Utility Design for Distributed Resource Allocation -- Part I: Characterizing and Optimizing the Exact Price of Anarchy

Game theory has emerged as a fruitful paradigm for the design of networked multiagent systems. A fundamental component of this approach is the design of agents' utility functions so that their self-interested maximization results in a desirable collective behavior. In this work we focus on a well-studied class of distributed resource allocation problems where each agent is requested to select a subset of resources with the goal of optimizing a given system-level objective. Our core contribution is the development of a novel framework to tightly characterize the worst case performance of any resulting Nash equilibrium (price of anarchy) as a function of the chosen agents' utility functions. Leveraging this result, we identify how to design such utilities so as to optimize the price of anarchy through a tractable linear program. This provides us with a priori performance certificates applicable to any existing learning algorithm capable of driving the system to an equilibrium. Part II of this work specializes these results to submodular and supermodular objectives, discusses the complexity of computing Nash equilibria, and provides multiple illustrations of the theoretical findings.Comment: 15 pages, 5 figure

A tutorial on optimization for multi-agent systems

Research on optimization in multi-agent systems (MASs) has contributed with a wealth of techniques to solve many of the challenges arising in a wide range of multi-agent application domains. Multi-agent optimization focuses on casting MAS problems into optimization problems. The solving of those problems could possibly involve the active participation of the agents in a MAS. Research on multi-agent optimization has rapidly become a very technical, specialized field. Moreover, the contributions to the field in the literature are largely scattered. These two factors dramatically hinder access to a basic, general view of the foundations of the field. This tutorial is intended to ease such access by providing a gentle introduction to fundamental concepts and techniques on multi-agent optimization. © 2013 The Author.Peer Reviewe

A Tutorial on Distributed Optimization for Cooperative Robotics: from Setups and Algorithms to Toolboxes and Research Directions

Several interesting problems in multi-robot systems can be cast in the framework of distributed optimization. Examples include multi-robot task allocation, vehicle routing, target protection and surveillance. While the theoretical analysis of distributed optimization algorithms has received significant attention, its application to cooperative robotics has not been investigated in detail. In this paper, we show how notable scenarios in cooperative robotics can be addressed by suitable distributed optimization setups. Specifically, after a brief introduction on the widely investigated consensus optimization (most suited for data analytics) and on the partition-based setup (matching the graph structure in the optimization), we focus on two distributed settings modeling several scenarios in cooperative robotics, i.e., the so-called constraint-coupled and aggregative optimization frameworks. For each one, we consider use-case applications, and we discuss tailored distributed algorithms with their convergence properties. Then, we revise state-of-the-art toolboxes allowing for the implementation of distributed schemes on real networks of robots without central coordinators. For each use case, we discuss their implementation in these toolboxes and provide simulations and real experiments on networks of heterogeneous robots

Solving DCOPs with Distributed Large Neighborhood Search

The field of Distributed Constraint Optimization has gained momentum in recent years, thanks to its ability to address various applications related to multi-agent cooperation. Nevertheless, solving Distributed Constraint Optimization Problems (DCOPs) optimally is NP-hard. Therefore, in large-scale, complex applications, incomplete DCOP algorithms are necessary. Current incomplete DCOP algorithms suffer of one or more of the following limitations: they (a) find local minima without providing quality guarantees; (b) provide loose quality assessment; or (c) are unable to benefit from the structure of the problem, such as domain-dependent knowledge and hard constraints. Therefore, capitalizing on strategies from the centralized constraint solving community, we propose a Distributed Large Neighborhood Search (D-LNS) framework to solve DCOPs. The proposed framework (with its novel repair phase) provides guarantees on solution quality, refining upper and lower bounds during the iterative process, and can exploit domain-dependent structures. Our experimental results show that D-LNS outperforms other incomplete DCOP algorithms on both structured and unstructured problem instances

Communication-efficient Distributed Multi-resource Allocation

In several smart city applications, multiple resources must be allocated among competing agents that are coupled through such shared resources and are constrained --- either through limitations of communication infrastructure or privacy considerations. We propose a distributed algorithm to solve such distributed multi-resource allocation problems with no direct inter-agent communication. We do so by extending a recently introduced additive-increase multiplicative-decrease (AIMD) algorithm, which only uses very little communication between the system and agents. Namely, a control unit broadcasts a one-bit signal to agents whenever one of the allocated resources exceeds capacity. Agents then respond to this signal in a probabilistic manner. In the proposed algorithm, each agent makes decision of its resource demand locally and an agent is unaware of the resource allocation of other agents. In empirical results, we observe that the average allocations converge over time to optimal allocations.Comment: To appear in IEEE International Smart Cities Conference (ISC2 2018), Kansas City, USA, September, 2018. arXiv admin note: substantial text overlap with arXiv:1711.0197