A Unified Framework for Multi-Agent Agreement

Multi-Agent Agreement problems (MAP) - the ability of a population of agents to search out and converge on a common state - are central issues in many multi-agent settings, from distributed sensor networks, to meeting scheduling, to development of norms, conventions, and language. While much work has been done on particular agreement problems, no unifying framework exists for comparing MAPs that vary in, e.g., strategy space complexity, inter-agent accessibility, and solution type, and understanding their relative complexities. We present such a unification, the Distributed Optimal Agreement Framework, and show how it captures a wide variety of agreement problems. To demonstrate DOA and its power, we apply it to two well-known MAPs: convention evolution and language convergence. We demonstrate the insights DOA provides toward improving known approaches to these problems. Using a careful comparative analysis of a range of MAPs and solution approaches via the DOA framework, we identify a single critical differentiating factor: how accurately an agent can discern other agent.s states. To demonstrate how variance in this factor influences solution tractability and complexity we show its effect on the convergence time and quality of Particle Swarm Optimization approach to a generalized MAP

Consensus based optimization with memory effects: random selection and applications

In this work we extend the class of Consensus-Based Optimization (CBO) metaheuristic methods by considering memory effects and a random selection strategy. The proposed algorithm iteratively updates a population of particles according to a consensus dynamics inspired by social interactions among individuals. The consensus point is computed taking into account the past positions of all particles. While sharing features with the popular Particle Swarm Optimization (PSO) method, the exploratory behavior is fundamentally different and allows better control over the convergence of the particle system. We discuss some implementation aspects which lead to an increased efficiency while preserving the success rate in the optimization process. In particular, we show how employing a random selection strategy to discard particles during the computation improves the overall performance. Several benchmark problems and applications to image segmentation and Neural Networks training are used to validate and test the proposed method. A theoretical analysis allows to recover convergence guarantees under mild assumptions on the objective function. This is done by first approximating the particles evolution with a continuous-in-time dynamics, and then by taking the mean-field limit of such dynamics. Convergence to a global minimizer is finally proved at the mean-field level