Distributed Bayesian: a continuous Distributed Constraint Optimization Problem solver

TL;DR

This paper introduces D-Bay, a novel distributed algorithm that uses Bayesian optimization to solve continuous DCOPs efficiently, avoiding discretization and achieving better solutions with fewer samples.

Contribution

The paper presents D-Bay, the first distributed Bayesian optimization approach for continuous DCOPs, which converges to the global optimum without discretizing the utility functions.

Findings

D-Bay outperforms centralized discretization methods in solution quality.

D-Bay requires fewer samples to achieve optimal solutions.

Theoretical proof of convergence for Lipschitz continuous utility functions.

Abstract

In this work, the novel Distributed Bayesian (D-Bay) algorithm is presented for solving multi-agent problems within the continuous Distributed Constraint Optimization Problem (DCOP) framework. This framework extends the classical DCOP framework towards utility functions with continuous domains. Traditional DCOP solvers discretize the continuous domains, which increases the problem size exponentially. D-Bay overcomes this problem by utilizing Bayesian optimization for the adaptive sampling of variables to avoid discretization entirely. We theoretically show that D-Bay converges to the global optimum of the DCOP for Lipschitz continuous utility functions. The performance of the algorithm is evaluated empirically based on the sample efficiency. The proposed algorithm is compared to a centralized approach with equidistant discretization of the continuous domains for the sensor coordination problem. We find that our algorithm generates better solutions while requiring less samples.