class torch.optim.Adam(params, lr=0.001, betas=(0.9, 0.999), eps=1e-08, weight_decay=0, amsgrad=False, *, maximize=False)[source]

Implements Adam algorithm.

input:γ (lr),β1,β2 (betas),θ0 (params),f(θ) (objective)λ (weight decay),amsgrad,maximizeinitialize:m00 ( first moment),v00 (second moment),v0^max0fort=1todoifmaximize:gtθft(θt1)elsegtθft(θt1)ifλ0gtgt+λθt1mtβ1mt1+(1β1)gtvtβ2vt1+(1β2)gt2mt^mt/(1β1t)vt^vt/(1β2t)ifamsgradvt^maxmax(vt^max,vt^)θtθt1γmt^/(vt^max+ϵ)elseθtθt1γmt^/(vt^+ϵ)returnθt\begin{aligned} &\rule{110mm}{0.4pt} \\ &\textbf{input} : \gamma \text{ (lr)}, \beta_1, \beta_2 \text{ (betas)},\theta_0 \text{ (params)},f(\theta) \text{ (objective)} \\ &\hspace{13mm} \lambda \text{ (weight decay)}, \: \textit{amsgrad}, \:\textit{maximize} \\ &\textbf{initialize} : m_0 \leftarrow 0 \text{ ( first moment)}, v_0\leftarrow 0 \text{ (second moment)},\: \widehat{v_0}^{max}\leftarrow 0\\[-1.ex] &\rule{110mm}{0.4pt} \\ &\textbf{for} \: t=1 \: \textbf{to} \: \ldots \: \textbf{do} \\ &\hspace{5mm}\textbf{if} \: \textit{maximize}: \\ &\hspace{10mm}g_t \leftarrow -\nabla_{\theta} f_t (\theta_{t-1}) \\ &\hspace{5mm}\textbf{else} \\ &\hspace{10mm}g_t \leftarrow \nabla_{\theta} f_t (\theta_{t-1}) \\ &\hspace{5mm}\textbf{if} \: \lambda \neq 0 \\ &\hspace{10mm} g_t \leftarrow g_t + \lambda \theta_{t-1} \\ &\hspace{5mm}m_t \leftarrow \beta_1 m_{t-1} + (1 - \beta_1) g_t \\ &\hspace{5mm}v_t \leftarrow \beta_2 v_{t-1} + (1-\beta_2) g^2_t \\ &\hspace{5mm}\widehat{m_t} \leftarrow m_t/\big(1-\beta_1^t \big) \\ &\hspace{5mm}\widehat{v_t} \leftarrow v_t/\big(1-\beta_2^t \big) \\ &\hspace{5mm}\textbf{if} \: amsgrad \\ &\hspace{10mm}\widehat{v_t}^{max} \leftarrow \mathrm{max}(\widehat{v_t}^{max}, \widehat{v_t}) \\ &\hspace{10mm}\theta_t \leftarrow \theta_{t-1} - \gamma \widehat{m_t}/ \big(\sqrt{\widehat{v_t}^{max}} + \epsilon \big) \\ &\hspace{5mm}\textbf{else} \\ &\hspace{10mm}\theta_t \leftarrow \theta_{t-1} - \gamma \widehat{m_t}/ \big(\sqrt{\widehat{v_t}} + \epsilon \big) \\ &\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 Adam: A Method for Stochastic Optimization.

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

  • lr (float, optional) – learning rate (default: 1e-3)

  • betas (Tuple[float, float], optional) – coefficients used for computing running averages of gradient and its square (default: (0.9, 0.999))

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

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

  • amsgrad (boolean, optional) – whether to use the AMSGrad variant of this algorithm from the paper On the Convergence of Adam and Beyond (default: False)

  • maximize (bool, optional) – maximize the params based on the objective, instead of minimizing (default: False)


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.


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


Loads the optimizer state.


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


Performs a single optimization step.


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


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


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).


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