相关论文: Last iterate convergence in no-regret learning: co…

A considerable chasm has been looming for decades between theory and practice in zero-sum game solving through first-order methods. Although a convergence rate of $T^{-1}$ has long been established, the most effective paradigm in practice…

We study online convex optimization where the possible actions are trace-one elements in a symmetric cone, generalizing the extensively-studied experts setup and its quantum counterpart. Symmetric cones provide a unifying framework for some…

In this paper, online convex optimization is applied to the problem of controlling linear dynamical systems. An algorithm similar to online gradient descent, which can handle time-varying and unknown cost functions, is proposed. Then,…

In this paper, we consider gradient methods for minimizing smooth convex functions, which employ the information obtained at the previous iterations in order to accelerate the convergence towards the optimal solution. This information is…

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…

A recent line of work has established uncoupled learning dynamics such that, when employed by all players in a game, each player's \emph{regret} after $T$ repetitions grows polylogarithmically in $T$, an exponential improvement over the…

We study the monotone inclusion problem $0\in F(z)+A(z)$, where $F$ is monotone and Lipschitz, and $A$ is maximally monotone, a framework that encompasses monotone variational inequalities and convex-concave saddle-point problems with…

We propose a new family of subgradient- and gradient-based methods which converges with optimal complexity for convex optimization problems whose feasible region is simple enough. This includes cases where the objective function is…

Recent applications that arise in machine learning have surged significant interest in solving min-max saddle point games. This problem has been extensively studied in the convex-concave regime for which a global equilibrium solution can be…

Min-max saddle point games appear in a wide range of applications in machine leaning and signal processing. Despite their wide applicability, theoretical studies are mostly limited to the special convex-concave structure. While some recent…

The need for fast and robust optimization algorithms are of critical importance in all areas of machine learning. This paper treats the task of designing optimization algorithms as an optimal control problem. Using regret as a metric for an…

We present a new family of min-max optimization algorithms that automatically exploit the geometry of the gradient data observed at earlier iterations to perform more informative extra-gradient steps in later ones. Thanks to this adaptation…

We study an online caching problem in which requests can be served by a local cache to avoid retrieval costs from a remote server. The cache can update its state after a batch of requests and store an arbitrarily small fraction of each…

This paper proposes a novel first-order algorithm that solves composite nonsmooth and stochastic convex optimization problem with function constraints. Most of the works in the literature provide convergence rate guarantees on the…

We study the framework of universal dynamic regret minimization with strongly convex losses. We answer an open problem in Baby and Wang 2021 by showing that in a proper learning setup, Strongly Adaptive algorithms can achieve the near…

We study the convergence of the last iterate (i.e., the $(N+1)$-th iterate) of the AdaGrad method. Although AdaGrad -- an adaptive subgradient method -- underpins a wide class of algorithms, most existing convergence analyses focus on…

A wide range of applications arising in machine learning and signal processing can be cast as convex optimization problems. These problems are often ill-posed, i.e., the optimal solution lacks a desired property such as uniqueness or…

Constrained Online Convex Optimization (COCO) can be seen as a generalization of the standard Online Convex Optimization (OCO) framework. At each round, a cost function and constraint function are revealed after a learner chooses an action.…

This paper studies bandit convex optimization with constraints, where the learner aims to generate a sequence of decisions under partial information of loss functions such that the cumulative loss is reduced as well as the cumulative…

In online convex optimization, the player aims to minimize regret, or the difference between her loss and that of the best fixed decision in hindsight over the entire repeated game. Algorithms that minimize (standard) regret may converge to…