ApplyCenteredRmsProp

Update '*var' according to the centered RMSProp algorithm.

The centered RMSProp algorithm uses an estimate of the centered second moment (i.e., the variance) for normalization, as opposed to regular RMSProp, which uses the (uncentered) second moment. This often helps with training, but is slightly more expensive in terms of computation and memory.

Note that in dense implementation of this algorithm, mg, ms, and mom will update even if the grad is zero, but in this sparse implementation, mg, ms, and mom will not update in iterations during which the grad is zero.

mean_square = decay * mean_square + (1-decay) * gradient ** 2 mean_grad = decay * mean_grad + (1-decay) * gradient

Delta = learning_rate * gradient / sqrt(mean_square + epsilon - mean_grad ** 2)

mg <- rho * mg_{t-1} + (1-rho) * grad ms <- rho * ms_{t-1} + (1-rho) * grad * grad mom <- momentum * mom_{t-1} + lr * grad / sqrt(ms - mg * mg + epsilon) var <- var - mom