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

arXiv: https://arxiv.org/abs/2403.09701 · HTML: https://mlsanity.com/paper/2403.09701/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Deep RL algorithms and representations, one of 15 directions in Deep reinforcement learning methods.
- Builds on 32 of its 34 references that are in the map.
- First posted on arXiv 7 Mar 2024.

## Placed in

- Deep reinforcement learning methods / [Deep RL algorithms and representations](https://mlsanity.com/deeprl/deep-rl-algorithms-and-representations/)

## Builds on (most cited first, 30 of 32)

- [Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2006.04779/) (2020)
- [Provably Efficient Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/1907.05388/) (2019)
- [Minimax Regret Bounds for Reinforcement Learning](https://mlsanity.com/paper/1703.05449/) (2017)
- [Bridging Offline Reinforcement Learning and Imitation Learning: A Tale of Pessimism](https://mlsanity.com/paper/2103.12021/) (2021)
- [Bellman-consistent Pessimism for Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06926/) (2021)
- [Cal-QL: Calibrated Offline RL Pre-Training for Efficient Online Fine-Tuning](https://mlsanity.com/paper/2303.05479/) (2023)
- [Bellman Eluder Dimension: New Rich Classes of RL Problems, and Sample-Efficient Algorithms](https://mlsanity.com/paper/2102.00815/) (2021)
- [Nearly Minimax Optimal Reinforcement Learning for Linear Mixture Markov Decision Processes](https://mlsanity.com/paper/2012.08507/) (2020)
- [Learning Near Optimal Policies with Low Inherent Bellman Error](https://mlsanity.com/paper/2003.00153/) (2020)
- [Provably efficient RL with Rich Observations via Latent State Decoding](https://mlsanity.com/paper/1901.09018/) (2019)
- [Pessimistic Model-based Offline Reinforcement Learning under Partial Coverage](https://mlsanity.com/paper/2107.06226/) (2021)
- [Hybrid RL: Using Both Offline and Online Data Can Make RL Efficient](https://mlsanity.com/paper/2210.06718/) (2022)
- [Policy Finetuning: Bridging Sample-Efficient Offline and Online Reinforcement Learning](https://mlsanity.com/paper/2106.04895/) (2021)
- [Offline Reinforcement Learning with Realizability and Single-policy Concentrability](https://mlsanity.com/paper/2202.04634/) (2022)
- [Kinematic State Abstraction and Provably Efficient Rich-Observation Reinforcement Learning](https://mlsanity.com/paper/1911.05815/) (2019)
- [Adversarially Trained Actor Critic for Offline Reinforcement Learning](https://mlsanity.com/paper/2202.02446/) (2022)
- [Toward the Fundamental Limits of Imitation Learning](https://mlsanity.com/paper/2009.05990/) (2020)
- [Is Q-Learning Minimax Optimal? A Tight Sample Complexity Analysis](https://mlsanity.com/paper/2102.06548/) (2021)
- [Better Exploration with Optimistic Actor-Critic](https://mlsanity.com/paper/1910.12807/) (2019)
- [Pessimistic Q-Learning for Offline Reinforcement Learning: Towards Optimal Sample Complexity](https://mlsanity.com/paper/2202.13890/) (2022)
- [The Role of Coverage in Online Reinforcement Learning](https://mlsanity.com/paper/2210.04157/) (2022)
- [Provably Good Batch Reinforcement Learning Without Great Exploration](https://mlsanity.com/paper/2007.08202/) (2020)
- [On Oracle-Efficient PAC RL with Rich Observations](https://mlsanity.com/paper/1803.00606/) (2018)
- [Tactical Optimism and Pessimism for Deep Reinforcement Learning](https://mlsanity.com/paper/2102.03765/) (2021)
- [Leveraging Offline Data in Online Reinforcement Learning](https://mlsanity.com/paper/2211.04974/) (2022)
- [Provably Efficient Causal Reinforcement Learning with Confounded Observational Data](https://mlsanity.com/paper/2006.12311/) (2020)
- [Pessimism in the Face of Confounders: Provably Efficient Offline Reinforcement Learning in Partially Observable Markov Decision Processes](https://mlsanity.com/paper/2205.13589/) (2022)
- [When is Realizability Sufficient for Off-Policy Reinforcement Learning?](https://mlsanity.com/paper/2211.05311/) (2022)
- [Reward-agnostic Fine-tuning: Provable Statistical Benefits of Hybrid Reinforcement Learning](https://mlsanity.com/paper/2305.10282/) (2023)
- [Harnessing Density Ratios for Online Reinforcement Learning](https://mlsanity.com/paper/2401.09681/) (2024)

## Built on by (most cited first, 5 of 5)

- [RL in Latent MDPs is Tractable: Online Guarantees via Off-Policy Evaluation](https://mlsanity.com/paper/2406.01389/) (2024)
- [Hybrid Reinforcement Learning Breaks Sample Size Barriers in Linear MDPs](https://mlsanity.com/paper/2408.04526/) (2024)
- [Augmenting Online RL with Offline Data is All You Need: A Unified Hybrid RL Algorithm Design and Analysis](https://mlsanity.com/paper/2505.13768/) (2025)
- [Offline-to-online Reinforcement Learning for Image-based Grasping with Scarce Demonstrations](https://mlsanity.com/paper/2410.14957/) (2024)
- [Sample-Mean Anchored Thompson Sampling for Offline-to-Online Learning with Distribution Shift](https://mlsanity.com/paper/2605.10289/) (2026)

## Abstract (arXiv)

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.