Optimizers

The various optimizers that you can use to tune your parameters

struct dynet::SimpleSGDTrainer
#include <training.h>

Stochastic gradient descent trainer.

This trainer performs stochastic gradient descent, the goto optimization procedure for neural networks. In the standard setting, the learning rate at epoch \(t\) is \(\eta_t=\frac{\eta_0}{1+\eta_{\mathrm{decay}}t}\)

Reference : reference needed

Inherits from dynet::Trainer

Public Functions

SimpleSGDTrainer(ParameterCollection &m, real e0 = 0.1, real edecay = 0.0)

Constructor.

Parameters
  • m: ParameterCollection to be trained
  • e0: Initial learning rate
  • edecay: Learning rate decay parameter.

struct dynet::CyclicalSGDTrainer
#include <training.h>

Cyclical learning rate SGD.

This trainer performs stochastic gradient descent with a cyclical learning rate as proposed in Smith, 2015.

This uses a triangular function with optional exponential decay.

More specifically, at each update, the learning rate \(\eta\) is updated according to :

\( \begin{split} \text{cycle} &= \left\lfloor 1 + \frac{\texttt{it}}{2 \times\texttt{step_size}} \right\rfloor\\ x &= \left\vert \frac{\texttt{it}}{\texttt{step_size}} - 2 \times \text{cycle} + 1\right\vert\\ \eta &= \eta_{\text{min}} + (\eta_{\text{max}} - \eta_{\text{min}}) \times \max(0, 1 - x) \times \gamma^{\texttt{it}}\\ \end{split} \)

Reference : Cyclical Learning Rates for Training Neural Networks

Inherits from dynet::Trainer

Public Functions

CyclicalSGDTrainer(ParameterCollection &m, float e0_min = 0.01, float e0_max = 0.1, float step_size = 2000, float gamma = 0.0, float edecay = 0.0)

Constructor.

Parameters
  • m: ParameterCollection to be trained
  • e0_min: Lower learning rate
  • e0_max: Upper learning rate
  • step_size: Period of the triangular function in number of iterations (not epochs). According to the original paper, this should be set around (2-8) x (training iterations in epoch)
  • gamma: Learning rate upper bound decay parameter
  • edecay: Learning rate decay parameter. Ideally you shouldn’t use this with cyclical learning rate since decay is already handled by \(\gamma\)

struct dynet::MomentumSGDTrainer
#include <training.h>

Stochastic gradient descent with momentum.

This is a modified version of the SGD algorithm with momentum to stablize the gradient trajectory. The modified gradient is \(\theta_{t+1}=\mu\theta_{t}+\nabla_{t+1}\) where \(\mu\) is the momentum.

Reference : reference needed

Inherits from dynet::Trainer

Public Functions

MomentumSGDTrainer(ParameterCollection &m, real e0 = 0.01, real mom = 0.9, real edecay = 0.0)

Constructor.

Parameters
  • m: ParameterCollection to be trained
  • e0: Initial learning rate
  • mom: Momentum
  • edecay: Learning rate decay parameter

struct dynet::AdagradTrainer
#include <training.h>

Adagrad optimizer.

The adagrad algorithm assigns a different learning rate to each parameter according to the following formula : \(\delta_\theta^{(t)}=-\frac{\eta_0}{\epsilon+\sum_{i=0}^{t-1}(\nabla_\theta^{(i)})^2}\nabla_\theta^{(t)}\)

Reference : Duchi et al., 2011

Inherits from dynet::Trainer

Public Functions

AdagradTrainer(ParameterCollection &m, real e0 = 0.1, real eps = 1e-20, real edecay = 0.0)

Constructor.

Parameters
  • m: ParameterCollection to be trained
  • e0: Initial learning rate
  • eps: Bias parameter \(\epsilon\) in the adagrad formula
  • edecay: Learning rate decay parameter

struct dynet::AdadeltaTrainer
#include <training.h>

AdaDelta optimizer.

