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Model-Based Reward Shaping for Adversarial Inverse Reinforcement Learning in Stochastic Environments

Simon Sinong Zhan, Philip Wang, Qingyuan Wu, Yixuan Wang, Ruochen Jiao, Chao Huang, Qi Zhu

TL;DR

This work tackles the weakness of adversarial IRL methods in stochastic environments by introducing Model-Enhanced AIRL, which injects learned transition dynamics into reward shaping to guarantee policy invariance and improve sample efficiency. The authors formulate a transition-aware reward design and an off-policy, model-based adversarial IRL framework with theoretical guarantees on reward and policy performance under transition-model errors. They establish bounds linking model error to reward learning and value differences, and demonstrate superior sample efficiency and robust performance on MuJoCo tasks with stochastic dynamics and on Atari with high-dimensional observations. Overall, the approach offers a principled, model-based enhancement to IRL that improves robustness to environment uncertainty while remaining competitive in deterministic settings and scalable to complex domains.

Abstract

In this paper, we aim to tackle the limitation of the Adversarial Inverse Reinforcement Learning (AIRL) method in stochastic environments where theoretical results cannot hold and performance is degraded. To address this issue, we propose a novel method which infuses the dynamics information into the reward shaping with the theoretical guarantee for the induced optimal policy in the stochastic environments. Incorporating our novel model-enhanced rewards, we present a novel Model-Enhanced AIRL framework, which integrates transition model estimation directly into reward shaping. Furthermore, we provide a comprehensive theoretical analysis of the reward error bound and performance difference bound for our method. The experimental results in MuJoCo benchmarks show that our method can achieve superior performance in stochastic environments and competitive performance in deterministic environments, with significant improvement in sample efficiency, compared to existing baselines.

Model-Based Reward Shaping for Adversarial Inverse Reinforcement Learning in Stochastic Environments

TL;DR

This work tackles the weakness of adversarial IRL methods in stochastic environments by introducing Model-Enhanced AIRL, which injects learned transition dynamics into reward shaping to guarantee policy invariance and improve sample efficiency. The authors formulate a transition-aware reward design and an off-policy, model-based adversarial IRL framework with theoretical guarantees on reward and policy performance under transition-model errors. They establish bounds linking model error to reward learning and value differences, and demonstrate superior sample efficiency and robust performance on MuJoCo tasks with stochastic dynamics and on Atari with high-dimensional observations. Overall, the approach offers a principled, model-based enhancement to IRL that improves robustness to environment uncertainty while remaining competitive in deterministic settings and scalable to complex domains.

Abstract

In this paper, we aim to tackle the limitation of the Adversarial Inverse Reinforcement Learning (AIRL) method in stochastic environments where theoretical results cannot hold and performance is degraded. To address this issue, we propose a novel method which infuses the dynamics information into the reward shaping with the theoretical guarantee for the induced optimal policy in the stochastic environments. Incorporating our novel model-enhanced rewards, we present a novel Model-Enhanced AIRL framework, which integrates transition model estimation directly into reward shaping. Furthermore, we provide a comprehensive theoretical analysis of the reward error bound and performance difference bound for our method. The experimental results in MuJoCo benchmarks show that our method can achieve superior performance in stochastic environments and competitive performance in deterministic environments, with significant improvement in sample efficiency, compared to existing baselines.
Paper Structure (33 sections, 12 theorems, 28 equations, 11 figures, 9 tables)

This paper contains 33 sections, 12 theorems, 28 equations, 11 figures, 9 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. MDP.
  4. Inverse RL.
  5. Transition-Aware Reward Shaping
  6. Model Enhanced IRL
  7. Adversarial Formulation of Reward Shaping
  8. Algorithm Framework
  9. Performance Analysis
  10. Experiments
  11. MuJuCo Experiment Setup.
  12. Stochastic MuJoCo.
  13. Sample Efficiency.
  14. Deterministic MuJoCo.
  15. Stochastic Atari Task.
  16. ...and 18 more sections

Key Result

theorem 1

Let $R$ and $\hat{R}$ be two reward functions. $R$ and $\hat{R}$ induce the same soft optimal policy under all transition dynamics $\mathcal{T}$ if $\hat{R}(s_t,a_t,\mathcal{T})=R(s_t,a_t)+\gamma\mathbb{E}_{\mathcal{T}}[\phi(s_{t+1})\vert s_t,a_t] - \phi(s_t)$ for some potential-shaping function $\p

Figures (11)

  • Figure 1: Framework overview of Model-Enhanced Adversarial IRL. Different color arrows stand for different sample flows. Purple stands for real environmental interaction samples, pink stands for synthetic samples generated from learned transition model, and blue stands for mixed of both.
  • Figure 2: Training return diagram averaging across three seeds for different numbers of expert trajectories in InvertedPendulum-v4.
  • Figure 3: Transition model learning error diagram averaging across three seeds for 10 expert trajectories in HalfCheetah-v4.
  • Figure 4: Training return diagram averaging across three seeds for 10 expert trajectories in HalfCheetah-v4.
  • Figure 5: Performance diagram averaging across three seeds for different algorithms in Hopper-v4 with 1000 expert trajectories provided. DAC is in green color; $mbirl\_sac$ is in blue; Our method is in red.
  • ...and 6 more figures

Theorems & Definitions (18)

  • definition 1
  • theorem 1: Policy Invariance
  • proposition 1
  • theorem 2: Reward Function Error Bound
  • theorem 3: Performance Difference Bound
  • theorem 4
  • proof
  • proposition 2
  • proof
  • lemma 1: Implicit Feasible Reward Set ng2000algorithms
  • ...and 8 more