先验独立算法的下界
Lower Bounds for Prior Independent Algorithms
摘要：
用于算法设计的先验独立框架考虑不知道其输入的分布的算法在多大程度上近似于针对该分布的最优算法的预期性能。本文给出了一种与问题设置无关的方法来证明任何算法的先验独立逼近因子的下界。该方法在输入上构造相关分布，该相关分布可以作为i.i.d.良好的算法分布，并作为分布在i.i.d.对算法不利的发行版即使真实分布是前者，先验独立算法的上限也由后者分布的最优算法确定。因此，这两个分解的贝叶斯最优算法的预期性能的比率是先验独立近似比率的下界。本文所采用的技术是将先验独立算法设计、姚极小极大原理和信息设计有机地结合起来的。我们应用这个框架，给出了新的下界的几个典型的先验独立的机制设计问题。
英文摘要：
The prior independent framework for algorithm design considers how well an algorithm that does not know the distribution of its inputs approximates the expected performance of the optimal algorithm for this distribution. This paper gives a method that is agnostic to problem setting for proving lower bounds on the prior independent approximation factor of any algorithm. The method constructs a correlated distribution over inputs that can be generated both as a distribution over i.i.d. good-for-algorithms distributions and as a distribution over i.i.d. bad-for-algorithms distributions. Prior independent algorithms are upper-bounded by the optimal algorithm for the latter distribution even when the true distribution is the former. Thus, the ratio of the expected performances of the Bayesian optimal algorithms for these two decompositions is a lower bound on the prior independent approximation ratio. The techniques of the paper connect prior independent algorithm design, Yao's Minimax Principle, and information design. We apply this framework to give new lower bounds on several canonical prior independent mechanism design problems.
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