Robust Utility Design in Distributed Resource Allocation Problems with Defective Agents

The use of multi-agent systems to solve largescale problems can be an effective method to reduce physical and computational burdens; however, these systems should be robust to sub-system failures. In this work, we consider the problem of designing utility functions, which agents seek to maximize, as a method of distributed optimization in resource allocation problems. Though recent work has shown that optimal utility design can bring system operation into a reasonable approximation of optimal, our results extend the existing literature by investigating how robust the system’s operation is to defective agents and by quantifying the achievable performance guarantees in this setting. Interestingly, we find that there is a trade-off between improving the robustness of the utility design and offering good nominal performance. We characterize this trade-off in the set of resource covering problems and find that there are considerable gains in robustness that can be made by sacrificing some nominal performance.