From 6829d94f913eaf905495bcf4d24f30b6efb94916 Mon Sep 17 00:00:00 2001 From: Travis CI Date: Mon, 6 Nov 2017 08:39:08 +0000 Subject: [PATCH] Deploy to GitHub Pages: 5eb0ebaf3bb68c462fdf6f4d0116aa65a3314a48 --- develop/doc/api/v2/config/optimizer.html | 59 ++++++++++----------- develop/doc/searchindex.js | 2 +- develop/doc_cn/api/v2/config/optimizer.html | 59 ++++++++++----------- develop/doc_cn/searchindex.js | 2 +- 4 files changed, 60 insertions(+), 62 deletions(-) diff --git a/develop/doc/api/v2/config/optimizer.html b/develop/doc/api/v2/config/optimizer.html index 2af0d0098c8..e7e63d2106b 100644 --- a/develop/doc/api/v2/config/optimizer.html +++ b/develop/doc/api/v2/config/optimizer.html @@ -188,35 +188,44 @@

Optimizer

Momentum

-

Optimizers(update equation) for SGD method.

-

TODO(yuyang18): Complete comments.

class paddle.v2.optimizer.Momentum(momentum=None, sparse=False, **kwargs)
-

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

+

Momentum Optimizer.

+

When sparse=False, the momentum update formula is as follows:

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

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

+\[\begin{split}v_{t} &= k * v_{t-1} - \gamma_t / (g_{t} + \lambda w_{t-1}) \\ +w_{t} &= w_{t-1} + v_{t} \\\end{split}\]
+

where, \(k\) is momentum, \(\lambda\) is decay rate, +\(\gamma_t\) is learning rate at the t’th iteration. +\(w_{t}\) is the weight as the t’th iteration. +And the \(v_{t}\) is the history momentum variable.

+

When sparse=True, the update scheme:

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

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

+\[\begin{split}\alpha_t &= \alpha_{t-1} / k \\ +\beta_t &= \beta_{t-1} / (1 + \lambda \gamma_t) \\ +u_t &= u_{t-1} - \alpha_t \gamma_t g_t \\ +v_t &= v_{t-1} + \tau_{t-1} \alpha_t \gamma_t g_t \\ +\tau_t &= \tau_{t-1} + \beta_t / \alpha_t\end{split}\] +

where \(k\) is momentum, \(\lambda\) is decay rate, +\(\gamma_t\) is learning rate at the t’th iteration.

+ +++ + + + +
Parameters:
    +
  • momentum (float) – the momentum factor.
    • +
  • sparse (bool) – with sparse support or not, False by default.
    • +
+

Adam

-

Optimizers(update equation) for SGD method.

-

TODO(yuyang18): Complete comments.

class paddle.v2.optimizer.Adam(beta1=0.9, beta2=0.999, epsilon=1e-08, **kwargs)
@@ -225,7 +234,7 @@ The details of please refer \[\begin{split}m(w, t) & = \beta_1 m(w, t-1) + (1 - \beta_1) \nabla Q_i(w) \\ v(w, t) & = \beta_2 v(w, t-1) + (1 - \beta_2)(\nabla Q_i(w)) ^2 \\ -w & = w - \frac{\eta}{\sqrt{v(w,t) + \epsilon}}\end{split}\]
+w & = w - \frac{\eta m(w, t)}{\sqrt{v(w,t) + \epsilon}}\end{split}\] @@ -245,8 +254,6 @@ divided by zero.

Adamax

-

Optimizers(update equation) for SGD method.

-

TODO(yuyang18): Complete comments.

class paddle.v2.optimizer.Adamax(beta1=0.9, beta2=0.999, **kwargs)
@@ -273,8 +280,6 @@ w_t & = w_{t-1} - (\eta/(1-\beta_1^t))*m_t/u_t\end{split}\]

AdaGrad

-

Optimizers(update equation) for SGD method.

-

TODO(yuyang18): Complete comments.

class paddle.v2.optimizer.AdaGrad(**kwargs)
@@ -289,8 +294,6 @@ w & = w - \eta diag(G)^{-\frac{1}{2}} \circ g\end{split}\]

DecayedAdaGrad

-

Optimizers(update equation) for SGD method.

-

TODO(yuyang18): Complete comments.

class paddle.v2.optimizer.DecayedAdaGrad(rho=0.95, epsilon=1e-06, **kwargs)
@@ -316,8 +319,6 @@ learning\_rate &= 1/sqrt( ( E(g_t^2) + \epsilon )\end{split}\]

AdaDelta

-

Optimizers(update equation) for SGD method.

-

TODO(yuyang18): Complete comments.

class paddle.v2.optimizer.AdaDelta(rho=0.95, epsilon=1e-06, **kwargs)
@@ -345,8 +346,6 @@ E(dx_t^2) &= \rho * E(dx_{t-1}^2) + (1-\rho) * (-g*learning\_rate)^2\end{spl

RMSProp

-

Optimizers(update equation) for SGD method.

