Related papers: Acceleration through Optimistic No-Regret Dynamics

In this paper, we consider an online optimization process, where the objective functions are not convex (nor concave) but instead belong to a broad class of continuous submodular functions. We first propose a variant of the Frank-Wolfe…

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…

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…

This paper investigates the equilibrium convergence properties of a proposed algorithm for potential games with continuous strategy spaces in the presence of feedback delays, a main challenge in multi-agent systems that compromises the…

This work is dedicated to the algorithm design in a competitive framework, with the primary goal of learning a stable equilibrium. We consider the dynamic price competition between two firms operating within an opaque marketplace, where…

We study algorithms for online linear optimization in Hilbert spaces, focusing on the case where the player is unconstrained. We develop a novel characterization of a large class of minimax algorithms, recovering, and even improving,…

This paper investigates accelerating the convergence of distributed optimization algorithms on non-convex problems. We propose a distributed primal-dual stochastic gradient descent~(SGD) equipped with "powerball" method to accelerate. We…

We propose the first loss function for approximate Nash equilibria of normal-form games that is amenable to unbiased Monte Carlo estimation. This construction allows us to deploy standard non-convex stochastic optimization techniques for…

Optimization of convex functions under stochastic zeroth-order feedback has been a major and challenging question in online learning. In this work, we consider the problem of optimizing second-order smooth and strongly convex functions…

In this paper, we study last-iterate convergence of learning algorithms in bilinear saddle-point problems, a preferable notion of convergence that captures the day-to-day behavior of learning dynamics. We focus on the challenging setting…

In this paper, we study adaptive online convex optimization, and aim to design a universal algorithm that achieves optimal regret bounds for multiple common types of loss functions. Existing universal methods are limited in the sense that…

Many important machine learning applications involve regularized nonconvex bi-level optimization. However, the existing gradient-based bi-level optimization algorithms cannot handle nonconvex or nonsmooth regularizers, and they suffer from…

In this paper, we derive a Fast Reflected Forward-Backward (Fast RFB) algorithm to solve the problem of finding a zero of the sum of a maximally monotone operator and a monotone and Lipschitz continuous operator in a real Hilbert space. Our…

In online learning an algorithm plays against an environment with losses possibly picked by an adversary at each round. The generality of this framework includes problems that are not adversarial, for example offline optimization, or saddle…

Traditional algorithms for stochastic optimization require projecting the solution at each iteration into a given domain to ensure its feasibility. When facing complex domains, such as positive semi-definite cones, the projection operation…

We study fast rates of convergence in the setting of nonparametric online regression, namely where regret is defined with respect to an arbitrary function class which has bounded complexity. Our contributions are two-fold: - In the…

Adversarial training, a special case of multi-objective optimization, is an increasingly prevalent machine learning technique: some of its most notable applications include GAN-based generative modeling and self-play techniques in…

We introduce an online convex optimization algorithm which utilizes projected subgradient descent with optimal adaptive learning rates. Our method provides second-order minimax-optimal dynamic regret guarantee (i.e. dependent on the sum of…

Momentum first-order optimization methods are the workhorses in various optimization tasks, e.g., in the training of deep neural networks. Recently, Lucas et al. (2019) proposed a method called Aggregated Heavy-Ball (AggHB) that uses…

Learning and equilibrium computation in games are fundamental problems across computer science and economics, with applications ranging from politics to machine learning. Much of the work in this area revolves around a simple algorithm…