The AdaDelta optimizer is a variant of Adagrad where \(\frac{\eta_0}{\sqrt{\epsilon+\sum_{i=0}^{t-1}(\nabla_\theta^{(i)})^2}}\) is replaced by \(\frac{\sqrt{\epsilon+\sum_{i=0}^{t-1}\rho^{t-i-1}(1-\rho)(\delta_\theta^{(i)})^2}}{\sqrt{\epsilon+\sum_{i=0}^{t-1}(\nabla_\theta^{(i)})^2}}\), hence eliminating the need for an initial learning rate.

Reference : ADADELTA: An Adaptive Learning Rate Method

Inherits from dynet::Trainer

Public Functions

AdadeltaTrainer(ParameterCollection &m, real eps = 1e-6, real rho = 0.95, real edecay = 0.0)

Constructor.

Parameters
  • m: ParameterCollection to be trained
  • eps: Bias parameter \(\epsilon\) in the adagrad formula
  • rho: Update parameter for the moving average of updates in the numerator
  • edecay: Learning rate decay parameter

struct dynet::RMSPropTrainer
#include <training.h>

RMSProp optimizer.

The RMSProp optimizer is a variant of Adagrad where the squared sum of previous gradients is replaced with a moving average with parameter \(\rho\).

Reference : reference needed

Inherits from dynet::Trainer

Public Functions

RMSPropTrainer(ParameterCollection &m, real e0 = 0.1, real eps = 1e-20, real rho = 0.95, real edecay = 0.0)

Constructor.

Parameters
  • m: ParameterCollection to be trained
  • e0: Initial learning rate
  • eps: Bias parameter \(\epsilon\) in the adagrad formula
  • rho: Update parameter for the moving average (rho = 0 is equivalent to using Adagrad)
  • edecay: Learning rate decay parameter

struct dynet::AdamTrainer
#include <training.h>

Adam optimizer.

The Adam optimizer is similar to RMSProp but uses unbiased estimates of the first and second moments of the gradient

Reference : Adam: A Method for Stochastic Optimization

Inherits from dynet::Trainer

Public Functions

AdamTrainer(ParameterCollection &m, float e0 = 0.001, float beta_1 = 0.9, float beta_2 = 0.999, float eps = 1e-8, real edecay = 0.0)

Constructor.

Parameters
  • m: ParameterCollection to be trained
  • e0: Initial learning rate
  • beta_1: Moving average parameter for the mean
  • beta_2: Moving average parameter for the variance
  • eps: Bias parameter \(\epsilon\)
  • edecay: Learning rate decay parameter

struct dynet::Trainer
#include <training.h>

General trainer struct.

Subclassed by dynet::AdadeltaTrainer, dynet::AdagradTrainer, dynet::AdamTrainer, dynet::CyclicalSGDTrainer, dynet::MomentumSGDTrainer, dynet::RMSPropTrainer, dynet::SimpleSGDTrainer

Public Functions

Trainer(ParameterCollection &m, real e0, real edecay = 0.0)

General constructor for a Trainer.

Parameters

void update(real scale = 1.0)

Update parameters.

Update the parameters according to the appropriate update rule

Parameters
  • scale: The scaling factor for the gradients

void update(const std::vector<unsigned> &updated_params, const std::vector<unsigned> &updated_lookup_params, real scale = 1.0)

Update subset of parameters.

Update some but not all of the parameters included in the model. This is the update_subset() function in the Python bindings. The parameters to be updated are specified by index, which can be found for Parameter and LookupParameter objects through the “index” variable (or the get_index() function in the Python bindings).

Parameters
  • updated_params: The parameter indices to be updated
  • updated_lookup_params: The lookup parameter indices to be updated
  • scale: The scaling factor for the gradients

float clip_gradients(real scale)

Clip gradient.

If clipping is enabled and the gradient is too big, return the amount to scale the gradient by (otherwise 1)

Return
The appropriate scaling factor
Parameters
  • scale: The clipping limit

Public Members

bool sparse_updates_enabled

Whether to perform sparse updates.

DyNet trainers support two types of updates for lookup parameters, sparse and dense. Sparse updates are the default. They have the potential to be faster, as they only touch the parameters that have non-zero gradients. However, they may not always be faster (particulary on GPU with mini-batch training), and are not precisely numerically correct for some update rules such as MomentumTrainer and AdamTrainer. Thus, if you set this variable to false, the trainer will perform dense updates and be precisely correct, and maybe faster sometimes.