# Information-Directed Offline-to-Online Reinforcement Learning

arXiv: https://arxiv.org/abs/2605.29405 · HTML: https://mlsanity.com/paper/2605.29405/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Offline RL algorithms, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 35 of its 46 references that are in the map.
- First posted on arXiv 28 May 2026.

## Placed in

- Offline RL and imitation learning from data / [Offline RL algorithms](https://mlsanity.com/offlinerl/offline-rl-algorithms/)

## Builds on (most cited first, 30 of 35)

- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2006.04779/) (2020)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [Offline Reinforcement Learning with Implicit Q-Learning](https://mlsanity.com/paper/2110.06169/) (2021)
- [Off-Policy Deep Reinforcement Learning without Exploration](https://mlsanity.com/paper/1812.02900/) (2018)
- [A Minimalist Approach to Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06860/) (2021)
- [AWAC: Accelerating Online Reinforcement Learning with Offline Datasets](https://mlsanity.com/paper/2006.09359/) (2020)
- [Provably Efficient Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/1907.05388/) (2019)
- [Is Pessimism Provably Efficient for Offline RL?](https://mlsanity.com/paper/2012.15085/) (2020)
- [Efficient Online Reinforcement Learning with Offline Data](https://mlsanity.com/paper/2302.02948/) (2023)
- [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)
- [Learning to Optimize Via Posterior Sampling](https://mlsanity.com/paper/1301.2609/) (2013)
- [Cal-QL: Calibrated Offline RL Pre-Training for Efficient Online Fine-Tuning](https://mlsanity.com/paper/2303.05479/) (2023)
- [(More) Efficient Reinforcement Learning via Posterior Sampling](https://mlsanity.com/paper/1306.0940/) (2013)
- [The Statistical Complexity of Interactive Decision Making](https://mlsanity.com/paper/2112.13487/) (2021)
- [Offline-to-Online Reinforcement Learning via Balanced Replay and Pessimistic Q-Ensemble](https://mlsanity.com/paper/2107.00591/) (2021)
- [An Information-Theoretic Analysis of Thompson Sampling](https://mlsanity.com/paper/1403.5341/) (2014)
- [Learning to Optimize via Information-Directed Sampling](https://mlsanity.com/paper/1403.5556/) (2014)
- [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 Expansion for Bridging Offline-to-Online Reinforcement Learning](https://mlsanity.com/paper/2302.00935/) (2023)
- [The Role of Coverage in Online Reinforcement Learning](https://mlsanity.com/paper/2210.04157/) (2022)
- [Information Directed Sampling and Bandits with Heteroscedastic Noise](https://mlsanity.com/paper/1801.09667/) (2018)
- [Reinforcement Learning, Bit by Bit](https://mlsanity.com/paper/2103.04047/) (2021)
- [Leveraging Offline Data in Online Reinforcement Learning](https://mlsanity.com/paper/2211.04974/) (2022)
- [Adaptive Policy Learning for Offline-to-Online Reinforcement Learning](https://mlsanity.com/paper/2303.07693/) (2023)
- [PROTO: Iterative Policy Regularized Offline-to-Online Reinforcement Learning](https://mlsanity.com/paper/2305.15669/) (2023)
- [Regret Bounds for Information-Directed Reinforcement Learning](https://mlsanity.com/paper/2206.04640/) (2022)
- [CoMAL: Collaborative Multi-Agent Large Language Models for Mixed-Autonomy Traffic](https://mlsanity.com/paper/2410.14368/) (2024)

## Abstract (arXiv)

Decision-making from offline datasets typically warm-starts a policy or score model from fixed offline data and then refines it with limited online interaction. Offline data reduces uncertainty, but it does not remove the need for exploration; it changes what remains to be explored. We formalise this residual uncertainty by the conditional mutual information I(chi;τ1:TmidDN) between a learning target chi and the online trajectories after conditioning on the offline dataset. This view leads naturally to information-directed sampling (IDS), a family parameterised by η≥ 0 that selects actions by trading off instantaneous regret against information gain. We prove a generic offline-to-online Bayesian regret bound for IDS through a ratio certificate: any information-ratio bound satisfied by a reference Thompson-sampling policy over the same randomised policy class is inherited by IDS. In a known-dynamics Bayesian linear-reward model, the conditional mutual information has a log-determinant form, and vanilla IDS (η=0) satisfies widetilde O!left(Hdminleft√ T,,T√C^daggerβ,IDS0(N,T)/Nrightright), where the coverage coefficient is tied to the visitation distribution induced by vanilla IDS itself. We also identify a warm-start regime with a dominated but informative probe in which vanilla IDS selects the probe while Thompson sampling never does, giving a constant-factor Bayesian regret separation. Controlled bandit experiments and D4RL offline-to-online RL experiments validate this mechanism: IDS is most beneficial when offline data is informative but leaves biased or low-probability residual uncertainty that targeted online actions can resolve, a regime shared by offline RL, offline black-box optimization, and Bayesian optimization.