Inverse Reinforcement Learning via Convex Optimization

TL;DR

This paper presents a convex optimization approach to inverse reinforcement learning, enabling more robust and reproducible estimation of reward functions from expert demonstrations, including scenarios with non-analytical policies.

Contribution

It reformulates the IRL problem as a convex optimization task, extends it to trajectory-based policies, and provides practical tools for hyperparameter auto-selection and user-friendly implementation.

Findings

Convex formulation simplifies IRL problem solving.

Extended the approach to trajectory-based policies.

Provided practical implementation and hyperparameter auto-selection methods.

Abstract

We consider the inverse reinforcement learning (IRL) problem, where an unknown reward function of some Markov decision process is estimated based on observed expert demonstrations. In most existing approaches, IRL is formulated and solved as a nonconvex optimization problem, posing challenges in scenarios where robustness and reproducibility are critical. We discuss a convex formulation of the IRL problem (CIRL) initially proposed by Ng and Russel, and reformulate the problem such that the domain-specific language CVXPY can be applied directly to specify and solve the convex problem. We also extend the CIRL problem to scenarios where the expert policy is not given analytically but by trajectory as state-action pairs, which can be strongly inconsistent with optimality, by augmenting some of the constraints. Theoretical analysis and practical implementation for hyperparameter auto-selection are introduced. This note helps the users to easily apply CIRL for their problems, without background knowledge on convex optimization.