# Long-Horizon Q-Learning: Accurate Value Learning via n-Step Inequalities

arXiv: https://arxiv.org/abs/2605.05812 · HTML: https://mlsanity.com/paper/2605.05812/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 34 of its 52 references that are in the map.
- First posted on arXiv 7 May 2026.

## 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 34)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [π0.5: a Vision-Language-Action Model with Open-World Generalization](https://mlsanity.com/paper/2504.16054/) (2025)
- [Learning Fine-Grained Bimanual Manipulation with Low-Cost Hardware](https://mlsanity.com/paper/2304.13705/) (2023)
- [Offline Reinforcement Learning with Implicit Q-Learning](https://mlsanity.com/paper/2110.06169/) (2021)
- [IMPALA: Scalable Distributed Deep-RL with Importance Weighted Actor-Learner Architectures](https://mlsanity.com/paper/1802.01561/) (2018)
- [Deep Reinforcement Learning at the Edge of the Statistical Precipice](https://mlsanity.com/paper/2108.13264/) (2021)
- [Rainbow: Combining Improvements in Deep Reinforcement Learning](https://mlsanity.com/paper/1710.02298/) (2017)
- [What Matters in Learning from Offline Human Demonstrations for Robot Manipulation](https://mlsanity.com/paper/2108.03298/) (2021)
- [Efficient Online Reinforcement Learning with Offline Data](https://mlsanity.com/paper/2302.02948/) (2023)
- [π*0.6: a VLA That Learns From Experience](https://mlsanity.com/paper/2511.14759/) (2025)
- [Diffusion Policy Policy Optimization](https://mlsanity.com/paper/2409.00588/) (2024)
- [Safe and Efficient Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1606.02647/) (2016)
- [OGBench: Benchmarking Offline Goal-Conditioned RL](https://mlsanity.com/paper/2410.20092/) (2024)
- [Flow Q-Learning](https://mlsanity.com/paper/2502.02538/) (2025)
- [Deep Reinforcement Learning and the Deadly Triad](https://mlsanity.com/paper/1812.02648/) (2018)
- [Steering Your Diffusion Policy with Latent Space Reinforcement Learning](https://mlsanity.com/paper/2506.15799/) (2025)
- [Bigger, Better, Faster: Human-level Atari with human-level efficiency](https://mlsanity.com/paper/2305.19452/) (2023)
- [Q-Transformer: Scalable Offline Reinforcement Learning via Autoregressive Q-Functions](https://mlsanity.com/paper/2309.10150/) (2023)
- [Revisiting the Minimalist Approach to Offline Reinforcement Learning](https://mlsanity.com/paper/2305.09836/) (2023)
- [Reinforcement Learning with Action Chunking](https://mlsanity.com/paper/2507.07969/) (2025)
- [Multi-step Reinforcement Learning: A Unifying Algorithm](https://mlsanity.com/paper/1703.01327/) (2017)
- [Understanding Multi-Step Deep Reinforcement Learning: A Systematic Study of the DQN Target](https://mlsanity.com/paper/1901.07510/) (2019)
- [Sample-Efficient Deep Reinforcement Learning via Episodic Backward Update](https://mlsanity.com/paper/1805.12375/) (2018)

## Abstract (arXiv)

Off-policy, value-based reinforcement learning methods such as Q-learning are appealing because they can learn from arbitrary experience, including data collected by older policies or other agents. In practice, however, bootstrapping makes long-horizon learning brittle: estimation errors at later states propagate backward through temporal-difference (TD) updates and can compound over time. We propose long-horizon Q-learning (LQL), which introduces a principled backstop against compounding error when learning the optimal action-value function. LQL builds on a prior optimality tightening observation: any realized action sequence lower-bounds what the optimal policy can achieve in expectation, so acting optimally earlier should not be worse than following the observed actions for several steps before switching to optimal behavior. Our contribution is to turn this inequality into a practical stabilization mechanism for Q-learning by using a hinge loss to penalize violations of these bounds. Importantly, LQL computes these penalties using network outputs already produced for the TD error, requiring no auxiliary networks and no additional forward passes relative to Q-learning. When combined with multiple state-of-the-art methods on a range of online and offline-to-online benchmarks, LQL consistently outperforms both 1-step TD and n-step TD learning at similar runtime.