Counter-Intuitive Effects of Q-Learning Exploration in a Congestion Dilemma

Abstract

Exploration is an integral part of learning dynamics which allows algorithms to search a space of solutions. When many algorithms simultaneously explore, this can lead to counter-intuitive effects. This paper contributes an analysis of the influence that exploration has on a multi-agent system of Q-learners in a famous congestion dilemma, the Braess paradox. I find ranges of the exploration rate for which ϵgreedy Q-learners show chaotic and oscillatory dynamics which do not converge, and yield better than Nash equilibrium results. I decouple the dynamics endogenous to Q-learning from the exogenous exploration rate ϵ, and find that Q-learners implicitly coordinate with low exploration rates ϵ ∈ (0, 0.1), but are disrupted in their coordination for larger exploration rates ϵ > 0.1. The best implicit coordination leads to a 20% reduction in average travel times which approaches the social optimum. I discuss how our results may inform multi-agent algorithm design, fit within a cognitive science perspective of cognitive noise during learning, and provide a mechanistic hypothesis for the lack of empirical evidence of the Braess Paradox in traffic systems.