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</pre><pre class="rust"><code><span class="doccomment">//! Gradient Descent
//!
//! Implementation of gradient descent algorithm. Module contains
//! the struct `GradientDesc` which is instantiated within models
//! implementing the Optimizable trait.
//!
//! Currently standard batch gradient descent is the only implemented
//! optimization algorithm but there is flexibility to introduce new
//! algorithms and git them into the same scheme easily.
</span><span class="kw">use </span>learning::optim::{Optimizable, OptimAlgorithm};
<span class="kw">use </span>linalg::Vector;
<span class="kw">use </span>linalg::{Matrix, BaseMatrix};
<span class="kw">use </span>rulinalg::utils;
<span class="kw">use </span>learning::toolkit::rand_utils;
<span class="kw">const </span>LEARNING_EPS: f64 = <span class="number">1e-20</span>;
<span class="doccomment">/// Batch Gradient Descent algorithm
</span><span class="attribute">#[derive(Clone, Copy, Debug)]
</span><span class="kw">pub struct </span>GradientDesc {
<span class="doccomment">/// The step-size for the gradient descent steps.
</span>alpha: f64,
<span class="doccomment">/// The number of iterations to run.
</span>iters: usize,
}
<span class="doccomment">/// The default gradient descent algorithm.
///
/// The defaults are:
///
/// - alpha = 0.3
/// - iters = 100
</span><span class="kw">impl </span>Default <span class="kw">for </span>GradientDesc {
<span class="kw">fn </span>default() -&gt; GradientDesc {
GradientDesc {
alpha: <span class="number">0.3</span>,
iters: <span class="number">100</span>,
}
}
}
<span class="kw">impl </span>GradientDesc {
<span class="doccomment">/// Construct a gradient descent algorithm.
///
/// Requires the step size and iteration count
/// to be specified.
///
/// # Examples
///
/// ```
/// use rusty_machine::learning::optim::grad_desc::GradientDesc;
///
/// let gd = GradientDesc::new(0.3, 10000);
/// ```
</span><span class="kw">pub fn </span>new(alpha: f64, iters: usize) -&gt; GradientDesc {
<span class="macro">assert!</span>(alpha &gt; <span class="number">0f64</span>,
<span class="string">&quot;The step size (alpha) must be greater than 0.&quot;</span>);
GradientDesc {
alpha: alpha,
iters: iters,
}
}
}
<span class="kw">impl</span>&lt;M: Optimizable&gt; OptimAlgorithm&lt;M&gt; <span class="kw">for </span>GradientDesc {
<span class="kw">fn </span>optimize(<span class="kw-2">&amp;</span><span class="self">self</span>,
model: <span class="kw-2">&amp;</span>M,
start: <span class="kw-2">&amp;</span>[f64],
inputs: <span class="kw-2">&amp;</span>M::Inputs,
targets: <span class="kw-2">&amp;</span>M::Targets)
-&gt; Vec&lt;f64&gt; {
<span class="comment">// Create the initial optimal parameters
</span><span class="kw">let </span><span class="kw-2">mut </span>optimizing_val = Vector::new(start.to_vec());
<span class="comment">// The cost at the start of each iteration
</span><span class="kw">let </span><span class="kw-2">mut </span>start_iter_cost = <span class="number">0f64</span>;
<span class="kw">for _ in </span><span class="number">0</span>..<span class="self">self</span>.iters {
<span class="comment">// Compute the cost and gradient for the current parameters
</span><span class="kw">let </span>(cost, grad) = model.compute_grad(optimizing_val.data(), inputs, targets);
<span class="comment">// Early stopping
</span><span class="kw">if </span>(start_iter_cost - cost).abs() &lt; LEARNING_EPS {
<span class="kw">break</span>;
} <span class="kw">else </span>{
<span class="comment">// Update the optimal parameters using gradient descent
</span>optimizing_val = <span class="kw-2">&amp;</span>optimizing_val - Vector::new(grad) * <span class="self">self</span>.alpha;
<span class="comment">// Update the latest cost
</span>start_iter_cost = cost;
}
}
optimizing_val.into_vec()
}
}
<span class="doccomment">/// Stochastic Gradient Descent algorithm.
