TY - GEN

T1 - Exploiting Locality and Structure for Distributed Optimization in Multi-Agent Systems

AU - Brown, Robin

AU - Rossi, Federico

AU - Solovey, Kiril

AU - Wolf, Michael T.

AU - Pavone, Marco

N1 - Publisher Copyright: © 2020 EUCA.

PY - 2020/5

Y1 - 2020/5

N2 - A number of prototypical optimization problems in multi-agent systems (e.g. task allocation and network load-sharing) exhibit a highly local structure: that is, each agent's decision variables are only directly coupled to few other agent's variables through the objective function or the constraints. Nevertheless, existing algorithms for distributed optimization generally do not exploit the locality structure of the problem, requiring all agents to compute or exchange the full set of decision variables. In this paper, we develop a rigorous notion of "locality" that relates the structural properties of a linearly- constrained convex optimization problem (in particular, the sparsity structure of the constraint matrix and the objective function) to the amount of information that agents should exchange to compute an arbitrarily high-quality approximation to the problem from a cold-start. We leverage the notion of locality to develop a locality-aware distributed optimization algorithm, and we show that, for problems where individual agents only require to know a small portion of the optimal solution, the algorithm requires very limited inter-agent communication. Numerical results show that the convergence rate of our algorithm is directly explained by the locality metric proposed, and that the proposed theoretical bounds are remarkably tight; comparison to the projected sub-gradient algorithm shows that our locality-aware algorithm requires orders of magnitude fewer communication rounds to achieve similar solution quality.

AB - A number of prototypical optimization problems in multi-agent systems (e.g. task allocation and network load-sharing) exhibit a highly local structure: that is, each agent's decision variables are only directly coupled to few other agent's variables through the objective function or the constraints. Nevertheless, existing algorithms for distributed optimization generally do not exploit the locality structure of the problem, requiring all agents to compute or exchange the full set of decision variables. In this paper, we develop a rigorous notion of "locality" that relates the structural properties of a linearly- constrained convex optimization problem (in particular, the sparsity structure of the constraint matrix and the objective function) to the amount of information that agents should exchange to compute an arbitrarily high-quality approximation to the problem from a cold-start. We leverage the notion of locality to develop a locality-aware distributed optimization algorithm, and we show that, for problems where individual agents only require to know a small portion of the optimal solution, the algorithm requires very limited inter-agent communication. Numerical results show that the convergence rate of our algorithm is directly explained by the locality metric proposed, and that the proposed theoretical bounds are remarkably tight; comparison to the projected sub-gradient algorithm shows that our locality-aware algorithm requires orders of magnitude fewer communication rounds to achieve similar solution quality.

UR - http://www.scopus.com/inward/record.url?scp=85090136539&partnerID=8YFLogxK

M3 - منشور من مؤتمر

T3 - European Control Conference 2020, ECC 2020

SP - 440

EP - 447

BT - European Control Conference 2020, ECC 2020

T2 - 18th European Control Conference, ECC 2020

Y2 - 12 May 2020 through 15 May 2020

ER -