论文标题
在对抗凸的身体追逐问题上
On the Adversarial Convex Body Chasing Problem
论文作者
论文摘要
在这项工作中，我们将追逐问题（CBC）扩展到对抗性环境，在该设置中，代理（玩家）的任务是追逐由另一个代理（对手）在对手处生成的一系列凸面。玩家的目标是最大程度地减少与自己的动作相关的总成本，而对手试图最大化相同的成本。可行的凸体集合是有限的，两种代理都知道，这使我们能够以最大的最佳性能提供性能保证。在某些假设下，我们显示了最佳值函数的连续性，并提出了一种算法，以数值近似于保证公差内的玩家和对手的最佳策略。最后，通过数值示例验证了理论结果。
In this work, we extend the convex bodies chasing problem (CBC) to an adversarial setting, where an agent (the Player) is tasked with chasing a sequence of convex bodies generated adversarially by another agent (the Opponent). The Player aims to minimize the total cost associated with its own movements, while the Opponent tries to maximize the same cost. The set of feasible convex bodies is finite and known to both agents, which allows us to provide performance guarantees with max-min optimality. Under certain assumptions, we show the continuity of the optimal value function, and propose an algorithm to numerically approximate the optimal policies for both the Player and the Opponent within a guaranteed tolerance. Finally, the theoretical results are verified through numerical examples.
