# Counterfactual Quotient Models: Learning What Actions Change, Not What the World Does

arXiv: https://arxiv.org/abs/2608.22092 · HTML: https://mlsanity.com/paper/2608.22092/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 29 references that are in the map.
- First posted on arXiv 22 Aug 2026.

## Builds on (most cited first, 17 of 17)

- [Dream to Control: Learning Behaviors by Latent Imagination](https://mlsanity.com/paper/1912.01603/) (2019)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [DeepMind Control Suite](https://mlsanity.com/paper/1801.00690/) (2018)
- [Recurrent World Models Facilitate Policy Evolution](https://mlsanity.com/paper/1809.01999/) (2018)
- [When to Trust Your Model: Model-Based Policy Optimization](https://mlsanity.com/paper/1906.08253/) (2019)
- [Learning Invariant Representations for Reinforcement Learning without Reconstruction](https://mlsanity.com/paper/2006.10742/) (2020)
- [Successor Features for Transfer in Reinforcement Learning](https://mlsanity.com/paper/1606.05312/) (2016)
- [DeepMDP: Learning Continuous Latent Space Models for Representation Learning](https://mlsanity.com/paper/1906.02736/) (2019)
- [The Distracting Control Suite -- A Challenging Benchmark for Reinforcement Learning from Pixels](https://mlsanity.com/paper/2101.02722/) (2021)
- [The Value Equivalence Principle for Model-Based Reinforcement Learning](https://mlsanity.com/paper/2011.03506/) (2020)
- [The Predictron: End-To-End Learning and Planning](https://mlsanity.com/paper/1612.08810/) (2016)
- [Transfer in Deep Reinforcement Learning Using Successor Features and Generalised Policy Improvement](https://mlsanity.com/paper/1901.10964/) (2019)
- [Denoised MDPs: Learning World Models Better Than the World Itself](https://mlsanity.com/paper/2206.15477/) (2022)
- [Counterfactual Credit Assignment in Model-Free Reinforcement Learning](https://mlsanity.com/paper/2011.09464/) (2020)
- [Towards Robust Bisimulation Metric Learning](https://mlsanity.com/paper/2110.14096/) (2021)
- [Would I have gotten that reward? Long-term credit assignment by counterfactual contribution analysis](https://mlsanity.com/paper/2306.16803/) (2023)

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

- [When Low Prediction Error Misleads Planning: Diagnosing Representation, Dynamics, and Decision Failures in Latent World Models](https://mlsanity.com/paper/2610.05550/) (2026)
- [Coarse-Graining Recursive Expert Computation: Continuation-Relative Interfaces and Failure Modes](https://mlsanity.com/paper/2610.14413/) (2026)

## Abstract (arXiv)

Reinforcement-learning models commonly predict complete future states, observations, or feature occupancies, even though action selection depends only on differences between the consequences of candidate actions. As a result, these models may devote substantial statistical and representational capacity to high-dimensional phenomena that evolve independently of the agent's current choice. We introduce the Counterfactual Quotient Model, which treats action-conditioned futures as equivalent when they differ only by a component shared across actions. Its canonical centered representation removes this common component while preserving every pairwise action comparison expressible by the modeled reward family. The implemented model learns these action-dependent effects directly from synchronized counterfactual rollouts, so shared stochastic dynamics cancel before function approximation rather than after complete futures have been predicted. We establish the decision sufficiency, identifiability, common-mode invariance, approximation behavior, and regret properties of the resulting representation. Controlled experiments in physics-based environments provide initial evidence for these properties: direct effect learning suppresses action-independent variation, supports previously unseen reward queries, and improves action ranking relative to models trained to predict absolute futures.