# Goal-Conditioned Reinforcement Learning from Sub-Optimal Data on Metric Spaces

arXiv: https://arxiv.org/abs/2402.10820 · HTML: https://mlsanity.com/paper/2402.10820/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Offline RL algorithms, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 44 of its 59 references that are in the map.
- First posted on arXiv 16 Feb 2024.

## Placed in

- Offline RL and imitation learning from data / [Offline RL algorithms](https://mlsanity.com/offlinerl/offline-rl-algorithms/)
- 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 44)

- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [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)
- [Stabilizing Off-Policy Q-Learning via Bootstrapping Error Reduction](https://mlsanity.com/paper/1906.00949/) (2019)
- [CURL: Contrastive Unsupervised Representations for Reinforcement Learning](https://mlsanity.com/paper/2004.04136/) (2020)
- [AWAC: Accelerating Online Reinforcement Learning with Offline Datasets](https://mlsanity.com/paper/2006.09359/) (2020)
- [BridgeData V2: A Dataset for Robot Learning at Scale](https://mlsanity.com/paper/2308.12952/) (2023)
- [MOPO: Model-based Offline Policy Optimization](https://mlsanity.com/paper/2005.13239/) (2020)
- [MOReL : Model-Based Offline Reinforcement Learning](https://mlsanity.com/paper/2005.05951/) (2020)
- [Time-Contrastive Networks: Self-Supervised Learning from Video](https://mlsanity.com/paper/1704.06888/) (2017)
- [VIP: Towards Universal Visual Reward and Representation via Value-Implicit Pre-Training](https://mlsanity.com/paper/2210.00030/) (2022)
- [COMBO: Conservative Offline Model-Based Policy Optimization](https://mlsanity.com/paper/2102.08363/) (2021)
- [Minigrid & Miniworld: Modular & Customizable Reinforcement Learning Environments for Goal-Oriented Tasks](https://mlsanity.com/paper/2306.13831/) (2023)
- [RoboNet: Large-Scale Multi-Robot Learning](https://mlsanity.com/paper/1910.11215/) (2019)
- [Decoupling Representation Learning from Reinforcement Learning](https://mlsanity.com/paper/2009.08319/) (2020)
- [Multi-Goal Reinforcement Learning: Challenging Robotics Environments and Request for Research](https://mlsanity.com/paper/1802.09464/) (2018)
- [Contrastive Learning as Goal-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2206.07568/) (2022)
- [Keep Doing What Worked: Behavioral Modelling Priors for Offline Reinforcement Learning](https://mlsanity.com/paper/2002.08396/) (2020)
- [Unsupervised State Representation Learning in Atari](https://mlsanity.com/paper/1906.08226/) (2019)
- [HIQL: Offline Goal-Conditioned RL with Latent States as Actions](https://mlsanity.com/paper/2307.11949/) (2023)
- [Scalable methods for computing state similarity in deterministic Markov Decision Processes](https://mlsanity.com/paper/1911.09291/) (2019)
- [PLAS: Latent Action Space for Offline Reinforcement Learning](https://mlsanity.com/paper/2011.07213/) (2020)
- [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)
- [Deployment-Efficient Reinforcement Learning via Model-Based Offline Optimization](https://mlsanity.com/paper/2006.03647/) (2020)
- [RAMBO-RL: Robust Adversarial Model-Based Offline Reinforcement Learning](https://mlsanity.com/paper/2204.12581/) (2022)

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

- [QuasiNav: Asymmetric Cost-Aware Navigation Planning with Constrained Quasimetric Reinforcement Learning](https://mlsanity.com/paper/2410.16666/) (2024)
- [Geometry of Uncertainty: Learning Metric Spaces for Multimodal State Estimation in RL](https://mlsanity.com/paper/2602.12087/) (2026)
- [World Models in Pieces: Structural Certification for General Agents](https://mlsanity.com/paper/2606.24842/) (2026)

## Abstract (arXiv)

We study the problem of learning optimal behavior from sub-optimal datasets for goal-conditioned offline reinforcement learning under sparse rewards, invertible actions and deterministic transitions. To mitigate the effects of distribution shift, we propose MetricRL, a method that combines metric learning for value function approximation with weighted imitation learning for policy estimation. MetricRL avoids conservative or behavior-cloning constraints, enabling effective learning even in severely sub-optimal regimes. We introduce distance monotonicity as a key property linking metric representations to optimality and design an objective that explicitly promotes it. Empirically, MetricRL consistently outperforms prior state-of-the-art goal-conditioned RL methods in recovering near-optimal behavior from sub-optimal offline data.