59 accepted papers
Most familiar equilibrium concepts, such as Nash and correlated equilibrium, guarantee only that no single player can improve their utility by deviating unilaterally. They offer no guarantees against profitable coordinated deviations by coalitions. Although the literature proposes notions to address…
We study equilibrium finding in polymatrix games under differential privacy constraints. Prior work in this area fails to achieve both high-accuracy equilibria and a low privacy budget. To better understand the fundamental limitations of differential privacy in games, we show hardness results establ…
Random Utility Models (RUMs) are a classical framework for modeling user preferences and play a key role in reward modeling for Reinforcement Learning from Human Feedback (RLHF). However, a crucial shortcoming of many of these techniques is the Independence of Irrelevant Alternatives (IIA) assumptio…
Online learning in arbitrary and possibly adversarial environments has been extensively studied in sequential decision-making, with a strong connection to equilibrium computation in game theory. Most existing online learning algorithms are based on \emph{numeric} utility feedback from the environmen…
In the past decade, motivated by the putative failure of naive self-play deep reinforcement learning (DRL) in adversarial imperfect-information games, researchers have developed numerous DRL algorithms based on fictitious play (FP), double oracle (DO), and counterfactual regret minimization (CFR). I…
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 avoidance of importance sampling corrections. In multi-agen…
We examine the problem of efficiently learning coarse correlated equilibria (CCE) in polyhedral games, that is, normal-form games with an exponentially large number of actions per player and an underlying combinatorial structure—such as the classic Colonel Blotto game or congestion games. Achieving…
*Variational inequalities (VIs)* encompass many fundamental problems in diverse areas ranging from engineering to economics and machine learning. However, their considerable expressivity comes at the cost of computational intractability. In this paper, we introduce and analyze a natural relaxation—w…
We study last-iterate convergence properties of algorithms for solving two-player zero-sum games based on Regret Matching$^+$ (RM$^+$). Despite their widespread use for solving real games, virtually nothing is known about their last-iterate convergence. A major obstacle to analyzing RM-type dynamics…
In this paper, we study the classical Hedge algorithm in combinatorial settings. In each round, the learner selects a vector $\mathbf{x}_t$ from a set $\mathcal{X} \subseteq$ {$0,1$}$^d$, observes a full loss vector $\mathbf{y}_t \in \mathbb{R}^d$, and incurs a loss $\langle \mathbf{x}_t, \mathbf{y}…
Multi-agent reinforcement learning (MARL) has long been seen as inseparable from Markov games (Littman 1994). Yet, the most remarkable achievements of practical MARL have arguably been in extensive-form games (EFGs)---spanning games like Poker, Stratego, and Hanabi. At the same time, little is known…
Correlated equilibria —and their generalization $\Phi$-equilibria— are a fundamental object of study in game theory, offering a more tractable alternative to Nash equilibria in multi-player settings. While computational aspects of equilibrium computation are well-understood in some settings, fundame…
Post-training has demonstrated its importance in enhancing the reasoning capabilities of large language models (LLMs). The primary post-training methods can be categorized into supervised fine-tuning (SFT) and reinforcement fine-tuning (RFT). SFT is efficient and well-suited for small language model…
Recent breakthrough results by Dagan, Daskalakis, Fishelson and Golowich [2023] and Peng and Rubinstein [2023] established an efficient algorithm attaining at most $\epsilon$ swap regret over extensive-form strategy spaces of dimension $N$ in $N^{\tilde O(1/\epsilon)}$ rounds. On the other extreme,…
We study online learning and equilibrium computation in games with polyhedral decision sets, a property shared by normal-form games (NFGs) and extensive-form games (EFGs), when the learning agent is restricted to utilizing a best-response oracle. We show how to achieve constant regret in zero-sum ga…
Self play via online learning is one of the premier ways to solve large-scale zero-sum games, both in theory and practice. Particularly popular algorithms include optimistic multiplicative weights update (OMWU) and optimistic gradient-descent-ascent (OGDA). While both algorithms enjoy $O(1/T)$ ergod…
A recent paper by Farina and Pipis (2023) established the existence of uncoupled no-linear-swap regret dynamics with polynomial-time iterations in extensive-form games. The equilibrium points reached by these dynamics, known as linear correlated equilibria, are currently the tightest known relaxatio…
First-order methods (FOMs) are arguably the most scalable algorithms for equilibrium computation in large extensive-form games. To operationalize these methods, a distance-generating function, acting as a regularizer for the strategy space, must be chosen. The ratio between the strong convexity mod…
Policy gradient methods enjoy strong practical performance in numerous tasks in reinforcement learning. Their theoretical understanding in multiagent settings, however, remains limited, especially beyond two-player competitive and potential Markov games. In this paper, we develop a new framework to…
It is a well-known fact that correlated equilibria can be computed in polynomial time in a large class of concisely represented games using the celebrated Ellipsoid Against Hope algorithm \citep{Papadimitriou2008:Computing, Jiang2015:Polynomial}. However, the landscape of efficiently computable equi…
