# Unifying Goal-Conditioned RL and Unsupervised Skill Learning via Control-Maximization

arXiv: https://arxiv.org/abs/2605.06145 · HTML: https://mlsanity.com/paper/2605.06145/

## Key facts

- Cited by 2 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 44 of its 71 references that are in the map.
- First posted on arXiv 7 May 2026.

## 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 44)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Meta-World: A Benchmark and Evaluation for Multi-Task and Meta Reinforcement Learning](https://mlsanity.com/paper/1910.10897/) (2019)
- [Curiosity-driven Exploration by Self-supervised Prediction](https://mlsanity.com/paper/1705.05363/) (2017)
- [Hindsight Experience Replay](https://mlsanity.com/paper/1707.01495/) (2017)
- [Diversity is All You Need: Learning Skills without a Reward Function](https://mlsanity.com/paper/1802.06070/) (2018)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Dynamics-Aware Unsupervised Discovery of Skills](https://mlsanity.com/paper/1907.01657/) (2019)
- [Large-Scale Study of Curiosity-Driven Learning](https://mlsanity.com/paper/1808.04355/) (2018)
- [Variational Intrinsic Control](https://mlsanity.com/paper/1611.07507/) (2016)
- [Automatic Goal Generation for Reinforcement Learning Agents](https://mlsanity.com/paper/1705.06366/) (2017)
- [Contrastive Learning as Goal-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2206.07568/) (2022)
- [Visual Reinforcement Learning with Imagined Goals](https://mlsanity.com/paper/1807.04742/) (2018)
- [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017)
- [Skew-Fit: State-Covering Self-Supervised Reinforcement Learning](https://mlsanity.com/paper/1903.03698/) (2019)
- [Variational Information Maximisation for Intrinsically Motivated Reinforcement Learning](https://mlsanity.com/paper/1509.08731/) (2015)
- [Discovering and Achieving Goals via World Models](https://mlsanity.com/paper/2110.09514/) (2021)
- [Variational Option Discovery Algorithms](https://mlsanity.com/paper/1807.10299/) (2018)
- [Optimal Goal-Reaching Reinforcement Learning via Quasimetric Learning](https://mlsanity.com/paper/2304.01203/) (2023)
- [C-Learning: Learning to Achieve Goals via Recursive Classification](https://mlsanity.com/paper/2011.08909/) (2020)
- [Unsupervised Control Through Non-Parametric Discriminative Rewards](https://mlsanity.com/paper/1811.11359/) (2018)
- [DeepReach: A Deep Learning Approach to High-Dimensional Reachability](https://mlsanity.com/paper/2011.02082/) (2020)
- [Temporal Difference Models: Model-Free Deep RL for Model-Based Control](https://mlsanity.com/paper/1802.09081/) (2018)
- [METRA: Scalable Unsupervised RL with Metric-Aware Abstraction](https://mlsanity.com/paper/2310.08887/) (2023)
- [Empowerment -- an Introduction](https://mlsanity.com/paper/1310.1863/) (2013)
- [CIC: Contrastive Intrinsic Control for Unsupervised Skill Discovery](https://mlsanity.com/paper/2202.00161/) (2022)
- [Lipschitz-constrained Unsupervised Skill Discovery](https://mlsanity.com/paper/2202.00914/) (2022)
- [The Information Geometry of Unsupervised Reinforcement Learning](https://mlsanity.com/paper/2110.02719/) (2021)

## Built on by (most cited first, 2 of 2)

- [Learning Object Manipulation from Scratch via Contrastive Interaction](https://mlsanity.com/paper/2606.11525/) (2026)
- [What Pretraining and Midtraining Make Learnable from Rewards?](https://mlsanity.com/paper/2609.38446/) (2026)

## Abstract (arXiv)

Unsupervised pretraining has driven empirical advances in goal-conditioned reinforcement learning (GCRL), but its theoretical foundations remain poorly understood. In particular, an influential class of methods, mutual information skill learning (MISL), discovers behaviorally diverse skills that can later be used for downstream goal-reaching. However, it remains a theoretical mystery why skills learned through MISL should support goal-reaching. A subtle challenge is that both GCRL and MISL are umbrella terms: different GCRL tasks use distinct criteria for measuring goal-reaching performance, while different MISL methods optimize distinct notions of behavioral diversity. We address this challenge and unify GCRL and MISL as instances of control maximization. We identify three canonical GCRL formulations and prove that they are fundamentally inequivalent: they can induce incompatible optimal policies even in the same environment. Nevertheless, they all share a common interpretation: a well-performing goal-conditioned policy is one whose future trajectory is highly sensitive to the commanded goal, with the precise notion of sensitivity determined by the GCRL formulation. Noting that MISL objectives can be understood as measures of skill-sensitivity akin to goal-sensitivity, we show that MISL objectives are bounded by formulation-specific downstream goal-sensitivities. These bounds establish a precise correspondence between MISL methods and downstream GCRL tasks: for every GCRL formulation, there exists a matching MISL objective for which more diverse skills afford greater downstream goal sensitivity. Our results thus lay a theoretical foundation for RL pretraining and have important practical implications, such as suggesting which pretraining objectives to use when a user cares about a specific class of downstream tasks.