///
/// Uses basic momentum to control the learning rate.
</span><span class="attribute">#[derive(Clone, Copy, Debug)]
</span><span class="kw">pub struct </span>StochasticGD {
<span class="doccomment">/// Controls the momentum of the descent
</span>alpha: f64,
<span class="doccomment">/// The square root of the raw learning rate.
</span>mu: f64,
<span class="doccomment">/// The number of passes through the data.
</span>iters: usize,
}
<span class="doccomment">/// The default Stochastic GD algorithm.
///
/// The defaults are:
///
/// - alpha = 0.1
/// - mu = 0.1
/// - iters = 20
</span><span class="kw">impl </span>Default <span class="kw">for </span>StochasticGD {
<span class="kw">fn </span>default() -&gt; StochasticGD {
StochasticGD {
alpha: <span class="number">0.1</span>,
mu: <span class="number">0.1</span>,
iters: <span class="number">20</span>,
}
}
}
<span class="kw">impl </span>StochasticGD {
<span class="doccomment">/// Construct a stochastic gradient descent algorithm.
///
/// Requires the learning rate, momentum rate and iteration count
/// to be specified.
///
/// With Nesterov momentum by default.
///
/// # Examples
///
/// ```
/// use rusty_machine::learning::optim::grad_desc::StochasticGD;
///
/// let sgd = StochasticGD::new(0.1, 0.3, 5);
/// ```
</span><span class="kw">pub fn </span>new(alpha: f64, mu: f64, iters: usize) -&gt; StochasticGD {
<span class="macro">assert!</span>(alpha &gt; <span class="number">0f64</span>, <span class="string">&quot;The momentum (alpha) must be greater than 0.&quot;</span>);
<span class="macro">assert!</span>(mu &gt; <span class="number">0f64</span>, <span class="string">&quot;The step size (mu) must be greater than 0.&quot;</span>);
StochasticGD {
alpha: alpha,
mu: mu,
iters: iters,
}
}
}
<span class="kw">impl</span>&lt;M&gt; OptimAlgorithm&lt;M&gt; <span class="kw">for </span>StochasticGD
<span class="kw">where </span>M: Optimizable&lt;Inputs = Matrix&lt;f64&gt;, Targets = Matrix&lt;f64&gt;&gt;
{
<span class="kw">fn </span>optimize(<span class="kw-2">&amp;</span><span class="self">self</span>,
model: <span class="kw-2">&amp;</span>M,
start: <span class="kw-2">&amp;</span>[f64],
inputs: <span class="kw-2">&amp;</span>M::Inputs,
targets: <span class="kw-2">&amp;</span>M::Targets)
-&gt; Vec&lt;f64&gt; {
<span class="comment">// Create the initial optimal parameters
</span><span class="kw">let </span><span class="kw-2">mut </span>optimizing_val = Vector::new(start.to_vec());
<span class="comment">// Create the momentum based gradient distance
</span><span class="kw">let </span><span class="kw-2">mut </span>delta_w = Vector::zeros(start.len());
<span class="comment">// Set up the indices for permutation
</span><span class="kw">let </span><span class="kw-2">mut </span>permutation = (<span class="number">0</span>..inputs.rows()).collect::&lt;Vec&lt;<span class="kw">_</span>&gt;&gt;();
<span class="comment">// The cost at the start of each iteration
</span><span class="kw">let </span><span class="kw-2">mut </span>start_iter_cost = <span class="number">0f64</span>;
<span class="kw">for _ in </span><span class="number">0</span>..<span class="self">self</span>.iters {
<span class="comment">// The cost at the end of each stochastic gd pass
</span><span class="kw">let </span><span class="kw-2">mut </span>end_cost = <span class="number">0f64</span>;
<span class="comment">// Permute the indices
</span>rand_utils::in_place_fisher_yates(<span class="kw-2">&amp;mut </span>permutation);
<span class="kw">for </span>i <span class="kw">in </span><span class="kw-2">&amp;</span>permutation {
<span class="comment">// Compute the cost and gradient for this data pair