We present a game-theoretic model of pragmatics that we call ReCo (for Regularized Conventions). This model formulates pragmatic communication as a game in which players are rewarded for communicating successfully and penalized for deviating from a shared, “default” semantics. As a result, players a…
When applied to question answering and other text generation tasks, language models (LMs) may be queried generatively (by sampling answers from their output distribution) or discriminatively (by using them to score or rank a set of candidate answers). These procedures sometimes yield very different…
The process of revising (or constructing) a policy at execution time---known as decision-time planning---has been key to achieving superhuman performance in perfect-information games like chess and Go. A recent line of work has extended decision-time planning to imperfect-information games, leading…
We introduce a new approach for computing optimal equilibria via learning in games. It applies to extensive-form settings with any number of players, including mechanism design, information design, and solution concepts such as correlated, communication, and certification equilibria. We observe that…
Recent techniques for approximating Nash equilibria in very large games leverage neural networks to learn approximately optimal policies (strategies). One promis- ing line of research uses neural networks to approximate counterfactual regret minimization (CFR) or its modern variants. DREAM, the only…
No-press Diplomacy is a complex strategy game involving both cooperation and competition that has served as a benchmark for multi-agent AI research. While self-play reinforcement learning has resulted in numerous successes in purely adversarial games like chess, Go, and poker, self-play alone is ins…
In the literature on game-theoretic equilibrium finding, focus has mainly been on solving a single game in isolation. In practice, however, strategic interactions—ranging from routing problems to online advertising auctions—evolve dynamically, thereby leading to many similar games to be solved. To a…
In this paper, we establish efficient and uncoupled learning dynamics so that, when employed by all players in multiplayer perfect-recall imperfect-information extensive-form games, the trigger regret of each player grows as $O(\log T)$ after $T$ repetitions of play. This improves exponentially over…
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 settings. In this paper, we characterize the convergence of…
No-regret learners seek to minimize the difference between the loss they cumulated through the actions they played, and the loss they would have cumulated in hindsight had they consistently modified their behavior according to some strategy transformation function. The size of the set of transformat…
Regret Matching$^+$ (RM$^+$) and its variants are important algorithms for solving large-scale games. However, a theoretical understanding of their success in practice is still a mystery. Moreover, recent advances on fast convergence in games are limited to no-regret algorithms such as online mirror…
A classic result in the theory of extensive-form games asserts that the set of strategies available to any perfect-recall player is strategically equivalent to a low-dimensional convex polytope, called the *sequence-form polytope*. Online convex optimization tools operating on this polytope are the…
Recent algorithms have achieved superhuman performance at a number of two-player zero-sum games such as poker and go. However, many real-world situations are multi-player games. Zero-sum two-team games, such as bridge and football, involve two teams where each member of the team shares the same rewa…
The practical scalability of many optimization algorithms for large extensive-form games is often limited by the games' huge payoff matrices. To ameliorate the issue, Zhang and Sandholm recently proposed a sparsification technique that factorizes the payoff matrix A into a sparser object A = Â + UVᵀ…
While extensive-form games (EFGs) can be converted into normal-form games (NFGs), doing so comes at the cost of an exponential blowup of the strategy space. So, progress on NFGs and EFGs has historically followed separate tracks, with the EFG community often having to catch up with advances (\eg las…
We consider the task of accurately modeling strong human policies in multi-agent decision-making problems, given examples of human behavior. Imitation learning is effective at predicting human actions but may not match the strength of expert humans (e.g., by sometimes committing blunders), while sel…
A recent line of work has established uncoupled learning dynamics such that, when employed by all players in a game, each player's regret after $T$ repetitions grows polylogarithmically in $T$, an exponential improvement over the traditional guarantees within the no-regret framework. However, so far…
Most existing results about last-iterate convergence of learning dynamics are limited to two-player zero-sum games, and only apply under rigid assumptions about what dynamics the players follow. In this paper we provide new results and techniques that apply to broader families of games and learning…
We show that, for any sufficiently small fixed $\epsilon > 0$, when both players in a general-sum two-player (bimatrix) game employ optimistic mirror descent (OMD) with smooth regularization, learning rate $\eta = O(\epsilon^2)$ and $T = \Omega(poly(1/\epsilon))$ repetitions, either the dynamics rea…
