# Transitive RL: Value Learning via Divide and Conquer

arXiv: https://arxiv.org/abs/2510.22512 · HTML: https://mlsanity.com/paper/2510.22512/

## Key facts

- Cited by 12 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 45 of its 53 references that are in the map.
- First posted on arXiv 26 Oct 2025.

## 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 45)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [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)
- [Offline Reinforcement Learning with Implicit Q-Learning](https://mlsanity.com/paper/2110.06169/) (2021)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [A Minimalist Approach to Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06860/) (2021)
- [QT-Opt: Scalable Deep Reinforcement Learning for Vision-Based Robotic Manipulation](https://mlsanity.com/paper/1806.10293/) (2018)
- [Behavior Regularized Offline Reinforcement Learning](https://mlsanity.com/paper/1911.11361/) (2019)
- [IDQL: Implicit Q-Learning as an Actor-Critic Method with Diffusion Policies](https://mlsanity.com/paper/2304.10573/) (2023)
- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)
- [Contrastive Learning as Goal-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2206.07568/) (2022)
- [OGBench: Benchmarking Offline Goal-Conditioned RL](https://mlsanity.com/paper/2410.20092/) (2024)
- [Breaking the Curse of Horizon: Infinite-Horizon Off-Policy Estimation](https://mlsanity.com/paper/1810.12429/) (2018)
- [Search on the Replay Buffer: Bridging Planning and Reinforcement Learning](https://mlsanity.com/paper/1906.05253/) (2019)
- [Flow Q-Learning](https://mlsanity.com/paper/2502.02538/) (2025)
- [Offline Reinforcement Learning via High-Fidelity Generative Behavior Modeling](https://mlsanity.com/paper/2209.14548/) (2022)
- [Offline RL Without Off-Policy Evaluation](https://mlsanity.com/paper/2106.08909/) (2021)
- [HIQL: Offline Goal-Conditioned RL with Latent States as Actions](https://mlsanity.com/paper/2307.11949/) (2023)
- [Revisiting the Minimalist Approach to Offline Reinforcement Learning](https://mlsanity.com/paper/2305.09836/) (2023)
- [Rapid Exploration for Open-World Navigation with Latent Goal Models](https://mlsanity.com/paper/2104.05859/) (2021)
- [Optimal Goal-Reaching Reinforcement Learning via Quasimetric Learning](https://mlsanity.com/paper/2304.01203/) (2023)
- [Extreme Q-Learning: MaxEnt RL without Entropy](https://mlsanity.com/paper/2301.02328/) (2023)
- [Offline RL with No OOD Actions: In-Sample Learning via Implicit Value Regularization](https://mlsanity.com/paper/2303.15810/) (2023)
- [EMaQ: Expected-Max Q-Learning Operator for Simple Yet Effective Offline and Online RL](https://mlsanity.com/paper/2007.11091/) (2020)
- [C-Learning: Learning to Achieve Goals via Recursive Classification](https://mlsanity.com/paper/2011.08909/) (2020)

## Built on by (most cited first, 12 of 12)

- [Can We Really Learn One Representation to Optimize All Rewards?](https://mlsanity.com/paper/2602.11399/) (2026)
- [Chunk-Guided Q-Learning](https://mlsanity.com/paper/2603.13971/) (2026)
- [Refining Compositional Diffusion for Reliable Long-Horizon Planning](https://mlsanity.com/paper/2605.03075/) (2026)
- [Offline Reinforcement Learning with Universal Horizon Models](https://mlsanity.com/paper/2605.15603/) (2026)
- [Abstraction for Offline Goal-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2605.22711/) (2026)
- [Mollified Value Learning](https://mlsanity.com/paper/2602.23280/) (2026)
- [Adaptive Coarse-to-Fine Subgoal Refinement for Long-Horizon Offline Goal-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2605.28127/) (2026)
- [Recursive Value Learning for Long-Horizon Offline Goal-Conditioned RL](https://mlsanity.com/paper/2609.02237/) (2026)
- [Zero-Shot Signal Temporal Logic Planning with Disjunctive Branch Selection in Dynamic Semantic Maps](https://mlsanity.com/paper/2605.01222/) (2026)
- [ChronoForest: Closed-Loop Multi-Tree Diffusion Planning for Efficient Bridge Search and Route Composition](https://mlsanity.com/paper/2606.06618/) (2026)
- [SegBench-GC: Testing Segmentation Invariance in Multi-Step Offline Goal-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2608.27678/) (2026)
- [GTRL: Grounding Divide-and-Conquer Value Learning with Temporal Differences](https://mlsanity.com/paper/2609.33259/) (2026)

## Abstract (arXiv)

In this work, we present Transitive Reinforcement Learning (TRL), a new value learning algorithm based on a divide-and-conquer paradigm. TRL is designed for offline goal-conditioned reinforcement learning (GCRL) problems, where the aim is to find a policy that can reach any state from any other state in the smallest number of steps. TRL converts a triangle inequality structure present in GCRL into a practical divide-and-conquer value update rule. This has several advantages compared to alternative value learning paradigms. Compared to temporal difference (TD) methods, TRL suffers less from bias accumulation, as in principle it only requires O(log T) recursions (as opposed to O(T) in TD learning) to handle a length-T trajectory. Unlike Monte Carlo methods, TRL suffers less from high variance as it performs dynamic programming. Experimentally, we show that TRL achieves the best performance in highly challenging, long-horizon benchmark tasks compared to previous offline GCRL algorithms.