Optimizers

class paddle.trainer_config_helpers.optimizers.BaseSGDOptimizer

SGD Optimizer.

SGD is an optimization method, trying to find a neural network that minimize the “cost/error” of it by iteration. In paddle’s implementation SGD Optimizer is synchronized, which means all gradients will be wait to calculate and reduced into one gradient, then do optimize operation.

The neural network consider the learning problem of minimizing an objective function, that has the form of a sum

\[Q(w) = \sum_{i}^{n} Q_i(w)\]

The value of function Q sometimes is the cost of neural network (Mean Square Error between prediction and label for example). The function Q is parametrised by w, the weight/bias of neural network. And weights is what to be learned. The i is the i-th observation in (trainning) data.

So, the SGD method will optimize the weight by

\[w:= w - \eta \nabla Q(w) = w - \eta \sum_{i}^{n} \nabla Q_i(w)\]

where \(\eta\) is learning rate. And \(n\) is batch size.

The SGD method is implemented by paddle with multiple extensions. Such as momentum, adagrad, rmsprop, adam. Please use method ‘use_xxx’, such as use_adam, to enhance the SGD method.

WARNING: IN PADDLE’S IMPLEMENTATION, BATCH_SIZE IS SET FOR ONE COMPUTE PROCESS(NODE). IF YOU USE MULTIPLE MACHINE TO TRAIN YOUR NETWORK, THE GLOBAL BATCH SIZE WILL BE (BATCH_SIZE * MACHINE_COUNT).

class paddle.trainer_config_helpers.optimizers.AdamOptimizer(beta1=0.9, beta2=0.999, epsilon=1e-08)

Adam optimizer. The details of please refer Adam: A Method for Stochastic Optimization

\[\begin{split}m(w, t) &:= \beta_1 m(w, t-1) + (1 - \beta_1) \nabla Q_i(w) \\ v(w, t) &:= \beta_2 v(w, t-1) + (1 - \beta_2)(\nabla Q_i(w)) ^2 \\ w &:= w - \frac{\eta}{\sqrt{v(w,t) + \epsilon}}\end{split}\]

Parameters:

• beta1 (float) – the \(\beta_1\) in equation.
• beta2 (float) – the \(\beta_2\) in equation.
• epsilon (float) – the \(\epsilon\) in equation. It is used to prevent divided by zero.

class paddle.trainer_config_helpers.optimizers.AdamaxOptimizer(beta1, beta2)

Adamax optimizer.

The details of please refer this Adam: A Method for Stochastic Optimization .. math:

m_t &:= \beta_1 * m_{t-1} + (1-\beta_1)* \nabla Q_i(w) \\
u_t &:= max(\beta_2*u_{t-1}, abs(\nabla Q_i(w))) \\
w_t &:= w_{t-1} - (\eta/(1-\beta_1^t))*m_t/u_t

Parameters:

• beta1 (float) – the \(\beta_1\) in the equation.
• beta2 (float) – the \(\beta_2\) in the equation.

class paddle.trainer_config_helpers.optimizers.AdaGradOptimizer

Adagrad(for ADAptive GRAdient algorithm) optimizer.

For details please refer this Adaptive Subgradient Methods for Online Learning and Stochastic Optimization.

\[\begin{split}G &= \sum_{\tau=1}^{t} g_{\tau} g_{\tau}^T \\ w &:= w - \eta diag(G)^{-\frac{1}{2}} \circ g\end{split}\]

class paddle.trainer_config_helpers.optimizers.RMSPropOptimizer(rho=0.95, epsilon=1e-06)

RMSProp(for Root Mean Square Propagation) optimizer. For details please refer this slide.

The equations of this method as follows:

\[\begin{split}v(w, t) &:= \rho v(w, t-1) + (1 - \rho)(\nabla Q_{i}(w))^2 \\ w &:= w - \frac{\eta} {\sqrt{v(w,t) + \epsilon}} \nabla Q_{i}(w)\end{split}\]

Parameters:

• rho (float) – the \(\rho\) in the equation. The forgetting factor.
• epsilon (float) – the \(\epsilon\) in the equation.

class paddle.trainer_config_helpers.optimizers.DecayedAdaGradOptimizer(rho=0.95, epsilon=1e-06)

AdaGrad method with decayed sum gradients. The equations of this method show as follow.

\[\begin{split}E(g_t^2) &= \rho * E(g_{t-1}^2) + (1-\rho) * g^2 \\ learning\_rate &= 1/sqrt( ( E(g_t^2) + \epsilon )\end{split}\]

Parameters:

• rho (float) – The \(\rho\) parameter in that equation
• epsilon (float) – The \(\epsilon\) parameter in that equation.

class paddle.trainer_config_helpers.optimizers.AdaDeltaOptimizer(rho=0.95, epsilon=1e-06)

AdaDelta method. The details of adadelta please refer to this ADADELTA: AN ADAPTIVE LEARNING RATE METHOD.

\[\begin{split}E(g_t^2) &= \rho * E(g_{t-1}^2) + (1-\rho) * g^2 \\ learning\_rate &= sqrt( ( E(dx_{t-1}^2) + \epsilon ) / ( \ E(g_t^2) + \epsilon ) ) \\ E(dx_t^2) &= \rho * E(dx_{t-1}^2) + (1-\rho) * (-g*learning\_rate)^2\end{split}\]

Parameters:

• rho (float) – \(\rho\) in equation
• epsilon (float) – \(\rho\) in equation

paddle.trainer_config_helpers.optimizers.settings(*args, **kwargs)

TODO(yuyang18): Complete docs.

Parameters:

• batch_size –
• learning_rate –
• learning_method –
• regularization –
• is_async –
• model_average –
• gradient_clipping_threshold –

Returns: