Related papers: Can Decentralized Stochastic Minimax Optimization …

Nonconvex minimax problems appear frequently in emerging machine learning applications, such as generative adversarial networks and adversarial learning. Simple algorithms such as the gradient descent ascent (GDA) are the common practice…

We consider the task of minimizing the sum of convex functions stored in a decentralized manner across the nodes of a communication network. This problem is relatively well-studied in the scenario when the objective functions are smooth, or…

Stochastic nonconvex-concave min-max saddle point problems appear in many machine learning and control problems including distributionally robust optimization, generative adversarial networks, and adversarial learning. In this paper, we…

In this paper, we study stochastic constrained minimax optimization problems with nonconvex-nonconcave structure, a central problem in modern machine learning, for which reliable and efficient algorithms remain largely unexplored due to its…

To understand the convergence behavior of the Push-Pull method for decentralized optimization with stochastic gradients (Stochastic Push-Pull), this paper presents a comprehensive analysis. Specifically, we first clarify the algorithm's…

The ProxSkip algorithm for distributed optimization is gaining increasing attention due to its effectiveness in reducing communication. However, existing analyses of ProxSkip are limited to the strongly convex setting and fail to achieve…

Stochastic multi-level compositional optimization problems cover many new machine learning paradigms, e.g., multi-step model-agnostic meta-learning, which require efficient optimization algorithms for large-scale data. This paper studies…

This paper considers distributed optimization for minimizing the average of local nonconvex cost functions, by using local information exchange over undirected communication networks. To reduce the required communication capacity, we…

Communication delays and synchronization are major bottlenecks for parallel computing, and tolerating asynchrony is therefore crucial for accelerating parallel computation. Motivated by optimization problems that do not satisfy convexity…

Nonconvex-nonconcave minimax optimization has gained widespread interest over the last decade. However, most existing works focus on variants of gradient descent-ascent (GDA) algorithms, which are only applicable to smooth nonconvex-concave…

Existing decentralized stochastic optimization methods assume the lower-level loss function is strongly convex and the stochastic gradient noise has finite variance. These strong assumptions typically are not satisfied in real-world machine…

This paper considers the distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of local cost functions by using local information exchange. We first consider a distributed first-order primal-dual…

This study develops a fixed-time convergent saddle point dynamical system for solving min-max problems under a relaxation of standard convexity-concavity assumption. In particular, it is shown that by leveraging the dynamical systems…

The use of min-max optimization in adversarial training of deep neural network classifiers and training of generative adversarial networks has motivated the study of nonconvex-nonconcave optimization objectives, which frequently arise in…

We study a class of constrained nonconvex-nonconcave minimax optimization problems in which the inner maximization involves potentially complex constraints. Under the assumption that the inner problem of a novel lifted minimax reformulation…

We consider the optimization problem of minimizing the sum-of-nonconvex function, i.e., a convex function that is the average of nonconvex components. The existing stochastic algorithms for such a problem only focus on a single machine and…

Non-convex optimization is ubiquitous in modern machine learning. Researchers devise non-convex objective functions and optimize them using off-the-shelf optimizers such as stochastic gradient descent and its variants, which leverage the…

We consider the task of decentralized minimization of the sum of smooth strongly convex functions stored across the nodes of a network. For this problem, lower bounds on the number of gradient computations and the number of communication…

This paper studies the stochastic nonconvex-strongly-concave minimax optimization over a multi-agent network. We propose an efficient algorithm, called Decentralized Recursive gradient descEnt Ascent Method (DREAM), which achieves the…

Minimax problems have achieved success in machine learning such as adversarial training, robust optimization, reinforcement learning. For theoretical analysis, current optimal excess risk bounds, which are composed by generalization error…