Related papers: Exponential Lower Bounds on the Double Oracle Algo…
This paper presents a new exponential lower bound for the two most popular deterministic variants of the strategy improvement algorithms for solving parity, mean payoff, discounted payoff and simple stochastic games. The first variant…
We study the randomized query complexity of approximate Nash equilibria (ANE) in large games. We prove that, for some constant $\epsilon>0$, any randomized oracle algorithm that computes an $\epsilon$-ANE in a binary-action, $n$-player game…
Partially Observable Markov Games (POMGs) provide a general framework for modeling multi-agent sequential decision-making under asymmetric information. A common approach is to reformulate a POMG as a fully observable Markov game over belief…
Computing approximate Nash equilibria in multi-player general-sum Markov games is a computationally intractable task. However, multi-player Markov games with certain cooperative or competitive structures might circumvent this…
To verify the robustness of a program or protocol, it is common in the computer science community to rely on the theoretical framework of game theory. In particular, if one seeks to enforce a desired property, or specification, despite an…
Parity games are simple infinite games played on finite graphs with a winning condition that is expressive enough to capture nested least and greatest fixpoints. Through their tight relationship to the modal mu-calculus, they are used in…
We prove lower bounds for higher-order methods in smooth non-convex finite-sum optimization. Our contribution is threefold: We first show that a deterministic algorithm cannot profit from the finite-sum structure of the objective, and that…
Coordinate descent methods are popular in machine learning and optimization for their simple sparse updates and excellent practical performance. In the context of large-scale sequential game solving, these same properties would be…
For any two-by-two game $\G$, we define a new two-player game $\G^Q$. The definition is motivated by a vision of players in game $\G$ communicating via quantum technology according to a certain standard protocol originally introduced by…
In this work we study binary two-stage robust optimization problems with objective uncertainty. We present an algorithm to calculate efficiently lower bounds for the binary two-stage robust problem by solving alternately the underlying…
Nash equilibrium is one of the most influential solution concepts in game theory. With the development of computer science and artificial intelligence, there is an increasing demand on Nash equilibrium computation, especially for Internet…
In this work, we establish near-linear and strong convergence for a natural first-order iterative algorithm that simulates Von Neumann's Alternating Projections method in zero-sum games. First, we provide a precise analysis of Optimistic…
Many real-world decision problems involve the interaction of multiple self-interested agents with limited sensing ability. The partially observable stochastic game (POSG) provides a mathematical framework for modeling these problems,…
Extensive-Form Game (EFG) represents a fundamental model for analyzing sequential interactions among multiple agents and the primary challenge to solve it lies in mitigating sample complexity. Existing research indicated that Double Oracle…
Despite the many recent practical and theoretical breakthroughs in computational game theory, equilibrium finding in extensive-form team games remains a significant challenge. While NP-hard in the worst case, there are provably efficient…
Bilevel optimization problems, which are problems where two optimization problems are nested, have more and more applications in machine learning. In many practical cases, the upper and the lower objectives correspond to empirical risk…
It is well-known that for infinitely repeated games, there are computable strategies that have best responses, but no computable best responses. These results were originally proved for either specific games (e.g., Prisoner's dilemma), or…
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…
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…
The Hybrid Online Learning Problem, where features are drawn i.i.d. from an unknown distribution but labels are generated adversarially, is a well-motivated setting positioned between statistical and fully-adversarial online learning. Prior…