Distributed learning and optimization of a multi-agent macroscopic probabilistic model

In this paper, we propose MAcroscopic Consensus and micRoscopic gradient-based OPTimization (MACROPT), a novel distributed method for a network of agents able to learn a probabilistic macroscopic model and concurrently optimize it by acting on the microscopic agents’ states. The macroscopic model is defined through the aggregation of local kernels each representing a probabilistic feature of a single agent (e.g., its local sensing model), while the optimization is done with respect to a given cost index, e.g., the Kullback–Leibler divergence with respect to a target distribution. MACROPT improves the macroscopic model by microscopically coordinating the agents according to a distributed gradient-based policy. Concurrently, it allows each agent to locally learn the macroscopic model through a consensus-based mechanism. We analyze the resulting interconnected method through the lens of system theory. We demonstrate that MACROPT asymptotically converges to the set of stationary points of the nonconvex cost function. The theoretical findings are supported by numerical simulations in sensor network event-detection scenarios.