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Provable Domain Adaptation for Offline Reinforcement Learning with Limited Samples

Weiqin Chen, Xinjie Zhang, Sandipan Mishra, Santiago Paternain

TL;DR

This work addresses offline reinforcement learning under limited target data by introducing a principled domain-adaptation framework that blends a sparse target dataset with a large source dataset using a weight $\lambda$. It derives both expected and worst-case performance bounds that decompose into a variance term $\varsigma$ (target data variability) and a dynamics-gap term $\xi$ (domain discrepancy), and proves convergence to a neighborhood of the optimal $Q$-function. The authors show the existence of an optimal weight $\lambda^*$ (with closed-form under simplifying assumptions) and validate the theory with Procgen experiments using CQL and IQL, demonstrating that the best trade-off is not always a trivial choice and depends on target-sample size and domain similarity. The results provide a rigorous, algorithm-agnostic blueprint for leveraging abundant source data (e.g., simulators) in offline RL, offering guidance for weight selection and pointing to practical methods for estimating the optimal balance in real applications.

Abstract

Offline reinforcement learning (RL) learns effective policies from a static target dataset. The performance of state-of-the-art offline RL algorithms notwithstanding, it relies on the size of the target dataset, and it degrades if limited samples in the target dataset are available, which is often the case in real-world applications. To address this issue, domain adaptation that leverages auxiliary samples from related source datasets (such as simulators) can be beneficial. However, establishing the optimal way to trade off the limited target dataset and the large-but-biased source dataset while ensuring provably theoretical guarantees remains an open challenge. To the best of our knowledge, this paper proposes the first framework that theoretically explores the impact of the weights assigned to each dataset on the performance of offline RL. In particular, we establish performance bounds and the existence of the optimal weight, which can be computed in closed form under simplifying assumptions. We also provide algorithmic guarantees in terms of convergence to a neighborhood of the optimum. Notably, these results depend on the quality of the source dataset and the number of samples in the target dataset. Our empirical results on the well-known offline Procgen benchmark substantiate the theoretical contributions in this work.

Provable Domain Adaptation for Offline Reinforcement Learning with Limited Samples

TL;DR

This work addresses offline reinforcement learning under limited target data by introducing a principled domain-adaptation framework that blends a sparse target dataset with a large source dataset using a weight . It derives both expected and worst-case performance bounds that decompose into a variance term (target data variability) and a dynamics-gap term (domain discrepancy), and proves convergence to a neighborhood of the optimal -function. The authors show the existence of an optimal weight (with closed-form under simplifying assumptions) and validate the theory with Procgen experiments using CQL and IQL, demonstrating that the best trade-off is not always a trivial choice and depends on target-sample size and domain similarity. The results provide a rigorous, algorithm-agnostic blueprint for leveraging abundant source data (e.g., simulators) in offline RL, offering guidance for weight selection and pointing to practical methods for estimating the optimal balance in real applications.

Abstract

Offline reinforcement learning (RL) learns effective policies from a static target dataset. The performance of state-of-the-art offline RL algorithms notwithstanding, it relies on the size of the target dataset, and it degrades if limited samples in the target dataset are available, which is often the case in real-world applications. To address this issue, domain adaptation that leverages auxiliary samples from related source datasets (such as simulators) can be beneficial. However, establishing the optimal way to trade off the limited target dataset and the large-but-biased source dataset while ensuring provably theoretical guarantees remains an open challenge. To the best of our knowledge, this paper proposes the first framework that theoretically explores the impact of the weights assigned to each dataset on the performance of offline RL. In particular, we establish performance bounds and the existence of the optimal weight, which can be computed in closed form under simplifying assumptions. We also provide algorithmic guarantees in terms of convergence to a neighborhood of the optimum. Notably, these results depend on the quality of the source dataset and the number of samples in the target dataset. Our empirical results on the well-known offline Procgen benchmark substantiate the theoretical contributions in this work.
Paper Structure (28 sections, 9 theorems, 112 equations, 9 figures, 5 tables)

This paper contains 28 sections, 9 theorems, 112 equations, 9 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Offline reinforcement learning with dataset distillation.
  4. Offline reinforcement learning with domain adaptation.
  5. Offline reinforcement learning with dynamics gap.
  6. Main Contributions
  7. Balancing Target and Source Datasets
  8. Performance and Convergence Guarantees
  9. Numerical Experiments
  10. Environments
  11. Experimental Setup
  12. Results
  13. Conclusion
  14. Omitted Proofs
  15. Proof of Proposition \ref{['proposition_two_solution']}
  16. ...and 13 more sections

Key Result

Proposition 1

Let Assumptions assumption_infinite_source and assumption_SAprobability hold. Recall the empirical Bellman operator $\hat{\mathcal{B}}$ in (eqn_TDerror_single). Denote by $\mathcal{B}_\mathcal{D}$ ($\mathcal{B}_\mathcal{D'}$) the Bellman operator in (eqn_q_bellman) or (eqn_ac_bellman) in which $s'$

Figures (9)

  • Figure 1: Schematic: the target dataset has limited samples (red), whereas the source dataset has unlimited samples (green) with a dynamics gap from the target dataset. How to strike a proper balance between the two datasets?
  • Figure 2: The performance of offline RL across five Procgen games. The source dataset contains $40000$ samples from levels $[0, 99]$, while the target dataset comprises $1000$ samples from levels $[100, 199]$. We consider seven weights, $\lambda \in \{0, 0.2, 0.4, 0.5, 0.6, 0.8, 1.0\}$, to trade off the source and target datasets with the star marking the optimal weight. Upper row: CQL as the backbone; Lower row: IQL as the backbone.
  • Figure 3: The performance of offline RL across five Procgen games. The target dataset comprises $1000$ samples from levels $[100, 199]$, and three source datasets are considered, each containing $40000$ samples from levels $[0, 99]$ (green, $\xi_1$), $[25, 124]$ (blue, $\xi_2$), and $[50, 149]$ (red, $\xi_3$), respectively. Seven weights, $\lambda \in \{0, 0.2, 0.4, 0.5, 0.6, 0.8, 1.0\}$, are evaluated to trade off the source and target datasets with the star marking the optimal weight for each $\xi$. Upper row: CQL as the backbone; Lower row: IQL as the backbone.
  • Figure 4: The performance of offline RL across five Procgen games. The source dataset comprises $40000$ samples from levels $[50, 149]$, and target datasets from levels $[100, 199]$ are considered with three different sample sizes: $N=1000$ (green), $N=2500$ (blue), and $N=4000$ (red). Seven weights, $\lambda \in \{0, 0.2, 0.4, 0.5, 0.6, 0.8, 1.0\}$, are evaluated to trade off the source and target datasets with the star marking the optimal weight for each $N$. Upper row: CQL as the backbone algorithm; Lower row: IQL as the backbone algorithm.
  • Figure 5: The screenshot of Caveflyercobbe2020leveraging.
  • ...and 4 more figures

Theorems & Definitions (26)

  • Remark 1
  • Remark 2
  • Proposition 1
  • proof
  • Theorem 1: Expected Performance Bound
  • proof
  • Theorem 2: Tighter Expected Performance Bound
  • proof
  • Corollary 1
  • proof
  • ...and 16 more