Updating the Latex equation for Adagrad (#6009)

* Updating the Latex equation for Adagrad

* Fixing Latex euqations for adadelta, adam and adamax

paddle/operators/adadelta_op.cc

@@ -92,12 +92,12 @@ for gradient descent.
 
 Adadelta updates are as follows:
 
-$$avgSquaredGradOut = \rho * avgSquaredGrad + (1 - \rho) * grad * grad \break
-paramUpdate =  - $\sqrt{((avgSquaredUpdate + \epsilon) /
-                       (avgSquaredGrad_out + \epsilon))}$ * grad \break
-avgSquaredUpdateOut = \rho * avgSquaredUpdate + (1 - \rho) *
-                                  {(paramUpdate)}^2 \break
-paramOut = param + paramUpdate$$
+$$
+avg\_squared\_grad\_out = \rho * avg\_squared\_grad + (1 - \rho) * grad * grad \\
+param\_update =  - \sqrt{\frac{avg\_squared\_update + \epsilon}{avg\_squared\_grad\_out + \epsilon}} * grad \\
+avg\_squared\_update\_out = \rho * avg\_squared\_update + (1 - \rho) * {param\_update}^2 \\
+param\_out = param + param\_update
+$$
 
 )DOC");
   }

paddle/operators/adagrad_op.cc

@@ -80,8 +80,8 @@ Adaptive Gradient Algorithm (Adagrad).
 
 The update is done as follows:
 
-$$momentOut = moment + grad * grad \break
-paramOut = param - learningRate * grad / ($\sqrt{momentOut}$ + \epsilon) \break
+$$moment\_out = moment + grad * grad \\
+param\_out = param - \frac{learning\_rate * grad}{\sqrt{moment\_out} + \epsilon}
 $$
 
 The original paper(http://www.jmlr.org/papers/volume12/duchi11a/duchi11a.pdf)

paddle/operators/adam_op.cc

@@ -112,11 +112,13 @@ adaptive estimates of lower-order moments.
 
 Adam updates:
 
-$$moment_1_{out} = \beta_1 * moment_1 + (1 - \beta_1) * grad \break
-moment_2_{out} = \beta_2 * moment_2 + (1 - \beta_2) * grad * grad \break
-learningRate = learningRate *
-                  $\sqrt{(1 - \beta_2_{pow})}$ / (1 - \beta_1_{pow}) \break
-paramOut = param - learningRate * moment_1/ ($\sqrt{(moment_2)} + \epsilon)$$
+$$
+moment\_1\_out = \beta_1 * moment\_1 + (1 - \beta_1) * grad \\
+moment\_2_\out = \beta_2 * moment\_2 + (1 - \beta_2) * grad * grad \\
+learning\_rate = learning\_rate *
+                  \frac{\sqrt{1 - \beta_{2\_pow}}}{1 - \beta_{1\_pow}} \\
+param\_out = param - learning\_rate * \frac{moment\_1}{\sqrt{moment\_2} + \epsilon}
+$$
 
 )DOC");
   }

paddle/operators/adamax_op.cc

@@ -108,10 +108,10 @@ Adam algorithm based on the infinity norm.
 Adamax updates:
 
 $$
-  momentOut = \beta_{1} * moment + (1 - \beta_{1}) * grad \\
-  infNormOut = max(\beta_{2} * infNorm + \epsilon, |grad|) \\
-  learningRate = \frac{learningRate}{1 - \beta_{1}^{Beta1Pow}} \\
-  paramOut = param - learningRate * \frac{momentOut}{infNormOut}
+moment\_out = \beta_1 * moment + (1 - \beta_1) * grad \\
+inf\_norm\_out = max(\beta_2 * inf\_norm + \epsilon, |grad|) \\
+learning\_rate = \frac{learning\_rate}{1 - \beta_{1\_pow}} \\
+param\_out = param - learning\_rate * \frac{moment\_out}{inf\_norm\_out}
 $$
 
 The original paper does not have an epsilon attribute.