Logarithmic-Regret Quantum Learning Algorithms for Zero-Sum Games

Minbo Gao, Zhengfeng Ji, Tongyang Li, Qisheng Wang

Keywords: Online learning, quantum computing, zero-sum games, optimistic multiplicative weight update

TL;DR: We propose the first online quantum algorithm for zero-sum games with logarithmic regret under the game setting.

Abstract: We propose the first online quantum algorithm for zero-sum games with $\widetilde O(1)$ regret under the game setting. Moreover, our quantum algorithm computes an $\varepsilon$-approximate Nash equilibrium of an $m \times n$ matrix zero-sum game in quantum time $\widetilde O(\sqrt{m+n}/\varepsilon^{2.5})$. Our algorithm uses standard quantum inputs and generates classical outputs with succinct descriptions, facilitating end-to-end applications. Technically, our online quantum algorithm "quantizes" classical algorithms based on the optimistic multiplicative weight update method. At the heart of our algorithm is a fast quantum multi-sampling procedure for the Gibbs sampling problem, which may be of independent interest.

Submission Number: 3101