Year: 2025
Type: article
Abstract: Recent developments in domains such as non-local games, quantum interactive proofs, and quantum generative adversarial networks have renewed interest in quantum game theory and, specifically, quantum zero-sum games. Central to classical game theory is the efficient algorithmic computation of Nash equilibria, which represent optimal strategies for both players. In 2008, Jain and Watrous proposed the first classical algorithm for computing equilibria in quantum zero-sum games using the Matrix Multiplicative Weight Updates (MMWU) method to achieve a convergence rate of O(d/ϵ2) iterations to ϵ -Nash equilibria in the 4d -dimensional spectraplex. In this work, we propose a hierarchy of quantum optimization algorithms that generalize MMWU via an extra-gradient mechanism. Notably, within this proposed hierarchy, we introduce the Optimistic Matrix Multiplicative Weights Update (OMMWU) algorithm and establish its average-iterate convergence complexity as O(d/ϵ) iterations to ϵ -Nash equilibria. This quadratic speed-up relative to Jain and Watrous' original algorithm sets a new benchmark for computing ϵ -Nash equilibria in quantum zero-sum games.
Source: Quantum
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $215
Funders: National Science Foundation, European Commission, National Research Foundation, Agency for Science, Technology and Research, National University of Singapore, National Research Foundation Singapore, Agence Nationale de la Recherche, National and Kapodistrian University of Athens, Simons Institute for the Theory of Computing, University of California Berkeley, Division of Mathematical Sciences, NextGenerationEU
Awards: MIAI @ Grenoble Alpes, G1575777884, G1894652637, G2121614283, Foundations of robustness and reliability in artificial intelligence, G2709766998, G2751347139, G2789258129, G292453335, G3010527862, G3063805291, G4441651082, Systemes et Algorithmes Pervasifs au confluent des mondes physique et numérique, G6276162139, Graduate Research Fellowship Program (GRFP), G6960108870, RI: Medium: Collaborative Research: Algorithmic High-Dimensional Statistics: Statistical Optimality, Computational Barriers, and High-Dimensional Corrections, G8751405378, G994248709
OpenAlex ID: W4410117337