无悔算法在系统设计中的应用
Exploiting No-Regret Algorithms in System Design
摘要：
我们研究了一个重复的两个玩家零和游戏设置列玩家也是系统的设计者，并完全控制设计的支付矩阵。此外，行玩家使用无遗憾算法来有效地学习如何随着时间的推移使他们的策略适应列玩家的行为，以实现良好的总收益。纵列参与者的目标是引导对手选择一个对系统设计者有利的混合策略。因此，她需要：（i）设计适当的支付矩阵$A$，其唯一的极大极小解包含行玩家的期望混合策略;以及（ii）在一系列游戏期间与行玩家策略性地交互，以便引导她的对手收敛到该期望行为。为了设计这样的支付矩阵，我们提出了一种新的解决方案，可证明有一个独特的极大极小解所需的行为。我们还研究了这个问题的唯一性是不需要的放松，但所有的极大极小解有相同的混合策略的行播放器。最后，我们提出了一个新的博弈算法的系统设计者，并证明它可以引导行的球员，谁可能发挥\emph{stable}无遗憾算法，收敛到一个极大极小解。
英文摘要：
We investigate a repeated two-player zero-sum game setting where the column player is also a designer of the system, and has full control on the design of the payoff matrix. In addition, the row player uses a no-regret algorithm to efficiently learn how to adapt their strategy to the column player's behaviour over time in order to achieve good total payoff. The goal of the column player is to guide her opponent to pick a mixed strategy which is favourable for the system designer. Therefore, she needs to: (i) design an appropriate payoff matrix $A$ whose unique minimax solution contains the desired mixed strategy of the row player; and (ii) strategically interact with the row player during a sequence of plays in order to guide her opponent to converge to that desired behaviour. To design such a payoff matrix, we propose a novel solution that provably has a unique minimax solution with the desired behaviour. We also investigate a relaxation of this problem where uniqueness is not required, but all the minimax solutions have the same mixed strategy for the row player. Finally, we propose a new game playing algorithm for the system designer and prove that it can guide the row player, who may play a \emph{stable} no-regret algorithm, to converge to a minimax solution.
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。
