# METRA: Scalable Unsupervised RL with Metric-Aware Abstraction

arXiv: https://arxiv.org/abs/2310.08887 · HTML: https://mlsanity.com/paper/2310.08887/

## Key facts

- Cited by 86 papers in the map (data through 14 Oct 2026).
- Builds on 82 of its 106 references that are in the map.
- First posted on arXiv 13 Oct 2023.

## Builds on (most cited first, 30 of 82)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Dream to Control: Learning Behaviors by Latent Imagination](https://mlsanity.com/paper/1912.01603/) (2019)
- [Soft Actor-Critic Algorithms and Applications](https://mlsanity.com/paper/1812.05905/) (2018)
- [Curiosity-driven Exploration by Self-supervised Prediction](https://mlsanity.com/paper/1705.05363/) (2017)
- [Exploration by Random Network Distillation](https://mlsanity.com/paper/1810.12894/) (2018)
- [DeepMind Control Suite](https://mlsanity.com/paper/1801.00690/) (2018)
- [Diversity is All You Need: Learning Skills without a Reward Function](https://mlsanity.com/paper/1802.06070/) (2018)
- [Unifying Count-Based Exploration and Intrinsic Motivation](https://mlsanity.com/paper/1606.01868/) (2016)
- [Image Augmentation Is All You Need: Regularizing Deep Reinforcement Learning from Pixels](https://mlsanity.com/paper/2004.13649/) (2020)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Temporal Difference Learning for Model Predictive Control](https://mlsanity.com/paper/2203.04955/) (2022)
- [Relay Policy Learning: Solving Long-Horizon Tasks via Imitation and Reinforcement Learning](https://mlsanity.com/paper/1910.11956/) (2019)
- [Planning to Explore via Self-Supervised World Models](https://mlsanity.com/paper/2005.05960/) (2020)
- [Dynamics-Aware Unsupervised Discovery of Skills](https://mlsanity.com/paper/1907.01657/) (2019)
- [#Exploration: A Study of Count-Based Exploration for Deep Reinforcement Learning](https://mlsanity.com/paper/1611.04717/) (2016)
- [Randomized Ensembled Double Q-Learning: Learning Fast Without a Model](https://mlsanity.com/paper/2101.05982/) (2021)
- [Variational Intrinsic Control](https://mlsanity.com/paper/1611.07507/) (2016)
- [First return, then explore](https://mlsanity.com/paper/2004.12919/) (2020)
- [Self-Supervised Exploration via Disagreement](https://mlsanity.com/paper/1906.04161/) (2019)
- [Count-Based Exploration with Neural Density Models](https://mlsanity.com/paper/1703.01310/) (2017)
- [Provably Efficient Maximum Entropy Exploration](https://mlsanity.com/paper/1812.02690/) (2018)
- [Never Give Up: Learning Directed Exploration Strategies](https://mlsanity.com/paper/2002.06038/) (2020)
- [Semi-parametric Topological Memory for Navigation](https://mlsanity.com/paper/1803.00653/) (2018)
- [Search on the Replay Buffer: Bridging Planning and Reinforcement Learning](https://mlsanity.com/paper/1906.05253/) (2019)