In adversarial team games, a team of players sequentially faces a team of adversaries. These games are the simplest setting with multiple players where cooperation and competition coexist, and it is known that the information asymmetry among the team members makes equilibrium approximation computati…
In this paper we establish efficient and \emph{uncoupled} learning dynamics so that, when employed by all players in a general-sum multiplayer game, the \emph{swap regret} of each player after $T$ repetitions of the game is bounded by $O(\log T)$, improving over the prior best bounds of $O(\log^4 (T…
Tree-form sequential decision making (TFSDM) extends classical one-shot decision making by modeling tree-form interactions between an agent and a potentially adversarial environment. It captures the online decision-making problems that each player faces in an extensive-form game, as well as Markov d…
We focus on the problem of finding an optimal strategy for a team of players that faces an opponent in an imperfect-information zero-sum extensive-form game. Team members are not allowed to communicate during play but can coordinate before the game. In this setting, it is known that the best the tea…
The existence of uncoupled no-regret learning dynamics converging to correlated equilibria in normal-form games is a celebrated result in the theory of multi-agent systems. Specifically, it has been known for more than 20 years that when all players seek to minimize their internal regret in a repea…
In two-player zero-sum extensive-form games, Nash equilibrium prescribes optimal strategies against perfectly rational opponents. However, it does not guarantee rational play in parts of the game tree that can only be reached by the players making mistakes. This can be problematic when operationaliz…
Blackwell approachability is a framework for reasoning about repeated games with vector-valued payoffs. We introduce predictive Blackwell approachability, where an estimate of the next payoff vector is given, and the decision maker tries to achieve better performance based on the accuracy of that es…
Regret minimization has proved to be a versatile tool for tree-form sequential decision making and extensive-form games. In large two-player zero-sum imperfect-information games, modern extensions of counterfactual regret minimization (CFR) are currently the practical state of the art for computing…
The existence of simple, uncoupled no-regret dynamics that converge to correlated equilibria in normal-form games is a celebrated result in the theory of multi-agent systems. Specifically, it has been known for more than 20 years that when all players seek to minimize their internal regret in a repe…
Unlike normal-form games, where correlated equilibria have been studied for more than 45 years, extensive-form correlation is still generally not well understood. Part of the reason for this gap is that the sequential nature of extensive-form games allows for a richness of behaviors and incentives t…
Monte-Carlo counterfactual regret minimization (MCCFR) is the state-of-the-art algorithm for solving sequential games that are too large for full tree traversals. It works by using gradient estimates that can be computed via sampling. However, stochastic methods for sequential games have not been in…
While Nash equilibrium in extensive-form games is well understood, very little is known about the properties of extensive-form correlated equilibrium (EFCE), both from a behavioral and from a computational point of view. In this setting, the strategic behavior of players is complemented by an extern…
Self-play methods based on regret minimization have become the state of the art for computing Nash equilibria in large two-players zero-sum extensive-form games. These methods fundamentally rely on the hierarchical structure of the players' sequential strategy spaces to construct a regret minimizer…
We study the performance of optimistic regret-minimization algorithms for both minimizing regret in, and computing Nash equilibria of, zero-sum extensive-form games. In order to apply these algorithms to extensive-form games, a distance-generating function is needed. We study the use of the dilated…
Regret minimization is a powerful tool for solving large-scale problems; it was recently used in breakthrough results for large-scale extensive-form game solving. This was achieved by composing simplex regret minimizers into an overall regret-minimization framework for extensive-form game strategy s…
The CFR framework has been a powerful tool for solving large-scale extensive-form games in practice. However, the theoretical rate at which past CFR-based algorithms converge to the Nash equilibrium is on the order of $O(T^{-1/2})$, where $T$ is the number of iterations. In contrast, first-order met…
Recent milestones in equilibrium computation, such as the success of Libratus, show that it is possible to compute strong solutions to two-player zero-sum games in theory and practice. This is not the case for games with more than two players, which remain one of the main open challenges in computat…
Nash equilibrium strategies have the known weakness that they do not prescribe rational play in situations that are reached with zero probability according to the strategies themselves, for example, if players have made mistakes. Trembling-hand refinements---such as extensive-form perfect equilibria…
There has been tremendous recent progress on equilibrium-finding algorithms for zero-sum imperfect-information extensive-form games, but there has been a puzzling gap between theory and practice. First-order methods have significantly better theoretical convergence rates than any counterfactual-regr…
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 information set of the game. We use an instantiation of the…