# Offline Goal-Conditioned Reinforcement Learning with Projective Quasimetric Planning

arXiv: https://arxiv.org/abs/2506.18847 · HTML: https://mlsanity.com/paper/2506.18847/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for offline RL, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 50 of its 70 references that are in the map.
- First posted on arXiv 23 Jun 2025.

## Placed in

- Offline RL and imitation learning from data / [Diffusion and flow policies for offline RL](https://mlsanity.com/offlinerl/diffusion-and-flow-policies-for-offline-rl/)

## Builds on (most cited first, 30 of 50)

- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Offline Reinforcement Learning with Implicit Q-Learning](https://mlsanity.com/paper/2110.06169/) (2021)
- [Hindsight Experience Replay](https://mlsanity.com/paper/1707.01495/) (2017)
- [Dota 2 with Large Scale Deep Reinforcement Learning](https://mlsanity.com/paper/1912.06680/) (2019)
- [VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2105.04906/) (2021)
- [Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1910.00177/) (2019)
- [CURL: Contrastive Unsupervised Representations for Reinforcement Learning](https://mlsanity.com/paper/2004.04136/) (2020)
- [A Brief Survey of Deep Reinforcement Learning](https://mlsanity.com/paper/1708.05866/) (2017)
- [Data-Efficient Hierarchical Reinforcement Learning](https://mlsanity.com/paper/1805.08296/) (2018)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [FeUdal Networks for Hierarchical Reinforcement Learning](https://mlsanity.com/paper/1703.01161/) (2017)
- [Hierarchical Deep Reinforcement Learning: Integrating Temporal Abstraction and Intrinsic Motivation](https://mlsanity.com/paper/1604.06057/) (2016)
- [OGBench: Benchmarking Offline Goal-Conditioned RL](https://mlsanity.com/paper/2410.20092/) (2024)
- [Cal-QL: Calibrated Offline RL Pre-Training for Efficient Online Fine-Tuning](https://mlsanity.com/paper/2303.05479/) (2023)
- [Accelerating Reinforcement Learning with Learned Skill Priors](https://mlsanity.com/paper/2010.11944/) (2020)
- [Semi-parametric Topological Memory for Navigation](https://mlsanity.com/paper/1803.00653/) (2018)
- [DeepMDP: Learning Continuous Latent Space Models for Representation Learning](https://mlsanity.com/paper/1906.02736/) (2019)
- [Search on the Replay Buffer: Bridging Planning and Reinforcement Learning](https://mlsanity.com/paper/1906.05253/) (2019)
- [OPAL: Offline Primitive Discovery for Accelerating Offline Reinforcement Learning](https://mlsanity.com/paper/2010.13611/) (2020)
- [Goal-conditioned Imitation Learning](https://mlsanity.com/paper/1906.05838/) (2019)
- [Goal-Conditioned Reinforcement Learning: Problems and Solutions](https://mlsanity.com/paper/2201.08299/) (2022)
- [Planning with Goal-Conditioned Policies](https://mlsanity.com/paper/1911.08453/) (2019)
- [HIQL: Offline Goal-Conditioned RL with Latent States as Actions](https://mlsanity.com/paper/2307.11949/) (2023)
- [Goal-Conditioned Reinforcement Learning with Imagined Subgoals](https://mlsanity.com/paper/2107.00541/) (2021)
- [Actionable Models: Unsupervised Offline Reinforcement Learning of Robotic Skills](https://mlsanity.com/paper/2104.07749/) (2021)
- [Optimal Goal-Reaching Reinforcement Learning via Quasimetric Learning](https://mlsanity.com/paper/2304.01203/) (2023)
- [Near-Optimal Representation Learning for Hierarchical Reinforcement Learning](https://mlsanity.com/paper/1810.01257/) (2018)
- [Foundation Policies with Hilbert Representations](https://mlsanity.com/paper/2402.15567/) (2024)
- [Rethinking Goal-conditioned Supervised Learning and Its Connection to Offline RL](https://mlsanity.com/paper/2202.04478/) (2022)

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

- [Temporal-Distance JEPA: Plan-Aware Representation Learning for Latent World Model Predictive Control](https://mlsanity.com/paper/2607.25337/) (2026)
- [Diffusion Subgoal Planning for Long-Horizon Offline Goal-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2609.34575/) (2026)
- [Aligning LLMs on a Budget: Inference-Time Alignment with Heuristic Reward Models](https://mlsanity.com/paper/2508.05165/) (2025)
- [Offline Reinforcement Learning of High-Quality Behaviors Under Robust Style Alignment](https://mlsanity.com/paper/2601.22823/) (2026)
- [Beyond Success Rates: Trainability and Extractability for Offline GCRL](https://mlsanity.com/paper/2602.05459/) (2026)

## Abstract (arXiv)

Offline Goal-Conditioned Reinforcement Learning seeks to train agents to reach specified goals from previously collected trajectories. Scaling that promises to long-horizon tasks remains challenging, notably due to compounding value-estimation errors. Principled geometric offers a potential solution to address these issues. Following this insight, we introduce Projective Quasimetric Planning (ProQ), a compositional framework that learns an asymmetric distance and then repurposes it, firstly as a repulsive energy forcing a sparse set of keypoints to uniformly spread over the learned latent space, and secondly as a structured directional cost guiding towards proximal sub-goals. In particular, ProQ couples this geometry with a Lagrangian out-of-distribution detector to ensure the learned keypoints stay within reachable areas. By unifying metric learning, keypoint coverage, and goal-conditioned control, our approach produces meaningful sub-goals and robustly drives long-horizon goal-reaching on diverse a navigation benchmarks.