Kinetic theory of decentralized learning for smart active matter

TL;DR

This paper develops a theoretical framework for decentralized learning in smart active matter, deriving hydrodynamic equations and validating them with simulations, to understand collective behavior and control.

Contribution

Introduces a formalism for decentralized policy exchange in active matter, deriving hydrodynamic equations and connecting microscopic models to collective dynamics.

Findings

Good agreement between theory and simulations

Derived control parameters and uncertainty relations

Established foundations for statistical physics analysis

Abstract

Smart active matter has the ability to control its motion guided by individual policies to achieve collective goals. We introduce a theoretical framework to study a decentralized learning process in which agents can locally exchange policies to adapt their behavior and maximize a predefined reward function. We use our formalism to derive explicit hydrodynamic equations for the policy dynamics. We apply the theory to two different microscopic models where policies correspond either to fixed parameters similar to evolutionary dynamics, or to state-dependent controllers known from the field of robotics. We find good agreement between theoretical predictions and agent-based simulations. By deriving fundamental control parameters and uncertainty relations, our work lays the foundations for a statistical physics analysis of decentralized learning.