Updates relevant entries according to the FOBOS(Forward Backward Splitting) algorithm.

$\begin{split}\begin{array}{ll} \\ \text{prox_v} = var - \alpha * \delta \\ var = \frac{sign(\text{prox_v})}{1 + \alpha * l2} * \max(\left| \text{prox_v} \right| - \alpha * l1, 0) \end{array}\end{split}$

where $$\alpha$$ represents alpha, $$\delta$$ represents delta.

Inputs of var and delta comply with the implicit type conversion rules to make the data types consistent. If they have different data types, the lower priority data type will be converted to the relatively highest priority data type.

Inputs:
• var (Parameter) - Variable tensor to be updated. With float32 or float16 data type. The shape is $$(N, *)$$ where $$*$$ means, any number of additional dimensions.

• alpha (Union[Number, Tensor]) - Scaling factor, must be a scalar. With float32 or float16 data type.

• l1 (Union[Number, Tensor]) - l1 regularization strength, must be a scalar. With float32 or float16 data type.

• l2 (Union[Number, Tensor]) - l2 regularization strength, must be a scalar. With float32 or float16 data type.

• delta (Tensor) - A tensor for the change, has the same shape and data type as var.

Outputs:

Tensor, represents the updated var.

Raises
• TypeError – If dtype of var, alpha, l1 or l2 is neither float16 nor float32.

• TypeError – If alpha, l1 or l2 is neither a Number nor a Tensor.

• TypeError – If delta is not a Tensor.

• RuntimeError – If the data type of var, and delta conversion of Parameter is not supported.

Supported Platforms:

Ascend

Examples

>>> class Net(nn.Cell):
...     def __init__(self):
...         super(Net, self).__init__()
...         self.var = Parameter(Tensor(np.ones([2, 2]).astype(np.float32)), name="var")
...         self.alpha = 0.001
...         self.l1 = 0.1
...         self.l2 = 0.1
...     def construct(self, delta):
...         out = self.apply_proximal_gradient_descent(self.var, self.alpha, self.l1, self.l2, delta)
...         return out
...
>>> net = Net()
>>> delta = Tensor(np.array([[0.1, 0.1], [0.1, 0.1]]).astype(np.float32))
>>> output = net(delta)
>>> print(output)
[[0.99969995 0.99969995]
[0.99969995 0.99969995]]