Opponent Learning Awareness and Modelling in Multi-Objective Normal Form Games

TL;DR

This paper investigates how opponent learning awareness and modelling influence multi-objective multi-agent interactions with non-linear utilities, demonstrating significant impacts on learning dynamics and solution convergence.

Contribution

It introduces novel actor-critic and policy gradient methods for reinforcement learning in multi-objective games with opponent modelling and learning awareness.

Findings

Opponent modelling can significantly change learning dynamics.

Learning with opponent awareness benefits agents in equilibrium and non-equilibrium scenarios.

Agents can approximate equilibria even without Nash equilibria present.

Abstract

Many real-world multi-agent interactions consider multiple distinct criteria, i.e. the payoffs are multi-objective in nature. However, the same multi-objective payoff vector may lead to different utilities for each participant. Therefore, it is essential for an agent to learn about the behaviour of other agents in the system. In this work, we present the first study of the effects of such opponent modelling on multi-objective multi-agent interactions with non-linear utilities. Specifically, we consider two-player multi-objective normal form games with non-linear utility functions under the scalarised expected returns optimisation criterion. We contribute novel actor-critic and policy gradient formulations to allow reinforcement learning of mixed strategies in this setting, along with extensions that incorporate opponent policy reconstruction and learning with opponent learning awareness (i.e., learning while considering the impact of one's policy when anticipating the opponent's learning step). Empirical results in five different MONFGs demonstrate that opponent learning awareness and modelling can drastically alter the learning dynamics in this setting. When equilibria are present, opponent modelling can confer significant benefits on agents that implement it. When there are no Nash equilibria, opponent learning awareness and modelling allows agents to still converge to meaningful solutions that approximate equilibria.