mxnet.ndarray.sparse.adam_update(weight=None, grad=None, mean=None, var=None, lr=_Null, beta1=_Null, beta2=_Null, epsilon=_Null, wd=_Null, rescale_grad=_Null, clip_gradient=_Null, lazy_update=_Null, out=None, name=None, **kwargs)

Adam update consists of the following steps, where g represents gradient and m, v are 1st and 2nd order moment estimates (mean and variance).

$\begin{split}g_t = \nabla J(W_{t-1})\\ m_t = \beta_1 m_{t-1} + (1 - \beta_1) g_t\\ v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2\\ W_t = W_{t-1} - \alpha \frac{ m_t }{ \sqrt{ v_t } + \epsilon }\end{split}$

m = beta1*m + (1-beta1)*grad
w += - learning_rate * m / (sqrt(v) + epsilon)


However, if grad’s storage type is row_sparse, lazy_update is True and the storage type of weight is the same as those of m and v, only the row slices whose indices appear in grad.indices are updated (for w, m and v):

for row in grad.indices:
w[row] += - learning_rate * m[row] / (sqrt(v[row]) + epsilon)


Defined in src/operator/optimizer_op.cc:L495

Parameters
• weight (NDArray) – Weight

• mean (NDArray) – Moving mean

• var (NDArray) – Moving variance

• lr (float, required) – Learning rate

• beta1 (float, optional, default=0.9) – The decay rate for the 1st moment estimates.

• beta2 (float, optional, default=0.999) – The decay rate for the 2nd moment estimates.

• epsilon (float, optional, default=1e-08) – A small constant for numerical stability.

• wd (float, optional, default=0) – Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.