">sum</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">'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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