[论文解读] Mechanism Design for Crowdsourcing: An Optimal 1-1/e Competitive Budget-Feasible Mechanism for Large Markets

Nima Anari, Gagan Goel+1 more|arXiv (Cornell University)|May 10, 2014

Mobile Crowdsensing and Crowdsourcing参考文献 2被引用 7

一句话总结

本文提出了一种新颖的、诚实的、预算可行的机制，适用于大规模众包市场，其竞争力比率为 $1 - 1/e \approx 0.63$，这是最优的。该机制推广了比例分配，并采用参数化的分配规则，辅以精心设计的支付机制，确保诚实性和预算可行性，在个体工人成本相对于请求者预算较小的大市场中，显著优于以往的界限。

ABSTRACT

In this paper we consider a mechanism design problem in the context of large-scale crowdsourcing markets such as Amazon's Mechanical Turk, ClickWorker, CrowdFlower. In these markets, there is a requester who wants to hire workers to accomplish some tasks. Each worker is assumed to give some utility to the requester. Moreover each worker has a minimum cost that he wants to get paid for getting hired. This minimum cost is assumed to be private information of the workers. The question then is - if the requester has a limited budget, how to design a direct revelation mechanism that picks the right set of workers to hire in order to maximize the requester's utility. We note that although the previous work has studied this problem, a crucial difference in which we deviate from earlier work is the notion of large-scale markets that we introduce in our model. Without the large market assumption, it is known that no mechanism can achieve an approximation factor better than 0.414 and 0.5 for deterministic and randomized mechanisms respectively (while the best known deterministic and randomized mechanisms achieve an approximation ratio of 0.292 and 0.33 respectively). In this paper, we design a budget-feasible mechanism for large markets that achieves an approximation factor of 1-1/e (i.e. almost 0.63). Our mechanism can be seen as a generalization of an alternate way to look at the proportional share mechanism which is used in all the previous works so far on this problem. Interestingly, we also show that our mechanism is optimal by showing that no truthful mechanism can achieve a factor better than 1-1/e; thus, fully resolving this setting. Finally we consider the more general case of submodular utility functions and give new and improved mechanisms for the case when the markets are large.

研究动机与目标

• 设计一种适用于大规模众包市场、个体工人成本相对于请求者预算较小的诚实、预算可行机制。
• 弥合已知上界与大市场中可实现近似比率之间的差距，其中先前的机制表现次优。
• 证明 $1 - 1/e$ 是任何诚实、预算可行机制所能达到的最佳近似比率。
• 将框架扩展至子模效用函数，为大市场提供改进的机制。

提出的方法

• 提出一类基于广义比例分配规则的、无嫉妒的、诚实的参数化机制。
• 设计一种支付规则，通过将激励与报告的成本对齐，确保机制的诚实性。
• 使用贪心序列构造和基于阈值的分配方法，在预算约束下近似最优解。
• 应用舍入过程，将分数分配转换为整数分配，同时保持近似保证。
• 引入预算缩减技术，将几乎预算可行的机制转换为严格预算可行的机制，近似损失最小化。
• 采用霍夫丁不等式分析大规模市场中效用和成本的集中性。

实验结果

研究问题

• RQ1 在大规模众包市场中，诚实、预算可行的机制能否实现优于 $1/2$ 的近似比率？
• RQ2 在大规模市场中，$1 - 1/e$ 近似比率对诚实、预算可行机制而言是否紧致？
• RQ3 该框架能否在保持强近似保证的前提下，扩展至子模效用函数？
• RQ4 如何将几乎预算可行的机制转换为严格预算可行的机制，而性能损失可忽略？

主要发现

• 所提出的机制实现了 $1 - 1/e \approx 0.63$ 的竞争力比率，这是最优的，且任何诚实机制都无法进一步提升。
• 通过证明任何诚实、预算可行机制都无法实现优于 $1 - 1/e$ 的比率，该机制被证明是最优的。
• 对于子模效用函数，本文提出了一种多项式时间机制，其近似比率优于以往工作。
• 该机制可被转换为严格预算可行的机制，在大规模市场中近似比率可任意接近 $1/2$。
• 大规模市场假设——即个体成本相对于预算较小——使得本研究显著优于小市场设定下的先前不可能性结果。