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This paper considers convex games involving multiple agents that aim to minimize their own cost functions using locally available information. A common assumption in the study of such games is that the agents are symmetric, meaning that…
We study the alternating gradient descent-ascent (AltGDA) algorithm in two-player zero-sum games. Alternating methods, where players take turns to update their strategies, have long been recognized as simple and practical approaches for…
This work tackles the complexities of multi-player scenarios in \emph{unknown games}, where the primary challenge lies in navigating the uncertainty of the environment through bandit feedback alongside strategic decision-making. We…
In online inverse linear optimization, a learner observes time-varying sets of feasible actions and an agent's optimal actions, selected by solving linear optimization over the feasible actions. The learner sequentially makes predictions of…
This study considers online learning with general directed feedback graphs. For this problem, we present best-of-both-worlds algorithms that achieve nearly tight regret bounds for adversarial environments as well as poly-logarithmic regret…
Existing studies on provably efficient algorithms for Markov games (MGs) almost exclusively build on the "optimism in the face of uncertainty" (OFU) principle. This work focuses on a different approach of posterior sampling, which is…
We show that learning algorithms satisfying a $\textit{low approximate regret}$ property experience fast convergence to approximate optimality in a large class of repeated games. Our property, which simply requires that each learner has…
This paper studies policy optimization algorithms for multi-agent reinforcement learning. We begin by proposing an algorithm framework for two-player zero-sum Markov Games in the full-information setting, where each iteration consists of a…
In this paper, we study online convex optimization in dynamic environments, and aim to bound the dynamic regret with respect to any sequence of comparators. Existing work have shown that online gradient descent enjoys an…
We study the problem of characterizing optimal learning algorithms for playing repeated games against an adversary with unknown payoffs. In this problem, the first player (called the learner) commits to a learning algorithm against a second…
We consider learning Nash equilibria in two-player zero-sum Markov Games with nonlinear function approximation, where the action-value function is approximated by a function in a Reproducing Kernel Hilbert Space (RKHS). The key challenge is…
Online linear programming plays an important role in both revenue management and resource allocation, and recent research has focused on developing efficient first-order online learning algorithms. Despite the empirical success of…
We prove that optimistic-follow-the-regularized-leader (OFTRL), together with smooth value updates, finds an $O(T^{-1})$-approximate Nash equilibrium in $T$ iterations for two-player zero-sum Markov games with full information. This…
Scale-invariance in games has recently emerged as a widely valued desirable property. Yet, almost all fast convergence guarantees in learning in games require prior knowledge of the utility scale. To address this, we develop learning…
We consider online convex optimization with a zero-order oracle feedback. In particular, the decision maker does not know the explicit representation of the time-varying cost functions, or their gradients. At each time step, she observes…
Stochastic and adversarial data are two widely studied settings in online learning. But many optimization tasks are neither i.i.d. nor fully adversarial, which makes it of fundamental interest to get a better theoretical understanding of…
We show that natural classes of regularized learning algorithms with a form of recency bias achieve faster convergence rates to approximate efficiency and to coarse correlated equilibria in multiplayer normal form games. When each player in…
This paper investigates online composite optimization in dynamic environments, where each objective or loss function contains a time-varying nondifferentiable regularizer. To resolve it, an online proximal gradient algorithm is studied for…
Online bilevel optimization (OBO) is a powerful framework for machine learning problems where both outer and inner objectives evolve over time, requiring dynamic updates. Current OBO approaches rely on deterministic \textit{window-smoothed}…
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,…