51. Fair Robust Assignment Using Redundancy
- Author
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Malencia, M, Kumar, V, Pappas, G, and Prorok, A
- Subjects
FOS: Computer and information sciences ,0209 industrial biotechnology ,Mathematical optimization ,Control and Optimization ,multi-robot systems ,Linear programming ,Computer science ,Ethics and philosophy ,Biomedical Engineering ,fairness ,02 engineering and technology ,Task (project management) ,submodular optimization ,Computer Science - Robotics ,020901 industrial engineering & automation ,Cardinality ,Redundancy (information theory) ,Artificial Intelligence ,Robustness (computer science) ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science - Multiagent Systems ,Mechanical Engineering ,020206 networking & telecommunications ,Computer Science Applications ,Human-Computer Interaction ,Constraint (information theory) ,Control and Systems Engineering ,Task analysis ,task planning ,Computer Vision and Pattern Recognition ,Relaxation (approximation) ,Robotics (cs.RO) ,Multiagent Systems (cs.MA) - Abstract
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 $\alpha$ 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, $\alpha$. 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., Comment: (c) 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works
- Published
- 2021