0/1-多面体博弈的核化乘法权重：弥合外延形式和范式博弈学习之间的差距
Kernelized Multiplicative Weights for 0/1-Polyhedral Games: Bridging the Gap Between Learning in Extensive-Form and Normal-Form Games
摘要：
虽然扩展形式博弈（EFG）可以转换为范式博弈（NFG），但这样做的代价是策略空间的指数级膨胀。因此，NFG和EFG的进展历史上一直遵循不同的轨道，EFG社区经常不得不赶上进步（例如，最后的收敛和预测遗憾界）从更大的NFG社区。在本文中，我们表明，乐观的乘法权重更新（OMWU）算法-总理学习算法NFG-可以模拟的范式相当于EFG在线性时间每次迭代的游戏树大小使用内核技巧。由此产生的算法，核OMWU（KOMWU），适用于更广泛的所有凸游戏的策略空间是一个多面体与0/1整顶点，只要内核可以有效地评估。在EFG的特定情况下，KOMWU关闭NFG和EFG学习之间的几个常设差距，使直接的，黑盒转移到EFG的学习动态的理想属性，迄今为止已知的只有在NFG中才能实现。具体来说，KOMWU给出了第一个算法，保证在同一时间的最后一个收敛，较低的依赖于游戏树的大小比所有以前的算法，和$\tilde{\mathcal{O}}(1)$遗憾时，遵循的所有球员。
英文摘要：
While extensive-form games (EFGs) can be converted into normal-form games (NFGs), doing so comes at the cost of an exponential blowup of the strategy space. So, progress on NFGs and EFGs has historically followed separate tracks, with the EFG community often having to catch up with advances (e.g., last-iterate convergence and predictive regret bounds) from the larger NFG community. In this paper we show that the Optimistic Multiplicative Weights Update (OMWU) algorithm -- the premier learning algorithm for NFGs -- can be simulated on the normal-form equivalent of an EFG in linear time per iteration in the game tree size using a kernel trick. The resulting algorithm, Kernelized OMWU (KOMWU), applies more broadly to all convex games whose strategy space is a polytope with 0/1 integral vertices, as long as the kernel can be evaluated efficiently. In the particular case of EFGs, KOMWU closes several standing gaps between NFG and EFG learning, by enabling direct, black-box transfer to EFGs of desirable properties of learning dynamics that were so far known to be achievable only in NFGs. Specifically, KOMWU gives the first algorithm that guarantees at the same time last-iterate convergence, lower dependence on the size of the game tree than all prior algorithms, and $\tilde{\mathcal{O}}(1)$ regret when followed by all players.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
