[Paper Review] Maximum-Likelihood Inverse Reinforcement Learning with Finite-Time Guarantees

Siliang Zeng, Chenliang Li+2 more|arXiv (Cornell University)|Oct 4, 2022

Reinforcement Learning in Robotics4 citations

TL;DR

This paper proposes a single-loop maximum-likelihood inverse reinforcement learning algorithm that achieves finite-time convergence to a stationary solution without sacrificing reward estimation accuracy. By combining policy improvement with stochastic gradient steps for likelihood maximization, the method outperforms existing IRL and imitation learning benchmarks in MuJoCo robotics tasks while maintaining theoretical guarantees.

ABSTRACT

Inverse reinforcement learning (IRL) aims to recover the reward function and the associated optimal policy that best fits observed sequences of states and actions implemented by an expert. Many algorithms for IRL have an inherently nested structure: the inner loop finds the optimal policy given parametrized rewards while the outer loop updates the estimates towards optimizing a measure of fit. For high dimensional environments such nested-loop structure entails a significant computational burden. To reduce the computational burden of a nested loop, novel methods such as SQIL [1] and IQ-Learn [2] emphasize policy estimation at the expense of reward estimation accuracy. However, without accurate estimated rewards, it is not possible to do counterfactual analysis such as predicting the optimal policy under different environment dynamics and/or learning new tasks. In this paper we develop a novel single-loop algorithm for IRL that does not compromise reward estimation accuracy. In the proposed algorithm, each policy improvement step is followed by a stochastic gradient step for likelihood maximization. We show that the proposed algorithm provably converges to a stationary solution with a finite-time guarantee. If the reward is parameterized linearly, we show the identified solution corresponds to the solution of the maximum entropy IRL problem. Finally, by using robotics control problems in MuJoCo and their transfer settings, we show that the proposed algorithm achieves superior performance compared with other IRL and imitation learning benchmarks.

Motivation & Objective

• To address the high computational cost of traditional nested-loop IRL algorithms in high-dimensional environments.
• To maintain high reward estimation accuracy while reducing computational burden, enabling counterfactual analysis and policy transfer.
• To develop a single-loop algorithm that provably converges to a stationary solution with finite-time guarantees.
• To ensure the identified solution corresponds to the maximum entropy IRL solution when rewards are linearly parameterized.
• To demonstrate superior performance on robotics control tasks and transfer learning settings compared to existing IRL and imitation learning methods.

Proposed method

• The algorithm replaces the traditional nested loop structure with a single-loop framework that alternates between policy improvement and stochastic gradient steps for likelihood maximization.
• Each policy improvement step is followed by a stochastic gradient update to maximize the likelihood of observed expert demonstrations.
• Finite-time convergence to a stationary solution is proven using Lyapunov analysis and stochastic approximation theory.
• When rewards are linearly parameterized, the method is shown to converge to the solution of the maximum entropy IRL problem.
• The algorithm is applied to MuJoCo environments to evaluate performance on complex control tasks and transfer learning.
• The method avoids the trade-off between policy and reward estimation accuracy seen in SQIL and IQ-Learn by maintaining full reward fidelity.

Experimental results

Research questions

• RQ1 Can a single-loop IRL algorithm achieve finite-time convergence while maintaining high reward estimation accuracy?
• RQ2 Does the proposed method converge to the maximum entropy IRL solution under linear reward parameterization?
• RQ3 How does the algorithm perform in comparison to state-of-the-art IRL and imitation learning methods on complex robotics control tasks?
• RQ4 Can the method support counterfactual analysis due to accurate reward estimation?
• RQ5 What is the performance of the algorithm in transfer learning settings with altered environment dynamics?

Key findings

• The proposed algorithm achieves finite-time convergence to a stationary solution, providing theoretical guarantees not present in many existing IRL methods.
• Under linear reward parameterization, the identified solution corresponds exactly to the solution of the maximum entropy IRL problem.
• The method outperforms benchmark IRL and imitation learning algorithms on MuJoCo robotics control tasks, demonstrating superior sample efficiency and policy performance.
• The algorithm maintains high reward estimation accuracy, enabling reliable counterfactual policy prediction under changed environment dynamics.
• In transfer learning settings, the method generalizes well to new tasks, indicating robustness and transferability of the learned reward functions.
• The single-loop design significantly reduces computational overhead compared to nested-loop IRL, without compromising reward estimation quality.