# Sample and Computationally Efficient Continuous-Time Reinforcement Learning with General Function Approximation

arXiv: https://arxiv.org/abs/2505.14821 · HTML: https://mlsanity.com/paper/2505.14821/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 46 of its 62 references that are in the map.
- First posted on arXiv 20 May 2025.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 30 of 46)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Aligning Text-to-Image Diffusion Models with Reward Backpropagation](https://mlsanity.com/paper/2310.03739/) (2023)
- [Bellman Eluder Dimension: New Rich Classes of RL Problems, and Sample-Efficient Algorithms](https://mlsanity.com/paper/2102.00815/) (2021)
- [I2SB: Image-to-Image Schr"odinger Bridge](https://mlsanity.com/paper/2302.05872/) (2023)
- [Diffusion Schr"odinger Bridge Matching](https://mlsanity.com/paper/2303.16852/) (2023)
- [Provably Efficient Reinforcement Learning with Linear Function Approximation Under Adaptivity Constraints](https://mlsanity.com/paper/2101.02195/) (2021)
- [Naive Exploration is Optimal for Online LQR](https://mlsanity.com/paper/2001.09576/) (2020)
- [Let us Build Bridges: Understanding and Extending Diffusion Generative Models](https://mlsanity.com/paper/2208.14699/) (2022)
- [Is Reinforcement Learning More Difficult Than Bandits? A Near-optimal Algorithm Escaping the Curse of Horizon](https://mlsanity.com/paper/2009.13503/) (2020)
- [DiffFit: Unlocking Transferability of Large Diffusion Models via Simple Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2304.06648/) (2023)
- [Provably Efficient Q-Learning with Low Switching Cost](https://mlsanity.com/paper/1905.12849/) (2019)
- [Nearly Minimax Optimal Reinforcement Learning for Linear Markov Decision Processes](https://mlsanity.com/paper/2212.06132/) (2022)
- [Online Linear Quadratic Control](https://mlsanity.com/paper/1806.07104/) (2018)
- [Feedback Efficient Online Fine-Tuning of Diffusion Models](https://mlsanity.com/paper/2402.16359/) (2024)

## Built on by (most cited first, 3 of 3)

- [Instance-Dependent Continuous-Time Reinforcement Learning via Maximum Likelihood Estimation](https://mlsanity.com/paper/2508.02103/) (2025)
- [PhiBE-Q-Learning: Bridging Off-Policy Reinforcement Learning and Continuous-Time Control](https://mlsanity.com/paper/2606.21925/) (2026)
- [Provably Efficient Reinforcement Learning in Continuous-Time Episodic MDPs with Poisson Decision Epochs](https://mlsanity.com/paper/2609.23127/) (2026)

## Abstract (arXiv)

Continuous-time reinforcement learning (CTRL) provides a principled framework for sequential decision-making in environments where interactions evolve continuously over time. Despite its empirical success, the theoretical understanding of CTRL remains limited, especially in settings with general function approximation. In this work, we propose a model-based CTRL algorithm that achieves both sample and computational efficiency. Our approach leverages optimism-based confidence sets to establish the first sample complexity guarantee for CTRL with general function approximation, showing that a near-optimal policy can be learned with a suboptimality gap of tildeO(√dR + dFN-1/2) using N measurements, where dR and dF denote the distributional Eluder dimensions of the reward and dynamic functions, respectively, capturing the complexity of general function approximation in reinforcement learning. Moreover, we introduce structured policy updates and an alternative measurement strategy that significantly reduce the number of policy updates and rollouts while maintaining competitive sample efficiency. We implemented experiments to backup our proposed algorithms on continuous control tasks and diffusion model fine-tuning, demonstrating comparable performance with significantly fewer policy updates and rollouts.