def step(self, closure=None):
        """
        Performs a single optimization step (parameter update).

        Arguments:
            closure: A closure that reevaluates the model and
                returns the loss. Optional for most optimizers.

        Returns:
            computed loss
        """
        loss = None
        if closure is not None:
            loss = closure()

        for group in self.param_groups:
            for p in group["params"]:
                if p.grad is None:
                    continue

                grad = p.grad.data
                beta1, beta2 = group["betas"]
                nesterov = group["nesterov"]

                state = self.state[p]

                # State initialization
                if len(state) == 0:
                    state["step"] = 0
                    state["exp_avg"] = torch.zeros_like(p.data)
                    state["exp_avg_sq"] = torch.zeros_like(p.data)

                # Adam
                exp_avg, exp_avg_sq = state["exp_avg"], state["exp_avg_sq"]

                state["step"] += 1
                bias_correction1 = 1 - beta1 ** state["step"]
                bias_correction2 = 1 - beta2 ** state["step"]

                exp_avg.mul_(beta1).add_(grad, alpha=1 - beta1)
                exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1 - beta2)

                denom = (exp_avg_sq.sqrt() / math.sqrt(bias_correction2)).add_(
                    group["eps"]
                )
                step_size = group["lr"] / bias_correction1

                if nesterov:
                    perturb = (beta1 * exp_avg + (1 - beta1) * grad) / denom
                else:
                    perturb = exp_avg / denom

                # Projection
                wd_ratio = 1
                if len(p.shape) > 1:
                    perturb, wd_ratio = self._projection(
                        p, grad, perturb, group["delta"], group["wd_ratio"], group["eps"]
                    )

                # Weight decay
                if group["weight_decay"] > 0:
                    p.data.mul_(1 - group["lr"] * group["weight_decay"] * wd_ratio)

                # Step
                p.data.add_(perturb, alpha=-step_size)

        return loss

        Performs a single optimization step (parameter update).

        Arguments:
            closure: A closure that reevaluates the model and
                returns the loss. Optional for most optimizers.

        Returns:
            computed loss
        
catalyst/contrib/optimizers/adamp.py