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Projection Implicit Q-Learning with Support Constraint for Offline Reinforcement Learning

Xinchen Han, Hossam Afifi, Michel Marot

TL;DR

Proj-IQL tackles offline RL extrapolation by replacing a fixed expectile conservatism with a projection-based adaptive parameter $\tau_{\text{proj}}(a|s)$ and coupling multi-step, in-sample expectile learning with a relaxed, support-constrained policy improvement. Theoretical results establish monotonic policy improvement under nondecreasing $\tau_{\text{proj}}$ and rigorous criteria for identifying superior actions, while practical implementations use clipping, batch-averaging, and SNIS to stabilize training. Empirically, Proj-IQL achieves state-of-the-art performance on D4RL benchmarks, notably in AntMaze-v0 and Kitchen-v0 tasks that require strong stitching capabilities. Overall, the approach provides a data-efficient, theoretically grounded offline RL algorithm with robust improvements over existing methods.

Abstract

Offline Reinforcement Learning (RL) faces a critical challenge of extrapolation errors caused by out-of-distribution (OOD) actions. Implicit Q-Learning (IQL) algorithm employs expectile regression to achieve in-sample learning, effectively mitigating the risks associated with OOD actions. However, the fixed hyperparameter in policy evaluation and density-based policy improvement method limit its overall efficiency. In this paper, we propose Proj-IQL, a projective IQL algorithm enhanced with the support constraint. In the policy evaluation phase, Proj-IQL generalizes the one-step approach to a multi-step approach through vector projection, while maintaining in-sample learning and expectile regression framework. In the policy improvement phase, Proj-IQL introduces support constraint that is more aligned with the policy evaluation approach. Furthermore, we theoretically demonstrate that Proj-IQL guarantees monotonic policy improvement and enjoys a progressively more rigorous criterion for superior actions. Empirical results demonstrate the Proj-IQL achieves state-of-the-art performance on D4RL benchmarks, especially in challenging navigation domains.

Projection Implicit Q-Learning with Support Constraint for Offline Reinforcement Learning

TL;DR

Proj-IQL tackles offline RL extrapolation by replacing a fixed expectile conservatism with a projection-based adaptive parameter and coupling multi-step, in-sample expectile learning with a relaxed, support-constrained policy improvement. Theoretical results establish monotonic policy improvement under nondecreasing and rigorous criteria for identifying superior actions, while practical implementations use clipping, batch-averaging, and SNIS to stabilize training. Empirically, Proj-IQL achieves state-of-the-art performance on D4RL benchmarks, notably in AntMaze-v0 and Kitchen-v0 tasks that require strong stitching capabilities. Overall, the approach provides a data-efficient, theoretically grounded offline RL algorithm with robust improvements over existing methods.

Abstract

Offline Reinforcement Learning (RL) faces a critical challenge of extrapolation errors caused by out-of-distribution (OOD) actions. Implicit Q-Learning (IQL) algorithm employs expectile regression to achieve in-sample learning, effectively mitigating the risks associated with OOD actions. However, the fixed hyperparameter in policy evaluation and density-based policy improvement method limit its overall efficiency. In this paper, we propose Proj-IQL, a projective IQL algorithm enhanced with the support constraint. In the policy evaluation phase, Proj-IQL generalizes the one-step approach to a multi-step approach through vector projection, while maintaining in-sample learning and expectile regression framework. In the policy improvement phase, Proj-IQL introduces support constraint that is more aligned with the policy evaluation approach. Furthermore, we theoretically demonstrate that Proj-IQL guarantees monotonic policy improvement and enjoys a progressively more rigorous criterion for superior actions. Empirical results demonstrate the Proj-IQL achieves state-of-the-art performance on D4RL benchmarks, especially in challenging navigation domains.
Paper Structure (17 sections, 7 theorems, 53 equations, 3 figures, 3 tables, 1 algorithm)

This paper contains 17 sections, 7 theorems, 53 equations, 3 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Offline RL
  5. Support Constraint Policy Improvement
  6. IQL
  7. Projection IQL with Support Constraint
  8. Policy Evaluation in Proj-IQL
  9. Policy Improvement in Proj-IQL
  10. Practical Implementation of Proj-IQL
  11. Experiments
  12. Comparisons on D4RL Benchmarks
  13. The Training Curves of $\tau_\text{proj}$
  14. Empirical Study on the Projection Parameter
  15. Conclusion
  16. ...and 2 more sections

Key Result

Lemma 4.1

For all $s$, $\tau_1$ and $\tau_2$ such that $\tau_1 < \tau_2$ we get

Figures (3)

  • Figure 1: The performance of IQL in $\tau=0.3, 0.6, 0.9$ on $10$ D4RL datasets, including Walker2d- Halfcheetah- Hopper- medium-v2 and medium-expert-v2 and AntMaze-umaze-v0, AntMaze-umaze-diverse-v0, AntMaze-medium-play-v0, AntMaze-medium-diverse-v0.
  • Figure 2: The training curves of normalized score and $\tau_{\text{proj}}(a|s)$ on AntMaze-v0 and Kitchen-v0 datasets. The solid line and shaded regions represent the mean and standard deviation, respectively.
  • Figure 3: The training curves of normalized score and $\tau_{\text{proj}}(a|s)$ on Kitchen-v0 datasets under $batch \; size = 16, 64, 128, 256$. The solid line and shaded regions represent the mean and standard deviation, respectively.

Theorems & Definitions (14)

  • Lemma 4.1
  • Theorem 4.2
  • Lemma 4.3
  • Theorem 4.4
  • Theorem 4.5
  • Lemma 4.6
  • Theorem 4.7
  • proof
  • proof
  • proof
  • ...and 4 more