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.

翻译：先前独立的算法设计框架考虑的是,不知道其投入分布的算法如何接近其投入分配的最佳算法的预期性能。 本文给出了一种方法,对证明任何算法先前独立近似系数的下限的设定有疑问。 该方法构建了对投入的关联性分布,这些投入既分布于i.d.d. 良好求algorithms分布,又分布于i.d.d. 坏求algorithms分布。 以前的独立算法在后一种分布的最佳算法中处于上方,即使真正分布为前者。 因此,巴伊西亚最佳算法对这两种分离的预期性能比率对先前独立近近似比率的制约较小。 纸张的技术将先前独立的算法设计、 Yao 的 Minimax 原理和信息设计联系起来。 我们应用这个框架来给前几个独立机制设计问题设定新的较低约束。