基准设计与先验无关优化
Benchmark Design and Prior-independent Optimization
摘要：
本文比较了在线算法模型和机制设计模型中两种主要的鲁棒优化方法。竞争分析比较在线算法与离线基准在最坏情况下的性能，而先验独立机制设计比较机制在未知分布（输入，即，代理值）到最坏情况下分布的最优机制。对于竞争分析，一个关键问题是基准的选择。本文给出了一种选择好的基准的方法。我们表明，最佳基准的最佳算法/机制等于先验独立的最佳算法/机制。我们解决了一个中心的开放问题，在先验独立的机制设计，即我们确定的先验独立的收入最优的机制，销售一个单一的项目，以两个代理i.i.d.有规律的分布值。通过这种解决方案和上述的先验独立的机制设计和竞争分析（a.k.a.无先验机制设计），我们表明，无先验机制的下限的标准方法对于基准设计程序通常不是严格的。
英文摘要：
This paper compares two leading approaches for robust optimization in the models of online algorithms and mechanism design. Competitive analysis compares the performance of an online algorithm to an offline benchmark in worst-case over inputs, and prior-independent mechanism design compares the expected performance of a mechanism on an unknown distribution (of inputs, i.e., agent values) to the optimal mechanism for the distribution in worst case over distributions. For competitive analysis, a critical concern is the choice of benchmark. This paper gives a method for selecting a good benchmark. We show that optimal algorithm/mechanism for the optimal benchmark are equal to the prior-independent optimal algorithm/mechanism. We solve a central open question in prior-independent mechanism design, namely we identify the prior-independent revenue-optimal mechanism for selling a single item to two agents with i.i.d. and regularly distributed values. Via this solution and the above equivalence of prior-independent mechanism design and competitive analysis (a.k.a. prior-free mechanism design) we show that the standard method for lower bounds of prior-free mechanisms is not generally tight for the benchmark design program.
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