Related papers: Efficient Phi-Regret Minimization in Extensive-For…

To efficiently solve online problems with complicated constraints, projection-free algorithms including online frank-wolfe (OFW) and its variants have received significant interest recently. However, in the general case, existing efficient…

We study the minimization of a convex function $f(X)$ over the set of $n\times n$ positive semi-definite matrices, but when the problem is recast as $\min_U g(U) := f(UU^\top)$, with $U \in \mathbb{R}^{n \times r}$ and $r \leq n$. We study…

Computational tractability and social welfare (aka. efficiency) of equilibria are two fundamental but in general orthogonal considerations in algorithmic game theory. Nevertheless, we show that when (approximate) full efficiency can be…

We study infinite-horizon discounted two-player zero-sum Markov games, and develop a decentralized algorithm that provably converges to the set of Nash equilibria under self-play. Our algorithm is based on running an Optimistic Gradient…

We study online learning in two-player uninformed Markov games, where the opponent's actions and policies are unobserved. In this setting, Tian et al. (2021) show that achieving no-external-regret is impossible without incurring an…

Attention mechanisms have revolutionized several domains of artificial intelligence, such as natural language processing and computer vision, by enabling models to selectively focus on relevant parts of the input data. While recent work has…

In this paper, we propose an initial value fomulation of the discrete mean field games on finite graphs (Graph MFG), and design a neural network based approach to solve it. Graph MFG describes infinite, non-cooperative and interactive…

We study online learning problems in which the learner has extra knowledge about the adversary's behaviour, i.e., in game-theoretic settings where opponents typically follow some no-external regret learning algorithms. Under this…

This paper investigates the problem of computing the equilibrium of competitive games, which is often modeled as a constrained saddle-point optimization problem with probability simplex constraints. Despite recent efforts in understanding…

Imperfect Information Games (IIGs) offer robust models for scenarios where decision-makers face uncertainty or lack complete information. Counterfactual Regret Minimization (CFR) has been one of the most successful family of algorithms for…

We introduce DREAM, a deep reinforcement learning algorithm that finds optimal strategies in imperfect-information games with multiple agents. Formally, DREAM converges to a Nash Equilibrium in two-player zero-sum games and to an…

An ideal strategy in zero-sum games should not only grant the player an average reward no less than the value of Nash equilibrium, but also exploit the (adaptive) opponents when they are suboptimal. While most existing works in Markov games…

We study the problem of repeated play in a zero-sum game in which the payoff matrix may change, in a possibly adversarial fashion, on each round; we call these Online Matrix Games. Finding the Nash Equilibrium (NE) of a two player zero-sum…

Decoding how rational agents should behave in shared systems remains a critical challenge within theoretical computer science, artificial intelligence and economics studies. Central to this challenge is the task of computing the solution…

First-order optimization methods tend to inherently favor certain solutions over others when minimizing an underdetermined training objective that has multiple global optima. This phenomenon, known as implicit bias, plays a critical role in…

We prove the familiar Lazy Online Gradient Descent algorithm is universal on polytope domains. That means it gets $O(1)$ pseudo-regret against i.i.d opponents, while simultaneously achieving the well-known $O(\sqrt N)$ worst-case regret…

Policy gradient methods have become a staple of any single-agent reinforcement learning toolbox, due to their combination of desirable properties: iterate convergence, efficient use of stochastic trajectory feedback, and theoretically-sound…

This paper presents a comprehensive analysis of the well-known extragradient (EG) method for solving both equations and inclusions. First, we unify and generalize EG for [non]linear equations to a wider class of algorithms, encompassing…

Mean Field Games (MFGs) have been introduced to efficiently approximate games with very large populations of strategic agents. Recently, the question of learning equilibria in MFGs has gained momentum, particularly using model-free…

We consider a family of learning strategies for online optimization problems that evolve in continuous time and we show that they lead to no regret. From a more traditional, discrete-time viewpoint, this continuous-time approach allows us…