Logarithmic-Regret Quantum Learning Algorithms for Zero-Sum Games

04/27/2023

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by   Minbo Gao, et al.

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We propose the first online quantum algorithm for zero-sum games with Õ(1) regret under the game setting. Moreover, our quantum algorithm computes an ε-approximate Nash equilibrium of an m × n matrix zero-sum game in quantum time Õ(√(m+n)/ε^2.5), yielding a quadratic improvement over classical algorithms in terms of m, n. Our algorithm uses standard quantum inputs and generates classical outputs with succinct descriptions, facilitating end-to-end applications. As an application, we obtain a fast quantum linear programming solver. 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.