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A Natural Extension To Online Algorithms For Hybrid RL With Limited Coverage

Kevin Tan, Ziping Xu

TL;DR

It is shown that a natural extension to standard optimistic online algorithms -- warm-starting them by including the offline dataset in the experience replay buffer -- achieves similar provable gains from hybrid data even when the offline dataset does not have single-policy concentrability.

Abstract

Hybrid Reinforcement Learning (RL), leveraging both online and offline data, has garnered recent interest, yet research on its provable benefits remains sparse. Additionally, many existing hybrid RL algorithms (Song et al., 2023; Nakamoto et al., 2023; Amortila et al., 2024) impose coverage assumptions on the offline dataset, but we show that this is unnecessary. A well-designed online algorithm should "fill in the gaps" in the offline dataset, exploring states and actions that the behavior policy did not explore. Unlike previous approaches that focus on estimating the offline data distribution to guide online exploration (Li et al., 2023b), we show that a natural extension to standard optimistic online algorithms -- warm-starting them by including the offline dataset in the experience replay buffer -- achieves similar provable gains from hybrid data even when the offline dataset does not have single-policy concentrability. We accomplish this by partitioning the state-action space into two, bounding the regret on each partition through an offline and an online complexity measure, and showing that the regret of this hybrid RL algorithm can be characterized by the best partition -- despite the algorithm not knowing the partition itself. As an example, we propose DISC-GOLF, a modification of an existing optimistic online algorithm with general function approximation called GOLF used in Jin et al. (2021); Xie et al. (2022a), and show that it demonstrates provable gains over both online-only and offline-only reinforcement learning, with competitive bounds when specialized to the tabular, linear and block MDP cases. Numerical simulations further validate our theory that hybrid data facilitates more efficient exploration, supporting the potential of hybrid RL in various scenarios.

A Natural Extension To Online Algorithms For Hybrid RL With Limited Coverage

TL;DR

It is shown that a natural extension to standard optimistic online algorithms -- warm-starting them by including the offline dataset in the experience replay buffer -- achieves similar provable gains from hybrid data even when the offline dataset does not have single-policy concentrability.

Abstract

Hybrid Reinforcement Learning (RL), leveraging both online and offline data, has garnered recent interest, yet research on its provable benefits remains sparse. Additionally, many existing hybrid RL algorithms (Song et al., 2023; Nakamoto et al., 2023; Amortila et al., 2024) impose coverage assumptions on the offline dataset, but we show that this is unnecessary. A well-designed online algorithm should "fill in the gaps" in the offline dataset, exploring states and actions that the behavior policy did not explore. Unlike previous approaches that focus on estimating the offline data distribution to guide online exploration (Li et al., 2023b), we show that a natural extension to standard optimistic online algorithms -- warm-starting them by including the offline dataset in the experience replay buffer -- achieves similar provable gains from hybrid data even when the offline dataset does not have single-policy concentrability. We accomplish this by partitioning the state-action space into two, bounding the regret on each partition through an offline and an online complexity measure, and showing that the regret of this hybrid RL algorithm can be characterized by the best partition -- despite the algorithm not knowing the partition itself. As an example, we propose DISC-GOLF, a modification of an existing optimistic online algorithm with general function approximation called GOLF used in Jin et al. (2021); Xie et al. (2022a), and show that it demonstrates provable gains over both online-only and offline-only reinforcement learning, with competitive bounds when specialized to the tabular, linear and block MDP cases. Numerical simulations further validate our theory that hybrid data facilitates more efficient exploration, supporting the potential of hybrid RL in various scenarios.
Paper Structure (38 sections, 10 theorems, 82 equations, 5 figures, 1 algorithm)

This paper contains 38 sections, 10 theorems, 82 equations, 5 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Our Contributions.
  3. Problem Setup
  4. Notation.
  5. Episodic MDPs.
  6. Hybrid RL.
  7. Function Approximation.
  8. Measures of Complexity
  9. Offline Complexity Measures.
  10. Online Complexity Measures.
  11. Reduced Complexity Through State-Action Space Partition.
  12. Partial All-Policy Concentrability Is Less Stringent Than Single-Policy Concentrability.
  13. Main Result.
  14. Online Finetuning From Offline Data
  15. An Optimistic Hybrid RL Algorithm Warm-Started With Offline Data.
  16. ...and 23 more sections

Key Result

Theorem 1

Let ${\mathcal{X}}_{\operatorname{off}}, {\mathcal{X}}_{\operatorname{on}}$ be an arbitrary partition over ${\mathcal{X}} = {\mathcal{S}} \times {\mathcal{A}} \times [H]$. Algorithm alg:GOLF satisfies the following regret bound with probability at least $1-\delta$: where $\beta = c_1\log \left(N H \mathcal{N}_{\mathcal{F}}(1/N) / \delta\right)$ for some constant $c_1$ with $N = N_{\operatorname{o

Figures (5)

  • Figure 1: Coverage of the online samples averaged over 30 trials, with $1.96\hat{\sigma}$ confidence intervals. Hybrid RL explores more of the online partition and less of the offline partition than online RL when the behavior policy is poor, and vice-versa when the behavior policy is good. Lower is better.
  • Figure 2: Plot of the full and partial all-policy concentrability coefficients of the online samples from $100$ online episodes. The solid line represents the mean over $30$ trials, and the shaded areas represent confidence intervals generated by $1.96$ times the sample standard deviation. We see that hybrid RL takes fewer online episodes than online-only RL to achieve a lower concentrability coefficient.
  • Figure 3: Cumulative visits to the offline and online partitions over the $200$ online episodes of horizon $20$. When the behavior policy is poor or middling, the hybrid algorithm visits the online partition more and the offline partition less than the online-only algorithm does. When the behavior policy is optimal, the converse occurs, as the model parameters in UCBVI azar2017minimax are warm-started by estimating them from the offline dataset, enabling the hybrid algorithm to learn that the offline partition contains the good state-action pairs. Solid lines indicate the mean over $30$ trials, and the shaded area denotes a confidence interval of $1.96$ sample standard deviations.
  • Figure 4: Average reward over $200$ episodes from running UCBVI azar2017minimax both in its original form and initialized with an offline dataset. When the behavior policy is optimal, the hybrid algorithm learns the optimal policy quickly. When it is not, we still gain an advantage over online-only learning, even when the behavior policy is adversarial, even though in these cases $200$ episodes are not sufficient to learn the optimal policy. Incidentally, the hybrid algorithm with poor behavior policies has a high reward at the start, but faces a drop in performance as it explores other states and actions due to the very large exploration bonus we chose to encourage exploration. Results averaged over $30$ trials, with $1$ standard deviation-wide shaded areas.
  • Figure 5: Average reward of each episode when running LSVI-UCB jin2020provably in its original form and initialized with an offline dataset. Results averaged over $30$ trials, with $1$ standard deviation-wide shaded areas. The hybrid version approaches the optimal weights almost instantaneously, while the online-only version takes many more episodes to do the same.

Theorems & Definitions (23)

  • Definition 1: Occupancy Measure
  • Theorem 1: Regret Bound for DISC-GOLF
  • Proposition 1
  • Definition 2: Linear MDP
  • Proposition 2
  • Definition 3: Block Structure
  • Proposition 3
  • Proposition 4
  • Lemma 1
  • Definition 4
  • ...and 13 more