Related papers: Proximal Point Method for Online Saddle Point Prob…
Centered around solving the Online Saddle Point problem, this paper introduces the Online Convex-Concave Optimization (OCCO) framework, which involves a sequence of two-player time-varying convex-concave games. We propose the generalized…
We propose and study an online version of min-max optimization based on cumulative saddle points under a variety of performance measures beyond convex-concave settings. After first observing the incompatibility of (static) Nash equilibrium…
We study the online saddle point problem, an online learning problem where at each iteration a pair of actions need to be chosen without knowledge of the current and future (convex-concave) payoff functions. The objective is to minimize the…
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…
The online optimization problem with non-convex loss functions over a closed convex set, coupled with a set of inequality (possibly non-convex) constraints is a challenging online learning problem. A proximal method of multipliers with…
Existing approaches to online convex optimization (OCO) make sequential one-slot-ahead decisions, which lead to (possibly adversarial) losses that drive subsequent decision iterates. Their performance is evaluated by the so-called regret…
Learning and computation of equilibria are central problems in game theory, theory of computation, and artificial intelligence. In this work, we introduce proximal regret, a new notion of regret based on proximal operators that lies…
Saddle point with a given Morse index on a potential energy surface is an important object related to energy landscape in physics and chemistry. Efficient numerical methods based on iterative minimization formulation have been proposed in…
We investigate online convex optimization in non-stationary environments and choose dynamic regret as the performance measure, defined as the difference between cumulative loss incurred by the online algorithm and that of any feasible…
We provide several applications of Optimistic Mirror Descent, an online learning algorithm based on the idea of predictable sequences. First, we recover the Mirror Prox algorithm for offline optimization, prove an extension to Holder-smooth…
This paper investigates the problem of Online Convex-Concave Optimization, which extends Online Convex Optimization to two-player time-varying convex-concave games. The goal is to minimize the dynamic duality gap (D-DGap), a critical…
This paper studies bandit convex optimization in non-stationary environments with two-point feedback, using dynamic regret as the performance measure. We propose an algorithm based on bandit mirror descent that extends naturally to…
In this paper, we study the distributed generalized Nash equilibrium seeking problem of non-cooperative games in dynamic environments. Each player in the game aims to minimize its own time-varying cost function subject to a local action…
Computing saddle points with a prescribed Morse index on potential energy surfaces is crucial for characterizing transition states for nosie-induced rare transition events in physics and chemistry. Many numerical algorithms for this type of…
This paper considers the distributed online bandit optimization problem with nonconvex loss functions over a time-varying digraph. This problem can be viewed as a repeated game between a group of online players and an adversary. At each…
Bandit algorithms have been predominantly analyzed in the convex setting with function-value based stationary regret as the performance measure. In this paper, motivated by online reinforcement learning problems, we propose and analyze…
In this paper, we investigate regrets of an online semi-proximal alternating direction method of multiplier (Online-spADMM) for solving online linearly constrained convex composite optimization problems. Under mild conditions, we establish…
We investigate online convex optimization in non-stationary environments and choose the dynamic regret as the performance measure, defined as the difference between cumulative loss incurred by the online algorithm and that of any feasible…
We consider online learning problems in the realizable setting, where there is a zero-loss solution, and propose new Differentially Private (DP) algorithms that obtain near-optimal regret bounds. For the problem of online prediction from…
In this paper, we consider the online proximal mirror descent for solving the time-varying composite optimization problems. For various applications, the algorithm naturally involves the errors in the gradient and proximal operator. We…