相关论文: Decentralized Saddle-Point Problems with Different…

Federated learning is a useful framework for centralized learning from distributed data under practical considerations of heterogeneity, asynchrony, and privacy. Federated architectures are frequently deployed in deep learning settings,…

In this paper, we propose a variance-reduced primal-dual algorithm with Bregman distance for solving convex-concave saddle-point problems with finite-sum structure and nonbilinear coupling function. This type of problems typically arises in…

This paper is devoted to the design of efficient primal-dual algorithm (PDA) for solving convex optimization problems with known saddle-point structure. We present a new PDA with larger acceptable range of parameters and correction, which…

We characterize the query complexity of finding stationary points of one-dimensional non-convex but smooth functions. We consider four settings, based on whether the algorithms under consideration are deterministic or randomized, and…

This paper considers continuous-time coordination algorithms for networks of agents that seek to collectively solve a general class of nonsmooth convex optimization problems with an inherent distributed structure. Our algorithm design…

Variational inequalities are a formalism that includes games, minimization, saddle point, and equilibrium problems as special cases. Methods for variational inequalities are therefore universal approaches for many applied tasks, including…

We study a stochastic first order primal-dual method for solving convex-concave saddle point problems over real reflexive Banach spaces using Bregman divergences and relative smoothness assumptions, in which we allow for stochastic error in…

Symmetric determinantal point processes (DPP's) are a class of probabilistic models that encode the random selection of items that exhibit a repulsive behavior. They have attracted a lot of attention in machine learning, when returning…

A central challenge to many fields of science and engineering involves minimizing non-convex error functions over continuous, high dimensional spaces. Gradient descent or quasi-Newton methods are almost ubiquitously used to perform such…

An interior-point algorithm framework is proposed, analyzed, and tested for solving nonlinearly constrained continuous optimization problems. The main setting of interest is when the objective and constraint functions may be nonlinear…

In this paper, we focus on a class of convexly constrained nonsmooth convex-concave saddle point problems with cardinality penalties. Although such nonsmooth nonconvex-nonconcave and discontinuous min-max problems may not have a saddle…

Saddle-point optimization problems are an important class of optimization problems with applications to game theory, multi-agent reinforcement learning and machine learning. A majority of the rich literature available for saddle-point…

This is a continuation of our previous work entitled \enquote{Alternating Proximity Mapping Method for Convex-Concave Saddle-Point Problems}, in which we proposed the alternating proximal mapping method and showed convergence results on the…

A variant of consensus based distributed gradient descent (\textbf{DGD}) is studied for finite sums of smooth but possibly non-convex functions. In particular, the local gradient term in the fixed step-size iteration of each agent is…

This paper presents a simple primal dual method named DPD which is a flexible framework for a class of saddle point problem with or without strongly convex component. The presented method has linearized version named LDPD and exact version…

We focus on decentralized stochastic non-convex optimization, where $n$ agents work together to optimize a composite objective function which is a sum of a smooth term and a non-smooth convex term. To solve this problem, we propose two…

The latent variable proximal point (LVPP) algorithm is a framework for solving infinite-dimensional variational problems with pointwise inequality constraints. The algorithm is a saddle point reformulation of the Bregman proximal point…

This paper considers continuously differentiable functions of two vector variables that have (possibly a continuum of) min-max saddle points. We study the asymptotic convergence properties of the associated saddle-point dynamics…

In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…

Decentralized optimization methods have been in the focus of optimization community due to their scalability, increasing popularity of parallel algorithms and many applications. In this work, we study saddle point problems of sum type,…