Proximal Adam for pytorch

pytorch-adaprox.py

from torch.optim import Optimizer
import math
import torch
from torch import Tensor
from typing import List, Optional, Callable

def adaprox(params: List[Tensor],
         proxes: List[Callable[[Tensor, float], Tensor]],
         grads: List[Tensor],
         exp_avgs: List[Tensor],
         exp_avg_sqs: List[Tensor],
         max_exp_avg_sqs: List[Tensor],
         state_steps: List[int],
         *,
         amsgrad: bool,
         beta1: float,
         beta2: float,
         lr: float,
         weight_decay: float,
         eps: float,
         maximize: bool,
         prox_max_iter: int,
         e_rel: float):
    r"""Functional API that performs Adam algorithm computation.
    See :class:`~torch.optim.Adam` for details.
    """

    for i, (param, prox) in enumerate(zip(params, proxes)):

        # ordinary Adam
        grad = grads[i] if not maximize else -grads[i]
        M = exp_avgs[i]
        V = exp_avg_sqs[i]
        step = state_steps[i]

        bias_correction1 = 1 - beta1 ** step
        bias_correction2 = 1 - beta2 ** step

        if weight_decay != 0:
            grad = grad.add(param, alpha=weight_decay)

        # Decay the first and second moment running average coefficient
        M.mul_(beta1).add_(grad, alpha=1 - beta1)
        V.mul_(beta2).addcmul_(grad, grad.conj(), value=1 - beta2)
        if amsgrad:
            # Maintains the maximum of all 2nd moment running avg. till now
            torch.maximum(max_exp_avg_sqs[i], V, out=max_exp_avg_sqs[i])
            # Use the max. for normalizing running avg. of gradient
            psi = (max_exp_avg_sqs[i].sqrt() / math.sqrt(bias_correction2)).add_(eps)
        else:
            psi = (V.sqrt() / math.sqrt(bias_correction2)).add_(eps)

        step_size = lr / bias_correction1
        param.addcdiv_(M, psi, value=-step_size)

        # proximal update(s)
        alpha = lr
        gamma = alpha / psi.max()
        x = param.data
        z = torch.clone(x)
        for tau in range(prox_max_iter):
            z_ = prox(z - gamma / alpha * psi * (z - x), gamma)
            if torch.square(z-z_).sum() <= e_rel*e_rel * torch.square(z).sum():
                break
            z = z_
        param.data = z_
            

class AdaProx(Optimizer):
    r"""Implements proximal Adam algorithm.
 
    For further details regarding the algorithm we refer to 
    `Proximal Adam: Robust Adaptive Update Scheme for Constrained Optimization`
    (https://arxiv.org/abs/1910.10094)
    
    Args:
        params (iterable): iterable of parameters to optimize or dicts defining
            parameter groups
        proxes (iterable): iterable of proximal operators with signature
            prox(x, gamma) -> x_
        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)
    """

    def __init__(self, params, proxes, lr=1e-3, betas=(0.9, 0.999), eps=1e-8,
                 weight_decay=0, amsgrad=False, *, maximize: bool = False):
        if not 0.0 <= lr:
            raise ValueError("Invalid learning rate: {}".format(lr))
        if not 0.0 <= eps:
            raise ValueError("Invalid epsilon value: {}".format(eps))
        if not 0.0 <= betas[0] < 1.0:
            raise ValueError("Invalid beta parameter at index 0: {}".format(betas[0]))
        if not 0.0 <= betas[1] < 1.0:
            raise ValueError("Invalid beta parameter at index 1: {}".format(betas[1]))
        if not 0.0 <= weight_decay:
            raise ValueError("Invalid weight_decay value: {}".format(weight_decay))
        defaults = dict(lr=lr, betas=betas, eps=eps,
                        weight_decay=weight_decay, amsgrad=amsgrad, maximize=maximize)
        super(AdaProx, self).__init__(params, defaults)
        
        # one prox per group
        if len(proxes) != len(self.param_groups):
            raise ValueError("Invalid length of argument proxs: {} instead of {}".format(len(proxes), len(self.param_groups)))

        for group, prox in zip(self.param_groups, list(proxes)):
            group.setdefault('prox', prox)

    def __setstate__(self, state):
        super(AdaProx, self).__setstate__(state)
        for group in self.param_groups:
            group.setdefault('amsgrad', False)
            group.setdefault('maximize', False)

    @torch.no_grad()
    def step(self, closure=None):
        """Performs a single optimization step.
        Args:
            closure (callable, optional): A closure that reevaluates the model
                and returns the loss.
        """
        loss = None
        if closure is not None:
            with torch.enable_grad():
                loss = closure()

        for group in self.param_groups:
            params_with_grad = []
            proxes_with_grad = []
            grads = []
            exp_avgs = []
            exp_avg_sqs = []
            max_exp_avg_sqs = []
            state_steps = []
            beta1, beta2 = group['betas']
            
            prox = group['prox']

            for p in group['params']:
                if p.grad is not None:
                    params_with_grad.append(p)
                    proxes_with_grad.append(prox)
                    if p.grad.is_sparse:
                        raise RuntimeError('Adam does not support sparse gradients, please consider SparseAdam instead')
                    grads.append(p.grad)

                    state = self.state[p]
                    # Lazy state initialization
                    if len(state) == 0:
                        state['step'] = 0
                        # Exponential moving average of gradient values
                        state['exp_avg'] = torch.zeros_like(p, memory_format=torch.preserve_format)
                        # Exponential moving average of squared gradient values
                        state['exp_avg_sq'] = torch.zeros_like(p, memory_format=torch.preserve_format)
                        if group['amsgrad']:
                            # Maintains max of all exp. moving avg. of sq. grad. values
                            state['max_exp_avg_sq'] = torch.zeros_like(p, memory_format=torch.preserve_format)

                    exp_avgs.append(state['exp_avg'])
                    exp_avg_sqs.append(state['exp_avg_sq'])

                    if group['amsgrad']:
                        max_exp_avg_sqs.append(state['max_exp_avg_sq'])

                    # update the steps for each param group update
                    state['step'] += 1
                    # record the step after step update
                    state_steps.append(state['step'])
            
            # regular Adam update step 
            adaprox(params_with_grad,
                 proxes_with_grad,
                   grads,
                   exp_avgs,
                   exp_avg_sqs,
                   max_exp_avg_sqs,
                   state_steps,
                   amsgrad=group['amsgrad'],
                   beta1=beta1,
                   beta2=beta2,
                   lr=group['lr'],
                   weight_decay=group['weight_decay'],
                   eps=group['eps'],
                   maximize=group['maximize'],
                   prox_max_iter=100,
                   e_rel=1e-4)
            
        return loss

Details about the proximal Adam optimizer are in this paper.