# Independently Controllable Factors

arXiv: https://arxiv.org/abs/1708.01289 · HTML: https://mlsanity.com/paper/1708.01289/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Aug 2017.

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

- [Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICA](https://mlsanity.com/paper/2107.10098/) (2021)
- [Desiderata for Representation Learning: A Causal Perspective](https://mlsanity.com/paper/2109.03795/) (2021)
- [Action-Sufficient State Representation Learning for Control with Structural Constraints](https://mlsanity.com/paper/2110.05721/) (2021)
- [Which Mutual-Information Representation Learning Objectives are Sufficient for Control?](https://mlsanity.com/paper/2106.07278/) (2021)
- [Continuous MDP Homomorphisms and Homomorphic Policy Gradient](https://mlsanity.com/paper/2209.07364/) (2022)
- [Homomorphism Autoencoder -- Learning Group Structured Representations from Observed Transitions](https://mlsanity.com/paper/2207.12067/) (2022)
- [Towards a Grounded Theory of Causation for Embodied AI](https://mlsanity.com/paper/2206.13973/) (2022)
- [Policy Gradient Methods in the Presence of Symmetries and State Abstractions](https://mlsanity.com/paper/2305.05666/) (2023)
- [Reinforcement Learning with Exogenous States and Rewards](https://mlsanity.com/paper/2303.12957/) (2023)
- [Disentangled (Un)Controllable Features](https://mlsanity.com/paper/2211.00086/) (2022)
- [Dueling World Models: Advantage-Style Action Channels for Common-Mode Distractor Rejection](https://mlsanity.com/paper/2608.06706/) (2026)
- [Curricula for Learning Robust Policies with Factored State Representations in Changing Environments](https://mlsanity.com/paper/2409.09169/) (2024)

## Abstract (arXiv)

It has been postulated that a good representation is one that disentangles the underlying explanatory factors of variation. However, it remains an open question what kind of training framework could potentially achieve that. Whereas most previous work focuses on the static setting (e.g., with images), we postulate that some of the causal factors could be discovered if the learner is allowed to interact with its environment. The agent can experiment with different actions and observe their effects. More specifically, we hypothesize that some of these factors correspond to aspects of the environment which are independently controllable, i.e., that there exists a policy and a learnable feature for each such aspect of the environment, such that this policy can yield changes in that feature with minimal changes to other features that explain the statistical variations in the observed data. We propose a specific objective function to find such factors and verify experimentally that it can indeed disentangle independently controllable aspects of the environment without any extrinsic reward signal.