提出两种高效算法,求解随机博弈中的相关均衡问题。
Efficiently Solving Turn-Taking Stochastic Games with Extensive-Form Correlation
- 设计首个多项式时间的承诺型相关均衡算法
- 近似最优相关均衡误差可达机器精度,计算时间仅对数依赖误差
- 适用于更紧凑的图形式随机博弈,无需额外假设
我们研究双人轮转随机博弈中的序列形式相关均衡计算问题。主要成果有两方面:(1) 提出一种计算堆叠式序列形式相关均衡(SEFCE)的算法,其运行时间在游戏规模及输入数值编码位数上均为多项式;(2) 提出一种高效近似计算最优序列形式相关均衡(EFCE)的算法,逼近误差为ε时,时间复杂度在游戏规模和log(1/ε)上为多项式。该SEFCE算法是此类广义随机博弈中首个实现承诺机制下的多项式时间均衡计算方法;以往算法通常需排除机会节点,且仅适用于树形表达的博弈。而本算法在近似最优性、误差对数依赖性以及与紧凑图形式博弈兼容性三方面首次同时满足,现有方法最多满足其中两项,且常依赖额外技术假设。
原文摘要 · Abstract (English)
We study equilibrium computation with extensive-form correlation in two-player turn-taking stochastic games. Our main results are two-fold: (1) We give an algorithm for computing a Stackelberg extensive-form correlated equilibrium (SEFCE), which runs in time polynomial in the size of the game, as well as the number of bits required to encode each input number. (2) We give an efficient algorithm for approximately computing an optimal extensive-form correlated equilibrium (EFCE) up to machine precision, i.e., the algorithm achieves approximation error $\varepsilon$ in time polynomial in the size of the game, as well as $\log(1 / \varepsilon)$. Our algorithm for SEFCE is the first polynomial-time algorithm for equilibrium computation with commitment in such a general class of stochastic games. Existing algorithms for SEFCE typically make stronger assumptions such as no chance moves, and are designed for extensive-form games in the less succinct tree form. Our algorithm for approximately optimal EFCE is, to our knowledge, the first algorithm that achieves 3 desiderata simultaneously: approximate optimality, polylogarithmic dependency on the approximation error, and compatibility with stochastic games in the more succinct graph form. Existing algorithms achieve at most 2 of these desiderata, often also relying on additional technical assumptions.
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