基于Reddit的公平鲁棒分配
Fair Robust Assignment using Redundancy
摘要：
研究了多智能体任务分配中冗余分配的公平性问题。它最近已被证明，冗余分配的代理任务提供了鲁棒性的任务性能的不确定性。然而，如何在任务之间公平地分配这些冗余资源的问题仍然没有得到解决。在本文中，我们提出了一个新的问题制定公平的冗余任务分配，我们投下的基数约束下的最坏情况下的任务成本的优化。解决这个问题的最优解是NP-难的。我们利用超模块性的性质，提出了一个多项式时间，接近最优的解决方案。在超模冗余分配中，使用额外的代理总是改善任务成本。因此，我们提供了一个比基数约束大$α$倍的解集。这种约束放松使我们的方法，以实现超最优的成本，通过使用次优的分配大小。我们推导出次最优约束的基数松弛，$α$。此外，我们证明了我们的算法在没有基数松弛的情况下接近最优。我们模拟的冗余分配的机器人的目标节点上的运输网络不确定的旅行时间。从经验上讲，我们的算法优于基准，规模大的问题，并提供公平性和平均效用的改善。
英文摘要：
We study the consideration of fairness in redundant assignment for multi-agent task allocation. It has recently been shown that redundant assignment of agents to tasks provides robustness to uncertainty in task performance. However, the question of how to fairly assign these redundant resources across tasks remains unaddressed. In this paper, we present a novel problem formulation for fair redundant task allocation, which we cast as the optimization of worst-case task costs under a cardinality constraint. Solving this problem optimally is NP-hard. We exploit properties of supermodularity to propose a polynomial-time, near-optimal solution. In supermodular redundant assignment, the use of additional agents always improves task costs. Therefore, we provide a solution set that is $α$ times larger than the cardinality constraint. This constraint relaxation enables our approach to achieve a super-optimal cost by using a sub-optimal assignment size. We derive the sub-optimality bound on this cardinality relaxation, $α$. Additionally, we demonstrate that our algorithm performs near-optimally without the cardinality relaxation. We show simulations of redundant assignments of robots to goal nodes on transport networks with uncertain travel times. Empirically, our algorithm outperforms benchmarks, scales to large problems, and provides improvements in both fairness and average utility.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
