论文标题
Minimax对部分监测感到遗憾：无限结果和Rustichini的遗憾
Minimax Regret for Partial Monitoring: Infinite Outcomes and Rustichini's Regret
论文作者
论文摘要
我们表明，Lattimore和Gyorgy（2020）的广义信息比例的版本决定了所有有限行动部分监测游戏的渐近minimax遗憾，前提是（a）（a）使用后悔的标准定义，但使用了对手游戏潜在无限的潜在空间；或（b）使用Rustichini（1999）引入的遗憾，潜在空间是有限的。我们的结果得到了许多例子的补充。对于[1/2,1] $中的任何$ p \，存在一个无限的部分监测游戏，在该游戏中，Minimax遗憾的是$ n $ grounds $ n^p $ to subsolynomial因素，并且存在有限的游戏，Minimax Rustichini遗憾的是$ n^{4/7} $ to to polynomial suppolynomial ripynomial因素。
We show that a version of the generalised information ratio of Lattimore and Gyorgy (2020) determines the asymptotic minimax regret for all finite-action partial monitoring games provided that (a) the standard definition of regret is used but the latent space where the adversary plays is potentially infinite; or (b) the regret introduced by Rustichini (1999) is used and the latent space is finite. Our results are complemented by a number of examples. For any $p \in [1/2,1]$ there exists an infinite partial monitoring game for which the minimax regret over $n$ rounds is $n^p$ up to subpolynomial factors and there exist finite games for which the minimax Rustichini regret is $n^{4/7}$ up to subpolynomial factors.
