计算近似最优效用函数的易处理机制
Tractable mechanisms for computing near-optimal utility functions
摘要：
大规模的多智能体系统必须依赖于分布式决策，因为集中协调要么是不切实际的，要么是不可能的。最近的作品接近这个问题下的博弈论的镜头，其中效用函数被分配给每个代理，希望他们的局部优化近似集中的最优解。然而，在不影响其准确性的情况下，无法获得广泛类别的问题的正式保证所得到的性能。在这项工作中，我们解决这一问题相对于非递减凹福利函数的资源分配的研究问题。我们表明，最佳设计的本地公用事业实现的近似比（无政府代价价格）1-c/e，其中c是函数的曲率和e是欧拉常数。我们的贡献的结果是分布式和高效的近似算法的设计，其性能匹配的最佳现有的多项式时间（和集中式）计划。
英文摘要：
Large scale multiagent systems must rely on distributed decision making, as centralized coordination is either impractical or impossible. Recent works approach this problem under a game theoretic lens, whereby utility functions are assigned to each of the agents with the hope that their local optimization approximates the centralized optimal solution. Yet, formal guarantees on the resulting performance cannot be obtained for broad classes of problems without compromising on their accuracy. In this work, we address this concern relative to the well-studied problem of resource allocation with nondecreasing concave welfare functions. We show that optimally designed local utilities achieve an approximation ratio (price of anarchy) of 1-c/e, where c is the function's curvature and e is Euler's constant. The upshot of our contributions is the design of approximation algorithms that are distributed and efficient, and whose performance matches that of the best existing polynomial-time (and centralized) schemes.
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