</span><span class="kw">let </span>(cost, vec_data) = model.compute_grad(optimizing_val.data(),
<span class="kw-2">&amp;</span>inputs.select_rows(<span class="kw-2">&amp;</span>[<span class="kw-2">*</span>i]),
<span class="kw-2">&amp;</span>targets.select_rows(<span class="kw-2">&amp;</span>[<span class="kw-2">*</span>i]));
<span class="comment">// Backup previous velocity
</span><span class="kw">let </span>prev_w = delta_w.clone();
<span class="comment">// Compute the difference in gradient using Nesterov momentum
</span>delta_w = Vector::new(vec_data) * <span class="self">self</span>.mu + <span class="kw-2">&amp;</span>delta_w * <span class="self">self</span>.alpha;
<span class="comment">// Update the parameters
</span>optimizing_val = <span class="kw-2">&amp;</span>optimizing_val -
(<span class="kw-2">&amp;</span>prev_w * (-<span class="self">self</span>.alpha) + <span class="kw-2">&amp;</span>delta_w * (<span class="number">1. </span>+ <span class="self">self</span>.alpha));
<span class="comment">// Set the end cost (this is only used after the last iteration)
</span>end_cost += cost;
}
end_cost /= inputs.rows() <span class="kw">as </span>f64;
<span class="comment">// Early stopping
</span><span class="kw">if </span>(start_iter_cost - end_cost).abs() &lt; LEARNING_EPS {
<span class="kw">break</span>;
} <span class="kw">else </span>{
<span class="comment">// Update the cost
</span>start_iter_cost = end_cost;
}
}
optimizing_val.into_vec()
}
}
<span class="doccomment">/// Adaptive Gradient Descent
///
/// The adaptive gradient descent algorithm (Duchi et al. 2010).
</span><span class="attribute">#[derive(Debug)]
</span><span class="kw">pub struct </span>AdaGrad {
alpha: f64,
tau: f64,
iters: usize,
}
<span class="kw">impl </span>AdaGrad {
<span class="doccomment">/// Constructs a new AdaGrad algorithm.
///
/// # Examples
///
/// ```
/// use rusty_machine::learning::optim::grad_desc::AdaGrad;
///
/// // Create a new AdaGrad algorithm with step size 0.5
/// // and adaptive scaling constant 1.0
/// let gd = AdaGrad::new(0.5, 1.0, 100);
/// ```
</span><span class="kw">pub fn </span>new(alpha: f64, tau: f64, iters: usize) -&gt; AdaGrad {
<span class="macro">assert!</span>(alpha &gt; <span class="number">0f64</span>,
<span class="string">&quot;The step size (alpha) must be greater than 0.&quot;</span>);
<span class="macro">assert!</span>(tau &gt;= <span class="number">0f64</span>,
<span class="string">&quot;The adaptive constant (tau) cannot be negative.&quot;</span>);
AdaGrad {
alpha: alpha,
tau: tau,
iters: iters,
}
}
}
<span class="kw">impl </span>Default <span class="kw">for </span>AdaGrad {
<span class="kw">fn </span>default() -&gt; AdaGrad {
AdaGrad {
alpha: <span class="number">1f64</span>,
tau: <span class="number">3f64</span>,
iters: <span class="number">100</span>,
}
}
}
<span class="kw">impl</span>&lt;M: Optimizable&lt;Inputs = Matrix&lt;f64&gt;, Targets = Matrix&lt;f64&gt;&gt;&gt; OptimAlgorithm&lt;M&gt; <span class="kw">for </span>AdaGrad {
<span class="kw">fn </span>optimize(<span class="kw-2">&amp;</span><span class="self">self</span>,
model: <span class="kw-2">&amp;</span>M,
start: <span class="kw-2">&amp;</span>[f64],
inputs: <span class="kw-2">&amp;</span>M::Inputs,
targets: <span class="kw-2">&amp;</span>M::Targets)
-&gt; Vec&lt;f64&gt; {
<span class="comment">// Initialize the adaptive scaling
</span><span class="kw">let </span><span class="kw-2">mut </span>ada_s = Vector::zeros(start.len());
<span class="comment">// Initialize the optimal parameters
</span><span class="kw">let </span><span class="kw-2">mut </span>optimizing_val = Vector::new(start.to_vec());
<span class="comment">// Set up the indices for permutation
