adding API doc for Lamb Phase 1 and 2

src/operator/optimizer_op.cc

@@ -924,7 +924,32 @@ Note that non-zero values for the weight decay option are not supported.
 .add_arguments(AdagradParam::__FIELDS__());
 
 NNVM_REGISTER_OP(lamb_update_phase1)
-.describe(R"code(Update function for lamb optimizer.
+.describe(R"code(Phase I of lamb update it performs the following operations and returns g:.
+
+Link to paper: https://arxiv.org/pdf/1904.00962.pdf
+
+.. math::
+    \begin{gather*}
+    grad = grad * rescale_grad
+    if (grad < -clip_gradient)
+    then
+         grad = -clip_gradient
+    if (grad > clip_gradient)
+    then
+         grad = clip_gradient
+
+    mean = beta1 * mean + (1 - beta1) * grad;
+    variance = beta2 * variance + (1. - beta2) * grad ^ 2;
+
+    if (bias_correction)
+    then
+         mean_hat = mean / (1. - beta1^t);
+         var_hat = var / (1 - beta2^t);
+         g = mean_hat / (var_hat^(1/2) + epsilon) + wd * weight;
+    else
+         g = mean / (var_data^(1/2) + epsilon) + wd * weight_data[i];
+    \end{gather*}
+
 )code" ADD_FILELINE)
 .set_num_inputs(4)
 .set_num_outputs(1)
@@ -943,7 +968,27 @@ NNVM_REGISTER_OP(lamb_update_phase1)
 .add_arguments(LambUpdatePhaseOneParam::__FIELDS__());
 
 NNVM_REGISTER_OP(lamb_update_phase2)
-.describe(R"code(Update function for lamb optimizer.
+.describe(R"code(Phase II of lamb update it performs the following operations and updates grad.
+
+Link to paper: https://arxiv.org/pdf/1904.00962.pdf
+
+.. math::
+    \begin{gather*}
+    if (lower_bound >= 0)
+    then
+         r1 = max(r1, lower_bound)
+    if (upper_bound >= 0)
+    then
+         r1 = max(r1, upper_bound)
+
+    if (r1 == 0 or r2 == 0)
+    then
+         lr = lr
+    else
+         lr = lr * (r1/r2)
+    weight = weight - lr * g
+    \end{gather*}
+
 )code" ADD_FILELINE)
 .set_num_inputs(4)
 .set_num_outputs(1)