-

TODO(yuyang18): Complete comments.

class paddle.v2.optimizer.RMSProp(rho=0.95, epsilon=1e-06, **kwargs)
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Code and Run Unit Test","Contribute Code","Write New Layers","How to write a new operator","How to use Eigen in Paddle","HOW TO","Tune GPU Performance","PaddlePaddle Distributed Training","Argument Outline","Detail Description","Set Command-line Parameters","Use Case","Distributed PaddlePaddle Training on AWS with Kubernetes","Paddle On Kubernetes","<no title>","<no title>","PaddlePaddle Documentation","Cluster bootstrapping tool survey","<no title>","Chinese Word Embedding Model Tutorial","Generative Adversarial Networks (GAN)","Model Zoo - ImageNet","Quick 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\ No newline at end of file diff --git a/develop/doc_cn/api/v2/config/optimizer.html b/develop/doc_cn/api/v2/config/optimizer.html index d73b5447f99..ba67264e056 100644 --- a/develop/doc_cn/api/v2/config/optimizer.html +++ b/develop/doc_cn/api/v2/config/optimizer.html @@ -201,35 +201,44 @@

Optimizer

Momentum

-

Optimizers(update equation) for SGD method.

-

TODO(yuyang18): Complete comments.

class paddle.v2.optimizer.Momentum(momentum=None, sparse=False, **kwargs)
-

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

+

Momentum Optimizer.

+

When sparse=False, the momentum update formula is as follows:

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

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

+\[\begin{split}v_{t} &= k * v_{t-1} - \gamma_t / (g_{t} + \lambda w_{t-1}) \\ +w_{t} &= w_{t-1} + v_{t} \\\end{split}\]
+

where, \(k\) is momentum, \(\lambda\) is decay rate, +\(\gamma_t\) is learning rate at the t’th iteration. +\(w_{t}\) is the weight as the t’th iteration. +And the \(v_{t}\) is the history momentum variable.

+

When sparse=True, the update scheme:

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

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

+\[\begin{split}\alpha_t &= \alpha_{t-1} / k \\ +\beta_t &= \beta_{t-1} / (1 + \lambda \gamma_t) \\ +u_t &= u_{t-1} - \alpha_t \gamma_t g_t \\ +v_t &= v_{t-1} + \tau_{t-1} \alpha_t \gamma_t g_t \\ +\tau_t &= \tau_{t-1} + \beta_t / \alpha_t\end{split}\]
+

where \(k\) is momentum, \(\lambda\) is decay rate, +\(\gamma_t\) is learning rate at the t’th iteration.

+
 +++ + + + +
参数:
    +
  • momentum (float) – the momentum factor.
    • +
  • sparse (bool) – with sparse support or not, False by default.
    • +
+

Adam

-

Optimizers(update equation) for SGD method.

-

TODO(yuyang18): Complete comments.

class paddle.v2.optimizer.Adam(beta1=0.9, beta2=0.999, epsilon=1e-08, **kwargs)
@@ -238,7 +247,7 @@ The details of please refer \[\begin{split}m(w, t) & = \beta_1 m(w, t-1) + (1 - \beta_1) \nabla Q_i(w) \\ v(w, t) & = \beta_2 v(w, t-1) + (1 - \beta_2)(\nabla Q_i(w)) ^2 \\ -w & = w - \frac{\eta}{\sqrt{v(w,t) + \epsilon}}\end{split}\]
+w & = w - \frac{\eta m(w, t)}{\sqrt{v(w,t) + \epsilon}}\end{split}\] @@ -258,8 +267,6 @@ divided by zero.

Adamax

-

Optimizers(update equation) for SGD method.

-

TODO(yuyang18): Complete comments.

class paddle.v2.optimizer.Adamax(beta1=0.9, beta2=0.999, **kwargs)
@@ -286,8 +293,6 @@ w_t & = w_{t-1} - (\eta/(1-\beta_1^t))*m_t/u_t\end{split}\]

AdaGrad

-

Optimizers(update equation) for SGD method.

-

TODO(yuyang18): Complete comments.

class paddle.v2.optimizer.AdaGrad(**kwargs)
@@ -302,8 +307,6 @@ w & = w - \eta diag(G)^{-\frac{1}{2}} \circ g\end{split}\]

DecayedAdaGrad

-

Optimizers(update equation) for SGD method.

-

TODO(yuyang18): Complete comments.

class paddle.v2.optimizer.DecayedAdaGrad(rho=0.95, epsilon=1e-06, **kwargs)
@@ -329,8 +332,6 @@ learning\_rate &= 1/sqrt( ( E(g_t^2) + \epsilon )\end{split}\]

AdaDelta

-

Optimizers(update equation) for SGD method.

-

TODO(yuyang18): Complete comments.

class paddle.v2.optimizer.AdaDelta(rho=0.95, epsilon=1e-06, **kwargs)
@@ -358,8 +359,6 @@ E(dx_t^2) &= \rho * E(dx_{t-1}^2) + (1-\rho) * (-g*learning\_rate)^2\end{spl

RMSProp

-

Optimizers(update equation) for SGD method.

-

TODO(yuyang18): Complete comments.

class paddle.v2.optimizer.RMSProp(rho=0.95, epsilon=1e-06, **kwargs)
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