</span><span class="kw">let </span><span class="kw-2">mut </span>permutation = (<span class="number">0</span>..inputs.rows()).collect::&lt;Vec&lt;<span class="kw">_</span>&gt;&gt;();
<span class="comment">// The cost at the start of each iteration
</span><span class="kw">let </span><span class="kw-2">mut </span>start_iter_cost = <span class="number">0f64</span>;
<span class="kw">for _ in </span><span class="number">0</span>..<span class="self">self</span>.iters {
<span class="comment">// The cost at the end of each stochastic gd pass
</span><span class="kw">let </span><span class="kw-2">mut </span>end_cost = <span class="number">0f64</span>;
<span class="comment">// Permute the indices
</span>rand_utils::in_place_fisher_yates(<span class="kw-2">&amp;mut </span>permutation);
<span class="kw">for </span>i <span class="kw">in </span><span class="kw-2">&amp;</span>permutation {
<span class="comment">// Compute the cost and gradient for this data pair
</span><span class="kw">let </span>(cost, <span class="kw-2">mut </span>vec_data) = model.compute_grad(optimizing_val.data(),
<span class="kw-2">&amp;</span>inputs.select_rows(<span class="kw-2">&amp;</span>[<span class="kw-2">*</span>i]),
<span class="kw-2">&amp;</span>targets.select_rows(<span class="kw-2">&amp;</span>[<span class="kw-2">*</span>i]));
<span class="comment">// Update the adaptive scaling by adding the gradient squared
</span>utils::in_place_vec_bin_op(ada_s.mut_data(), <span class="kw-2">&amp;</span>vec_data, |x, <span class="kw-2">&amp;</span>y| <span class="kw-2">*</span>x += y * y);
<span class="comment">// Compute the change in gradient
</span>utils::in_place_vec_bin_op(<span class="kw-2">&amp;mut </span>vec_data, ada_s.data(), |x, <span class="kw-2">&amp;</span>y| {
<span class="kw-2">*</span>x = <span class="self">self</span>.alpha * (<span class="kw-2">*</span>x / (<span class="self">self</span>.tau + (y).sqrt()))
});
<span class="comment">// Update the parameters
</span>optimizing_val = <span class="kw-2">&amp;</span>optimizing_val - Vector::new(vec_data);
<span class="comment">// Set the end cost (this is only used after the last iteration)
</span>end_cost += cost;
}
end_cost /= inputs.rows() <span class="kw">as </span>f64;
<span class="comment">// Early stopping
</span><span class="kw">if </span>(start_iter_cost - end_cost).abs() &lt; LEARNING_EPS {
<span class="kw">break</span>;
} <span class="kw">else </span>{
<span class="comment">// Update the cost
</span>start_iter_cost = end_cost;
}
}
optimizing_val.into_vec()
}
}
<span class="doccomment">/// RMSProp
///
/// The RMSProp algorithm (Hinton et al. 2012).
</span><span class="attribute">#[derive(Debug, Clone, Copy)]
</span><span class="kw">pub struct </span>RMSProp {
<span class="doccomment">/// The base step size of gradient descent steps
</span>learning_rate: f64,
<span class="doccomment">/// Rate at which running total of average square gradients decays
</span>decay_rate: f64,
<span class="doccomment">/// Small value used to avoid divide by zero
</span>epsilon: f64,
<span class="doccomment">/// The number of passes through the data
</span>iters: usize,
}
<span class="doccomment">/// The default RMSProp configuration
///
/// The defaults are:
///
/// - learning_rate = 0.01
/// - decay_rate = 0.9
/// - epsilon = 1.0e-5
/// - iters = 50
</span><span class="kw">impl </span>Default <span class="kw">for </span>RMSProp {
<span class="kw">fn </span>default() -&gt; RMSProp {
RMSProp {
learning_rate: <span class="number">0.01</span>,
decay_rate: <span class="number">0.9</span>,
epsilon: <span class="number">1.0e-5</span>,
iters: <span class="number">50
</span>}
}
}
<span class="kw">impl </span>RMSProp {
<span class="doccomment">/// Construct an RMSProp algorithm.
///
/// Requires learning rate, decay rate, epsilon, and iteration count.
///
/// #Examples
///
/// ```
/// use rusty_machine::learning::optim::grad_desc::RMSProp;
///
/// let rms = RMSProp::new(0.99, 0.01, 1e-5, 20);
/// ```
</span><span class="kw">pub fn </span>new(learning_rate: f64, decay_rate: f64, epsilon: f64, iters: usize) -&gt; RMSProp {
<span class="macro">assert!</span>(<span class="number">0f64 </span>&lt; learning_rate, <span class="string">&quot;The learning rate must be positive&quot;</span>);
<span class="macro">assert!</span>(<span class="number">0f64 </span>&lt; decay_rate &amp;&amp; decay_rate &lt; <span class="number">1f64</span>, <span class="string">&quot;The decay rate must be between 0 and 1&quot;</span>);
<span class="macro">assert!</span>(<span class="number">0f64 </span>&lt; epsilon, <span class="string">&quot;Epsilon must be positive&quot;</span>);
RMSProp {
decay_rate: decay_rate,
learning_rate: learning_rate,
epsilon: epsilon,
iters: iters
}
}
}
<span class="kw">impl</span>&lt;M&gt; OptimAlgorithm&lt;M&gt; <span class="kw">for </span>RMSProp
<span class="kw">where </span>M: Optimizable&lt;Inputs = Matrix&lt;f64&gt;, Targets = Matrix&lt;f64&gt;&gt; {
<span class="kw">fn </span>optimize(<span class="kw-2">&amp;</span><span class="self">self</span>,
model: <span class="kw-2">&amp;</span>M,
start: <span class="kw-2">&amp;</span>[f64],
inputs: <span class="kw-2">&amp;</span>M::Inputs,
targets: <span class="kw-2">&amp;</span>M::Targets)
-&gt; Vec&lt;f64&gt; {
<span class="comment">// Initial parameters
</span><span class="kw">let </span><span class="kw-2">mut </span>params = Vector::new(start.to_vec());
<span class="comment">// Running average of squared gradients
</span><span class="kw">let </span><span class="kw-2">mut </span>rmsprop_cache = Vector::zeros(start.len());
<span class="comment">// Set up indices for permutation
</span><span class="kw">let </span><span class="kw-2">mut </span>permutation = (<span class="number">0</span>..inputs.rows()).collect::&lt;Vec&lt;<span class="kw">_</span>&gt;&gt;();
<span class="comment">// The cost from the previous iteration
</span><span class="kw">let </span><span class="kw-2">mut </span>prev_cost = <span class="number">0f64</span>;
<span class="kw">for _ in </span><span class="number">0</span>..<span class="self">self</span>.iters {
<span class="comment">// The cost at end of each pass
</span><span class="kw">let </span><span class="kw-2">mut </span>end_cost = <span class="number">0f64</span>;
<span class="comment">// Permute the vertices
</span>rand_utils::in_place_fisher_yates(<span class="kw-2">&amp;mut </span>permutation);
<span class="kw">for </span>i <span class="kw">in </span><span class="kw-2">&amp;</span>permutation {
<span class="kw">let </span>(cost, grad) = model.compute_grad(params.data(),
<span class="kw-2">&amp;</span>inputs.select_rows(<span class="kw-2">&amp;</span>[<span class="kw-2">*</span>i]),
<span class="kw-2">&amp;</span>targets.select_rows(<span class="kw-2">&amp;</span>[<span class="kw-2">*</span>i]));
<span class="kw">let </span><span class="kw-2">mut </span>grad = Vector::new(grad);
<span class="kw">let </span>grad_squared = grad.clone().apply(<span class="kw-2">&amp;</span>|x| x<span class="kw-2">*</span>x);
<span class="comment">// Update cached average of squared gradients
