Timezone: »
In many game settings, the game is not explicitly given but is only accessible by playing it. While there have been impressive demonstrations in such settings, prior techniques have not offered safety guarantees, that is, guarantees on the game-theoretic exploitability of the computed strategies. In this paper we introduce an approach that shows that it is possible to provide exploitability guarantees in such settings without ever exploring the entire game. We introduce a notion of a certificatae of an extensive-form approximate Nash equilibrium. For verifying a certificate, we give an algorithm that runs in time linear in the size of the certificate rather than the size of the whole game. In zero-sum games, we further show that an optimal certificate---given the exploration so far---can be computed with any standard game-solving algorithm (e.g., using a linear program or counterfactual regret minimization). However, unlike in the cases of normal form or perfect information, we show that certain families of extensive-form games do not have small approximate certificates, even after making extremely nice assumptions on the structure of the game. Despite this difficulty, we find experimentally that very small certificates, even exact ones, often exist in large and even in infinite games. Overall, our approach enables one to try one's favorite exploration strategies while offering exploitability guarantees, thereby decoupling the exploration strategy from the equilibrium-finding process.
Author Information
Brian Zhang (Carnegie Mellon University)
Tuomas Sandholm (CMU, Strategic Machine, Strategy Robot, Optimized Markets)
More from the Same Authors
-
2021 Spotlight: Subgame solving without common knowledge »
Brian Zhang · Tuomas Sandholm -
2021 Spotlight: Sample Complexity of Tree Search Configuration: Cutting Planes and Beyond »
Maria-Florina Balcan · Siddharth Prasad · Tuomas Sandholm · Ellen Vitercik -
2022 : ESCHER: ESCHEWING IMPORTANCE SAMPLING IN GAMES BY COMPUTING A HISTORY VALUE FUNCTION TO ESTIMATE REGRET »
Stephen McAleer · Gabriele Farina · Marc Lanctot · Tuomas Sandholm -
2022 Poster: Structural Analysis of Branch-and-Cut and the Learnability of Gomory Mixed Integer Cuts »
Maria-Florina Balcan · Siddharth Prasad · Tuomas Sandholm · Ellen Vitercik -
2022 Poster: Uncoupled Learning Dynamics with $O(\log T)$ Swap Regret in Multiplayer Games »
Ioannis Anagnostides · Gabriele Farina · Christian Kroer · Chung-Wei Lee · Haipeng Luo · Tuomas Sandholm -
2022 Poster: Maximizing Revenue under Market Shrinkage and Market Uncertainty »
Maria-Florina Balcan · Siddharth Prasad · Tuomas Sandholm -
2022 Poster: Polynomial-Time Optimal Equilibria with a Mediator in Extensive-Form Games »
Brian Zhang · Tuomas Sandholm -
2022 Poster: Optimistic Mirror Descent Either Converges to Nash or to Strong Coarse Correlated Equilibria in Bimatrix Games »
Ioannis Anagnostides · Gabriele Farina · Ioannis Panageas · Tuomas Sandholm -
2022 Poster: Subgame Solving in Adversarial Team Games »
Brian Zhang · Luca Carminati · Federico Cacciamani · Gabriele Farina · Pierriccardo Olivieri · Nicola Gatti · Tuomas Sandholm -
2022 Poster: Near-Optimal No-Regret Learning Dynamics for General Convex Games »
Gabriele Farina · Ioannis Anagnostides · Haipeng Luo · Chung-Wei Lee · Christian Kroer · Tuomas Sandholm -
2021 Poster: Subgame solving without common knowledge »
Brian Zhang · Tuomas Sandholm -
2021 Poster: Equilibrium Refinement for the Age of Machines: The One-Sided Quasi-Perfect Equilibrium »
Gabriele Farina · Tuomas Sandholm -
2021 Poster: Sample Complexity of Tree Search Configuration: Cutting Planes and Beyond »
Maria-Florina Balcan · Siddharth Prasad · Tuomas Sandholm · Ellen Vitercik -
2020 Poster: Polynomial-Time Computation of Optimal Correlated Equilibria in Two-Player Extensive-Form Games with Public Chance Moves and Beyond »
Gabriele Farina · Tuomas Sandholm -
2020 Poster: Improving Policy-Constrained Kidney Exchange via Pre-Screening »
Duncan McElfresh · Michael Curry · Tuomas Sandholm · John Dickerson -
2019 Poster: Correlation in Extensive-Form Games: Saddle-Point Formulation and Benchmarks »
Gabriele Farina · Chun Kai Ling · Fei Fang · Tuomas Sandholm -
2019 Poster: Efficient Regret Minimization Algorithm for Extensive-Form Correlated Equilibrium »
Gabriele Farina · Chun Kai Ling · Fei Fang · Tuomas Sandholm -
2019 Spotlight: Efficient Regret Minimization Algorithm for Extensive-Form Correlated Equilibrium »
Gabriele Farina · Chun Kai Ling · Fei Fang · Tuomas Sandholm -
2019 Poster: Optimistic Regret Minimization for Extensive-Form Games via Dilated Distance-Generating Functions »
Gabriele Farina · Christian Kroer · Tuomas Sandholm -
2018 Poster: A Unified Framework for Extensive-Form Game Abstraction with Bounds »
Christian Kroer · Tuomas Sandholm -
2018 Poster: Depth-Limited Solving for Imperfect-Information Games »
Noam Brown · Tuomas Sandholm · Brandon Amos -
2018 Poster: Solving Large Sequential Games with the Excessive Gap Technique »
Christian Kroer · Gabriele Farina · Tuomas Sandholm -
2018 Poster: Practical exact algorithm for trembling-hand equilibrium refinements in games »
Gabriele Farina · Nicola Gatti · Tuomas Sandholm -
2018 Spotlight: Solving Large Sequential Games with the Excessive Gap Technique »
Christian Kroer · Gabriele Farina · Tuomas Sandholm -
2018 Poster: Ex ante coordination and collusion in zero-sum multi-player extensive-form games »
Gabriele Farina · Andrea Celli · Nicola Gatti · Tuomas Sandholm -
2018 Poster: A Spectral View of Adversarially Robust Features »
Shivam Garg · Vatsal Sharan · Brian Zhang · Gregory Valiant -
2018 Spotlight: A Spectral View of Adversarially Robust Features »
Shivam Garg · Vatsal Sharan · Brian Zhang · Gregory Valiant -
2017 Demonstration: Libratus: Beating Top Humans in No-Limit Poker »
Noam Brown · Tuomas Sandholm -
2017 Poster: Safe and Nested Subgame Solving for Imperfect-Information Games »
Noam Brown · Tuomas Sandholm -
2017 Oral: Safe and Nested Subgame Solving for Imperfect-Information Games »
Noam Brown · Tuomas Sandholm -
2016 Poster: Sample Complexity of Automated Mechanism Design »
Maria-Florina Balcan · Tuomas Sandholm · Ellen Vitercik -
2015 Poster: Regret-Based Pruning in Extensive-Form Games »
Noam Brown · Tuomas Sandholm -
2015 Demonstration: Claudico: The World's Strongest No-Limit Texas Hold'em Poker AI »
Noam Brown · Tuomas Sandholm -
2014 Poster: Diverse Randomized Agents Vote to Win »
Albert Jiang · Leandro Soriano Marcolino · Ariel Procaccia · Tuomas Sandholm · Nisarg Shah · Milind Tambe