Learning to Steer Markovian Agents under Model Uncertainty

TL;DR

This paper develops a model-based reinforcement learning approach to design incentives that steer multi-agent systems towards desired behaviors without prior knowledge of their learning dynamics, focusing on history-dependent strategies under model uncertainty.

Contribution

It introduces a novel non-episodic RL formulation for steering Markovian agents with unknown dynamics, including a new objective and algorithms for history-dependent strategies.

Findings

Theoretical conditions for the existence of steering strategies.

Empirical algorithms effectively learn history-dependent incentives.

Successful empirical evaluation demonstrating approach efficacy.

Abstract

Designing incentives for an adapting population is a ubiquitous problem in a wide array of economic applications and beyond. In this work, we study how to design additional rewards to steer multi-agent systems towards desired policies \emph{without} prior knowledge of the agents' underlying learning dynamics. Motivated by the limitation of existing works, we consider a new and general category of learning dynamics called \emph{Markovian agents}. We introduce a model-based non-episodic Reinforcement Learning (RL) formulation for our steering problem. Importantly, we focus on learning a \emph{history-dependent} steering strategy to handle the inherent model uncertainty about the agents' learning dynamics. We introduce a novel objective function to encode the desiderata of achieving a good steering outcome with reasonable cost. Theoretically, we identify conditions for the existence of steering strategies to guide agents to the desired policies. Complementing our theoretical contributions, we provide empirical algorithms to approximately solve our objective, which effectively tackles the challenge in learning history-dependent strategies. We demonstrate the efficacy of our algorithms through empirical evaluations.