Logarithmic-Regret Quantum Learning Algorithms for Zero-Sum Games

Minbo Gao; Zhengfeng Ji; Tongyang Li; Qisheng Wang

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arXiv · 2304.14197

Logarithmic-Regret Quantum Learning Algorithms for Zero-Sum Games

Minbo Gao·Zhengfeng Ji·Tongyang Li·Qisheng Wang

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Abstract

We propose the first online quantum algorithm for solving 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.

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BibTeX RIS

Minbo Gao, Zhengfeng Ji, Tongyang Li, Qisheng Wang. 2023-04-27. Logarithmic-Regret Quantum Learning Algorithms for Zero-Sum Games. https://arxiv.org/abs/2304.14197

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