Recent Advancements in Inverse Reinforcement Learning
Authors: Metelli Alberto Maria 
Published: March 2024

Inverse reinforcement learning (IRL) has seen significant advancements in recent years. This class of approaches aims to efficiently learn the underlying reward function that rationalizes the behavior exhibited by expert agents, often represented by humans. In contrast to mere behavioral cloning, the reconstruction of a reward function yields appealing implications, as it allows for more effective interpretability of the expert’s decisions and provides a transferable specification of the expert’s objectives for application in even different environments. Unlike the well-understood field of reinforcement learning (RL) from a theoretical perspective, IRL still grapples with limited understanding, significantly constraining its applicability. A fundamental challenge in IRL is the inherent ambiguity in selecting a reward function, given the existence of multiple candidate functions, all explaining the expert’s behavior.

In this talk, I will survey three of my papers that have made notable contributions to the IRL field: “Provably Efficient Learning of Transferable Rewards”, “Towards Theoretical Understanding of Inverse Reinforcement Learning”, and “Inverse Reinforcement Learning with Sub-optimal Experts".

The central innovation introduced by the first paper is a novel formulation of the IRL problem that overcomes the issue of ambiguity. IRL is reframed as the problem of learning the feasible reward set, which is the set of all rewards that can explain the expert’s behavior. This approach postpones the selection of the reward function, thereby circumventing the ambiguity issues. Furthermore, the feasible reward set exhibits convenient geometric properties that enable the development of efficient algorithms for its computation.

Building on this novel formulation of IRL, the second paper addresses the problem of efficiently learning the feasible reward set when the environment and the expert’s policy are not known in advance. It introduces a novel way to assess the dissimilarity between feasible reward sets based on the Hausdorff distance and presents a new PAC (probabilistic approximately correct) framework. The most significant contribution of this paper is the introduction of the first sample complexity lower bound, which highlights the challenges inherent in the IRL problem. Deriving this lower bound necessitated the development of novel technical tools. The paper also demonstrates that when a generative model of the environment is available, a uniform sampling strategy achieves a sample complexity that matches the lower bound, up to logarithmic factors.

Finally, in the third paper, the IRL problem in the presence of sub-optimal experts is investigated. Specifically, the paper assumes the availability of multiple sub-optimal experts, in addition to the expert agent, which provides additional demonstrations, associated with a known quantification of the maximum amount of sub-optimality. The paper shows that this richer information mitigates the ambiguity problem, significantly reducing the size of the feasible reward set while retaining its favorable geometric properties. Furthermore, the paper explores the associated statistical problem and derives novel lower bounds for sample complexity, along with almost matching algorithms. These selected papers represent notable advancements in IRL, contributing to the establishment of a solid theoretical foundation for IRL and extending the framework to accommodate scenarios with sub-optimal experts.