class torch.optim.Adadelta(params, lr=1.0, rho=0.9, eps=1e-06, weight_decay=0, foreach=None, *, maximize=False)[source]

Implements Adadelta algorithm.

input:γ (lr),θ0 (params),f(θ) (objective),ρ (decay),λ (weight decay)initialize:v00 (square avg),u00 (accumulate variables)fort=1todogtθft(θt1)ifλ0gtgt+λθt1vtvt1ρ+gt2(1ρ)Δxtut1+ϵvt+ϵgtutut1ρ+Δxt2(1ρ)θtθt1γΔxtreturnθt\begin{aligned} &\rule{110mm}{0.4pt} \\ &\textbf{input} : \gamma \text{ (lr)}, \: \theta_0 \text{ (params)}, \: f(\theta) \text{ (objective)}, \: \rho \text{ (decay)}, \: \lambda \text{ (weight decay)} \\ &\textbf{initialize} : v_0 \leftarrow 0 \: \text{ (square avg)}, \: u_0 \leftarrow 0 \: \text{ (accumulate variables)} \\[-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 v_{t-1} \rho + g^2_t (1 - \rho) \\ &\hspace{5mm}\Delta x_t \leftarrow \frac{\sqrt{u_{t-1} + \epsilon }}{ \sqrt{v_t + \epsilon} }g_t \hspace{21mm} \\ &\hspace{5mm} u_t \leftarrow u_{t-1} \rho + \Delta x^2_t (1 - \rho) \\ &\hspace{5mm}\theta_t \leftarrow \theta_{t-1} - \gamma \Delta x_t \\ &\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 ADADELTA: An Adaptive Learning Rate Method.

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

  • rho (float, optional) – coefficient used for computing a running average of squared gradients (default: 0.9)

  • eps (float, optional) – term added to the denominator to improve numerical stability (default: 1e-6)

  • lr (float, optional) – coefficient that scale delta before it is applied to the parameters (default: 1.0)

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

  • foreach (bool, optional) – whether foreach implementation of optimizer is used (default: None)

  • 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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