# RMSprop¶

class torch.optim.RMSprop(params, lr=0.01, alpha=0.99, eps=1e-08, weight_decay=0, momentum=0, centered=False)[source]

Implements RMSprop algorithm.

\begin{aligned} &\rule{110mm}{0.4pt} \\ &\textbf{input} : \alpha \text{ (alpha)},\: \gamma \text{ (lr)}, \: \theta_0 \text{ (params)}, \: f(\theta) \text{ (objective)} \\ &\hspace{13mm} \lambda \text{ (weight decay)},\: \mu \text{ (momentum)},\: centered\\ &\textbf{initialize} : v_0 \leftarrow 0 \text{ (square average)}, \: \textbf{b}_0 \leftarrow 0 \text{ (buffer)}, \: g^{ave}_0 \leftarrow 0 \\[-1.ex] &\rule{110mm}{0.4pt} \\ &\textbf{for} \: t=1 \: \textbf{to} \: \ldots \: \textbf{do} \\ &\hspace{5mm}g_t \leftarrow \nabla_{\theta} f_t (\theta_{t-1}) \\ &\hspace{5mm}if \: \lambda \neq 0 \\ &\hspace{10mm} g_t \leftarrow g_t + \lambda \theta_{t-1} \\ &\hspace{5mm}v_t \leftarrow \alpha v_{t-1} + (1 - \alpha) g^2_t \hspace{8mm} \\ &\hspace{5mm} \tilde{v_t} \leftarrow v_t \\ &\hspace{5mm}if \: centered \\ &\hspace{10mm} g^{ave}_t \leftarrow g^{ave}_{t-1} \alpha + (1-\alpha) g_t \\ &\hspace{10mm} \tilde{v_t} \leftarrow \tilde{v_t} - \big(g^{ave}_{t} \big)^2 \\ &\hspace{5mm}if \: \mu > 0 \\ &\hspace{10mm} \textbf{b}_t\leftarrow \mu \textbf{b}_{t-1} + g_t/ \big(\sqrt{\tilde{v_t}} + \epsilon \big) \\ &\hspace{10mm} \theta_t \leftarrow \theta_{t-1} - \gamma \textbf{b}_t \\ &\hspace{5mm} else \\ &\hspace{10mm}\theta_t \leftarrow \theta_{t-1} - \gamma g_t/ \big(\sqrt{\tilde{v_t}} + \epsilon \big) \hspace{3mm} \\ &\rule{110mm}{0.4pt} \\[-1.ex] &\bf{return} \: \theta_t \\[-1.ex] &\rule{110mm}{0.4pt} \\[-1.ex] \end{aligned}

For further details regarding the algorithm we refer to lecture notes by G. Hinton. and centered version Generating Sequences With Recurrent Neural Networks. The implementation here takes the square root of the gradient average before adding epsilon (note that TensorFlow interchanges these two operations). The effective learning rate is thus $\gamma/(\sqrt{v} + \epsilon)$ where $\gamma$ is the scheduled learning rate and $v$ is the weighted moving average of the squared gradient.

Parameters
• params (iterable) – iterable of parameters to optimize or dicts defining parameter groups

• lr (float, optional) – learning rate (default: 1e-2)

• momentum (float, optional) – momentum factor (default: 0)

• alpha (float, optional) – smoothing constant (default: 0.99)

• eps (float, optional) – term added to the denominator to improve numerical stability (default: 1e-8)

• centered (bool, optional) – if True, compute the centered RMSProp, the gradient is normalized by an estimation of its variance

• weight_decay (float, optional) – weight decay (L2 penalty) (default: 0)

add_param_group(param_group)

Add a param group to the Optimizer s param_groups.

This can be useful when fine tuning a pre-trained network as frozen layers can be made trainable and added to the Optimizer as training progresses.

Parameters

param_group (dict) – Specifies what Tensors should be optimized along with group specific optimization options.

load_state_dict(state_dict)

Parameters

state_dict (dict) – optimizer state. Should be an object returned from a call to state_dict().

state_dict()

Returns the state of the optimizer as a dict.

It contains two entries:

• state - a dict holding current optimization state. Its content

differs between optimizer classes.

• param_groups - a list containing all parameter groups where each

parameter group is a dict

step(closure=None)[source]

Performs a single optimization step.

Parameters

closure (callable, optional) – A closure that reevaluates the model and returns the loss.

zero_grad(set_to_none=False)

Sets the gradients of all optimized torch.Tensor s to zero.

Parameters

set_to_none (bool) – instead of setting to zero, set the grads to None. This will in general have lower memory footprint, and can modestly improve performance. However, it changes certain behaviors. For example: 1. When the user tries to access a gradient and perform manual ops on it, a None attribute or a Tensor full of 0s will behave differently. 2. If the user requests zero_grad(set_to_none=True) followed by a backward pass, .grads are guaranteed to be None for params that did not receive a gradient. 3. torch.optim optimizers have a different behavior if the gradient is 0 or None (in one case it does the step with a gradient of 0 and in the other it skips the step altogether).