</span>rmsprop_cache = <span class="kw-2">&amp;</span>rmsprop_cache<span class="kw-2">*</span><span class="self">self</span>.decay_rate + <span class="kw-2">&amp;</span>grad_squared<span class="kw-2">*</span>(<span class="number">1.0 </span>- <span class="self">self</span>.decay_rate);
<span class="comment">// RMSProp update rule
</span>utils::in_place_vec_bin_op(grad.mut_data(), rmsprop_cache.data(), |x, <span class="kw-2">&amp;</span>y| {
<span class="kw-2">*</span>x = <span class="kw-2">*</span>x * <span class="self">self</span>.learning_rate / (y + <span class="self">self</span>.epsilon).sqrt();
});
params = <span class="kw-2">&amp;</span>params - <span class="kw-2">&amp;</span>grad;
end_cost += cost;
}
end_cost /= inputs.rows() <span class="kw">as </span>f64;
<span class="comment">// Early stopping
</span><span class="kw">if </span>(prev_cost - end_cost).abs() &lt; LEARNING_EPS {
<span class="kw">break</span>;
} <span class="kw">else </span>{
prev_cost = end_cost;
}
}
params.into_vec()
}
}
<span class="attribute">#[cfg(test)]
</span><span class="kw">mod </span>tests {
<span class="kw">use super</span>::{GradientDesc, StochasticGD, AdaGrad, RMSProp};
<span class="attribute">#[test]
#[should_panic]
</span><span class="kw">fn </span>gd_neg_stepsize() {
<span class="kw">let _ </span>= GradientDesc::new(-<span class="number">0.5</span>, <span class="number">0</span>);
}
<span class="attribute">#[test]
#[should_panic]
</span><span class="kw">fn </span>stochastic_gd_neg_momentum() {
<span class="kw">let _ </span>= StochasticGD::new(-<span class="number">0.5</span>, <span class="number">1f64</span>, <span class="number">0</span>);
}
<span class="attribute">#[test]
#[should_panic]
</span><span class="kw">fn </span>stochastic_gd_neg_stepsize() {
<span class="kw">let _ </span>= StochasticGD::new(<span class="number">0.5</span>, -<span class="number">1f64</span>, <span class="number">0</span>);
}
<span class="attribute">#[test]
#[should_panic]
</span><span class="kw">fn </span>adagrad_neg_stepsize() {
<span class="kw">let _ </span>= AdaGrad::new(-<span class="number">0.5</span>, <span class="number">1f64</span>, <span class="number">0</span>);
}
<span class="attribute">#[test]
#[should_panic]
</span><span class="kw">fn </span>adagrad_neg_adaptive_scale() {
<span class="kw">let _ </span>= AdaGrad::new(<span class="number">0.5</span>, -<span class="number">1f64</span>, <span class="number">0</span>);
}
<span class="attribute">#[test]
#[should_panic]
</span><span class="kw">fn </span>rmsprop_neg_decay_rate() {
<span class="kw">let _ </span>= RMSProp::new(-<span class="number">0.5</span>, <span class="number">0.005</span>, <span class="number">1.0e-5</span>, <span class="number">0</span>);
}
<span class="attribute">#[test]
#[should_panic]
</span><span class="kw">fn </span>rmsprop_neg_epsilon() {
<span class="kw">let _ </span>= RMSProp::new(<span class="number">0.5</span>, <span class="number">0.005</span>, -<span class="number">1.0e-5</span>, <span class="number">0</span>);
}
<span class="attribute">#[test]
#[should_panic]
</span><span class="kw">fn </span>rmsprop_neg_learning_rate() {
<span class="kw">let _ </span>= RMSProp::new(<span class="number">0.5</span>, -<span class="number">0.005</span>, <span class="number">1.0e-5</span>, <span class="number">0</span>);
}
}
</code></pre></div>
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