## Built on by (most cited first, 30 of 86)

- [OGBench: Benchmarking Offline Goal-Conditioned RL](https://mlsanity.com/paper/2410.20092/) (2024)
- [Flow Q-Learning](https://mlsanity.com/paper/2502.02538/) (2025)
- [Foundation Policies with Hilbert Representations](https://mlsanity.com/paper/2402.15567/) (2024)
- [SimBa: Simplicity Bias for Scaling Up Parameters in Deep Reinforcement Learning](https://mlsanity.com/paper/2410.09754/) (2024)
- [Sparse Diffusion Policy: A Sparse, Reusable, and Flexible Policy for Robot Learning](https://mlsanity.com/paper/2407.01531/) (2024)
- [Learning Temporal Distances: Contrastive Successor Features Can Provide a Metric Structure for Decision-Making](https://mlsanity.com/paper/2406.17098/) (2024)
- [Zero-Shot Whole-Body Humanoid Control via Behavioral Foundation Models](https://mlsanity.com/paper/2504.11054/) (2025)
- [Unsupervised Zero-Shot Reinforcement Learning via Functional Reward Encodings](https://mlsanity.com/paper/2402.17135/) (2024)
- [Reward Models in Deep Reinforcement Learning: A Survey](https://mlsanity.com/paper/2506.15421/) (2025)
- [Overcoming the Sim-to-Real Gap: Leveraging Simulation to Learn to Explore for Real-World RL](https://mlsanity.com/paper/2410.20254/) (2024)
- [Can a MISL Fly? Analysis and Ingredients for Mutual Information Skill Learning](https://mlsanity.com/paper/2412.08021/) (2024)
- [Fast Adaptation with Behavioral Foundation Models](https://mlsanity.com/paper/2504.07896/) (2025)
- [Proto Successor Measure: Representing the Behavior Space of an RL Agent](https://mlsanity.com/paper/2411.19418/) (2024)
- [TLDR: Unsupervised Goal-Conditioned RL via Temporal Distance-Aware Representations](https://mlsanity.com/paper/2407.08464/) (2024)
- [Language Guided Skill Discovery](https://mlsanity.com/paper/2406.06615/) (2024)
- [Episodic Novelty Through Temporal Distance](https://mlsanity.com/paper/2501.15418/) (2025)
- [Dual Goal Representations](https://mlsanity.com/paper/2510.06714/) (2025)
- [Leveraging Skills from Unlabeled Prior Data for Efficient Online Exploration](https://mlsanity.com/paper/2410.18076/) (2024)
- [State-Covering Trajectory Stitching for Diffusion Planners](https://mlsanity.com/paper/2506.00895/) (2025)
- [DISCOVER: Automated Curricula for Sparse-Reward Reinforcement Learning](https://mlsanity.com/paper/2505.19850/) (2025)
- [Unsupervised-to-Online Reinforcement Learning](https://mlsanity.com/paper/2408.14785/) (2024)
- [PEAC: Unsupervised Pre-training for Cross-Embodiment Reinforcement Learning](https://mlsanity.com/paper/2405.14073/) (2024)
- [Disentangled Unsupervised Skill Discovery for Efficient Hierarchical Reinforcement Learning](https://mlsanity.com/paper/2410.11251/) (2024)
- [Intention-Conditioned Flow Occupancy Models](https://mlsanity.com/paper/2506.08902/) (2025)
- [Align Your Intents: Offline Imitation Learning via Optimal Transport](https://mlsanity.com/paper/2402.13037/) (2024)
- [Constrained Ensemble Exploration for Unsupervised Skill Discovery](https://mlsanity.com/paper/2405.16030/) (2024)
- [Do's and Don'ts: Learning Desirable Skills with Instruction Videos](https://mlsanity.com/paper/2406.00324/) (2024)
- [Epistemically-guided forward-backward exploration](https://mlsanity.com/paper/2507.05477/) (2025)
- [RLZero: Direct Policy Inference from Language Without In-Domain Supervision](https://mlsanity.com/paper/2412.05718/) (2024)
- [Dr. Strategy: Model-Based Generalist Agents with Strategic Dreaming](https://mlsanity.com/paper/2402.18866/) (2024)

## Abstract (arXiv)

Unsupervised pre-training strategies have proven to be highly effective in natural language processing and computer vision. Likewise, unsupervised reinforcement learning (RL) holds the promise of discovering a variety of potentially useful behaviors that can accelerate the learning of a wide array of downstream tasks. Previous unsupervised RL approaches have mainly focused on pure exploration and mutual information skill learning. However, despite the previous attempts, making unsupervised RL truly scalable still remains a major open challenge: pure exploration approaches might struggle in complex environments with large state spaces, where covering every possible transition is infeasible, and mutual information skill learning approaches might completely fail to explore the environment due to the lack of incentives. To make unsupervised RL scalable to complex, high-dimensional environments, we propose a novel unsupervised RL objective, which we call Metric-Aware Abstraction (METRA). Our main idea is, instead of directly covering the entire state space, to only cover a compact latent space Z that is metrically connected to the state space S by temporal distances. By learning to move in every direction in the latent space, METRA obtains a tractable set of diverse behaviors that approximately cover the state space, being scalable to high-dimensional environments. Through our experiments in five locomotion and manipulation environments, we demonstrate that METRA can discover a variety of useful behaviors even in complex, pixel-based environments, being the first unsupervised RL method that discovers diverse locomotion behaviors in pixel-based Quadruped and Humanoid. Our code and videos are available at https://seohong.me/projects/metra/