Fair Robust Assignment Using Redundancy

We study the consideration of fairness in redundant assignment for multi-agent task allocation. It has recently been shown that agents to tasks provides robustness uncertainty performance. However, question how fairly assign these resources across remains unaddressed. In this letter, we present a novel problem formulation fair allocation, which cast as optimization worst-case costs under cardinality constraint. Solving optimally is NP-hard. exploit properties supermodularity propose polynomial-time, near-optimal solution. supermodular assignment, use additional always improves costs. Therefore, provide solution set $\alpha$ times larger than This constraint relaxation enables our approach achieve super-optimal cost by using sub-optimal size. derive sub-optimality bound on relaxation, . Additionally, demonstrate algorithm performs near-optimally without relaxation. show simulations assignments robots goal nodes transport networks with uncertain travel times. Empirically, outperforms benchmarks, scales large problems, and improvements both average utility.