Statistical-mechanics approach to a reinforcement learning model with memory

TL;DR

This paper models reinforcement learning with memory using statistical mechanics, revealing phase transitions and strategy performance differences in symmetric versus asymmetric games.

Contribution

It introduces a novel two-player reinforcement learning model with memory and analyzes its behavior using approximate methods and simulations.

Findings

Infinite memory leads to an absorbing-state phase transition.

Large memory benefits symmetric game strategies.

Short memory is advantageous in asymmetric games.

Abstract

We introduce a two-player model of reinforcement learning with memory. Past actions of an iterated game are stored in a memory and used to determine player's next action. To examine the behaviour of the model some approximate methods are used and confronted against numerical simulations and exact master equation. When the length of memory of players increases to infinity the model undergoes an absorbing-state phase transition. Performance of examined strategies is checked in the prisoner' dilemma game. It turns out that it is advantageous to have a large memory in symmetric games, but it is better to have a short memory in asymmetric ones.