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AlignIQL: Policy Alignment in Implicit Q-Learning through Constrained Optimization

Longxiang He, Li Shen, Xueqian Wang

TL;DR

The work reframes implicit policy extraction in IQL as a policy-alignment constrained optimization (IPF) problem. It introduces two practical algorithms, AlignIQL-hard (global-optimal but complex) and AlignIQL (soft-constraint, tractable), to recover the implicit policy from the learned Q/V, generalizing policy extraction beyond optimal value functions. The authors show that policy alignment explains why AWR-style weighting can recover implicit policies in IQL, and they demonstrate competitive or superior performance on D4RL benchmarks, particularly in challenging AntMaze tasks, as well as robustness improvements in noisy and vision-based settings. The approach also accommodates diffusion-based behavior models, offering a versatile framework for offline RL with complex behavior distributions.

Abstract

Implicit Q-learning (IQL) serves as a strong baseline for offline RL, which learns the value function using only dataset actions through quantile regression. However, it is unclear how to recover the implicit policy from the learned implicit Q-function and why IQL can utilize weighted regression for policy extraction. IDQL reinterprets IQL as an actor-critic method and gets weights of implicit policy, however, this weight only holds for the optimal value function. In this work, we introduce a different way to solve the implicit policy-finding problem (IPF) by formulating this problem as an optimization problem. Based on this optimization problem, we further propose two practical algorithms AlignIQL and AlignIQL-hard, which inherit the advantages of decoupling actor from critic in IQL and provide insights into why IQL can use weighted regression for policy extraction. Compared with IQL and IDQL, we find our method keeps the simplicity of IQL and solves the implicit policy-finding problem. Experimental results on D4RL datasets show that our method achieves competitive or superior results compared with other SOTA offline RL methods. Especially in complex sparse reward tasks like Antmaze and Adroit, our method outperforms IQL and IDQL by a significant margin.

AlignIQL: Policy Alignment in Implicit Q-Learning through Constrained Optimization

TL;DR

The work reframes implicit policy extraction in IQL as a policy-alignment constrained optimization (IPF) problem. It introduces two practical algorithms, AlignIQL-hard (global-optimal but complex) and AlignIQL (soft-constraint, tractable), to recover the implicit policy from the learned Q/V, generalizing policy extraction beyond optimal value functions. The authors show that policy alignment explains why AWR-style weighting can recover implicit policies in IQL, and they demonstrate competitive or superior performance on D4RL benchmarks, particularly in challenging AntMaze tasks, as well as robustness improvements in noisy and vision-based settings. The approach also accommodates diffusion-based behavior models, offering a versatile framework for offline RL with complex behavior distributions.

Abstract

Implicit Q-learning (IQL) serves as a strong baseline for offline RL, which learns the value function using only dataset actions through quantile regression. However, it is unclear how to recover the implicit policy from the learned implicit Q-function and why IQL can utilize weighted regression for policy extraction. IDQL reinterprets IQL as an actor-critic method and gets weights of implicit policy, however, this weight only holds for the optimal value function. In this work, we introduce a different way to solve the implicit policy-finding problem (IPF) by formulating this problem as an optimization problem. Based on this optimization problem, we further propose two practical algorithms AlignIQL and AlignIQL-hard, which inherit the advantages of decoupling actor from critic in IQL and provide insights into why IQL can use weighted regression for policy extraction. Compared with IQL and IDQL, we find our method keeps the simplicity of IQL and solves the implicit policy-finding problem. Experimental results on D4RL datasets show that our method achieves competitive or superior results compared with other SOTA offline RL methods. Especially in complex sparse reward tasks like Antmaze and Adroit, our method outperforms IQL and IDQL by a significant margin.
Paper Structure (29 sections, 4 theorems, 47 equations, 2 figures, 13 tables, 3 algorithms)

This paper contains 29 sections, 4 theorems, 47 equations, 2 figures, 13 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Background
  4. Implicit Policy-finding Problem
  5. Optimization
  6. Hard Constraint Solving
  7. Soft Constraint Solving
  8. Experiments
  9. D4RL AntMaze Results
  10. Noise Data and Vision-based Experiments
  11. Ablation Study
  12. Conclusion
  13. Related Works
  14. Diffusion model
  15. Implicit Diffusion Q-learning (IDQL)
  16. ...and 14 more sections

Key Result

Theorem 5.1

For problem align_p, the optimal policy $\pi^*$ and its optimal Lagrange multipliers satisfy the following optimality condition for all states and actions: where $\alpha^*,\beta^*$ is the Lagrange multiplier, $g_f$ is the inverse function of h$'_f(x)$.

Figures (2)

  • Figure 1: Training curves of D-AlignIQL, IDQL, and Diffusion+AWR. The normalized score is calculated by averaging the scores across three different $N$ ($N=16,64,256$).
  • Figure : AlignIQL Training

Theorems & Definitions (14)

  • Definition 4.1
  • Remark 4.4
  • Theorem 5.1
  • Lemma 5.2
  • proof
  • Remark 5.3
  • Remark 5.4
  • Theorem 5.5
  • Proposition 5.6
  • Remark 5.7
  • ...and 4 more