Quantum Speedups for Zero-Sum Games via Improved Dynamic Gibbs Sampling

• URL: http://arxiv.org/abs/2301.03763v1
• Date: Tue, 10 Jan 2023 02:56:49 GMT
• Title: Quantum Speedups for Zero-Sum Games via Improved Dynamic Gibbs Sampling
• Authors: Adam Bouland, Yosheb Getachew, Yujia Jin, Aaron Sidford, Kevin Tian
• Abstract summary: We give a quantum algorithm for computing an $epsilon$-approximate Nash equilibrium of a zero-sum game in a $m times n$ payoff matrix with bounded entries. Given a standard quantum oracle for accessing the payoff matrix our algorithm runs in time $widetildeO(sqrtm + ncdot epsilon-2.5 + epsilon-3)$ and outputs a classical representation of the $epsilon$-approximate Nash equilibrium.
• Score: 30.53587208999909
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We give a quantum algorithm for computing an $\epsilon$-approximate Nash equilibrium of a zero-sum game in a $m \times n$ payoff matrix with bounded entries. Given a standard quantum oracle for accessing the payoff matrix our algorithm runs in time $\widetilde{O}(\sqrt{m + n}\cdot \epsilon^{-2.5} + \epsilon^{-3})$ and outputs a classical representation of the $\epsilon$-approximate Nash equilibrium. This improves upon the best prior quantum runtime of $\widetilde{O}(\sqrt{m + n} \cdot \epsilon^{-3})$ obtained by [vAG19] and the classic $\widetilde{O}((m + n) \cdot \epsilon^{-2})$ runtime due to [GK95] whenever $\epsilon = \Omega((m +n)^{-1})$. We obtain this result by designing new quantum data structures for efficiently sampling from a slowly-changing Gibbs distribution.

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