ProxiCBO: A Provably Convergent Consensus-Based Method for Composite Optimization

Abstract: This paper introduces an interacting-particle optimization method tailored to possibly non-convex composite optimization problems, which arise widely in signal processing. The proposed method, \emph{ProxiCBO}, integrates consensus-based optimization (CBO) with proximal gradient techniques to handle challenging optimization landscapes and exploit the composite structure of the objective function. We establish global convergence guarantees for the continuous-time finite-particle dynamics and develop an alternating update scheme for efficient practical implementation. Simulation results for signal processing tasks, including signal recovery from one-bit quantized measurements and parameter estimation from single-photon lidar data, demonstrate that ProxiCBO outperforms existing proximal gradient methods and CBO methods in terms of both accuracy and particle-efficiency.