Related papers: No-Regret Dynamics in the Fenchel Game: A Unified …

We consider regret minimization in repeated games with non-convex loss functions. Minimizing the standard notion of regret is computationally intractable. Thus, we define a natural notion of regret which permits efficient optimization and…

This paper presents a new framework for analyzing and designing no-regret algorithms for dynamic (possibly adversarial) systems. The proposed framework generalizes the popular online convex optimization framework and extends it to its…

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 consider the problem of minimizing a smooth convex function by reducing the optimization to computing the Nash equilibrium of a particular zero-sum convex-concave game. Zero-sum games can be solved using online learning dynamics, where a…

Regret minimization is a powerful tool for solving large-scale extensive-form games. State-of-the-art methods rely on minimizing regret locally at each decision point. In this work we derive a new framework for regret minimization on…

We study the regret of optimal strategies for online convex optimization games. Using von Neumann's minimax theorem, we show that the optimal regret in this adversarial setting is closely related to the behavior of the empirical…

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…

In game-theoretic learning, several agents are simultaneously following their individual interests, so the environment is non-stationary from each player's perspective. In this context, the performance of a learning algorithm is often…

We consider the use of no-regret algorithms to compute equilibria for particular classes of convex-concave games. While standard regret bounds would lead to convergence rates on the order of $O(T^{-1/2})$, recent work \citep{RS13,SALS15}…

The behavior of no-regret learning algorithms is well understood in two-player min-max (i.e, zero-sum) games. In this paper, we investigate the behavior of no-regret learning in min-max games with dependent strategy sets, where the strategy…

In the first part of this dissertation research, we develop a modular framework that can serve as a recipe for constructing and analyzing iterative algorithms for convex optimization. Specifically, our work casts optimization as iteratively…

No-regret learning has emerged as a powerful tool for solving extensive-form games. This was facilitated by the counterfactual-regret minimization (CFR) framework, which relies on the instantiation of regret minimizers for simplexes at each…

Most of the literature on learning in games has focused on the restrictive setting where the underlying repeated game does not change over time. Much less is known about the convergence of no-regret learning algorithms in dynamic multiagent…

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…

We examine the problem of regret minimization when the learner is involved in a continuous game with other optimizing agents: in this case, if all players follow a no-regret algorithm, it is possible to achieve significantly lower regret…

The literature on game-theoretic equilibrium finding predominantly focuses on single games or their repeated play. Nevertheless, numerous real-world scenarios feature playing a game sampled from a distribution of similar, but not identical…

Regret minimization is a general approach to online optimization which plays a crucial role in many algorithms for approximating Nash equilibria in two-player zero-sum games. The literature mainly focuses on solving individual games in…

We consider online learning in multi-player smooth monotone games. Existing algorithms have limitations such as (1) being only applicable to strongly monotone games; (2) lacking the no-regret guarantee; (3) having only asymptotic or slow…

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…

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…