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Learning Causal Dynamics Models in Object-Oriented Environments

Zhongwei Yu, Jingqing Ruan, Dengpeng Xing

TL;DR

The paper tackles scalable learning of causal dynamics in large-scale object-oriented environments by proposing OOCDM, which shares causal structure and predictors across objects of the same class. It formalizes an Object-Oriented Canonical Graph (OOCG), develops class-shared field predictors with attention, and introduces a class-level causal discovery mechanism using CMIs. The approach dramatically reduces causal-discovery complexity, improves graph and predictive accuracy, and enhances generalization and planning performance, especially in tasks with many objects or varying instance counts. Augmentations to handle asymmetric dynamics extend applicability beyond strictly symmetric OO settings, positioning OOCDM as a practical framework for scalable, causality-aware world models in RL.

Abstract

Causal dynamics models (CDMs) have demonstrated significant potential in addressing various challenges in reinforcement learning. To learn CDMs, recent studies have performed causal discovery to capture the causal dependencies among environmental variables. However, the learning of CDMs is still confined to small-scale environments due to computational complexity and sample efficiency constraints. This paper aims to extend CDMs to large-scale object-oriented environments, which consist of a multitude of objects classified into different categories. We introduce the Object-Oriented CDM (OOCDM) that shares causalities and parameters among objects belonging to the same class. Furthermore, we propose a learning method for OOCDM that enables it to adapt to a varying number of objects. Experiments on large-scale tasks indicate that OOCDM outperforms existing CDMs in terms of causal discovery, prediction accuracy, generalization, and computational efficiency.

Learning Causal Dynamics Models in Object-Oriented Environments

TL;DR

The paper tackles scalable learning of causal dynamics in large-scale object-oriented environments by proposing OOCDM, which shares causal structure and predictors across objects of the same class. It formalizes an Object-Oriented Canonical Graph (OOCG), develops class-shared field predictors with attention, and introduces a class-level causal discovery mechanism using CMIs. The approach dramatically reduces causal-discovery complexity, improves graph and predictive accuracy, and enhances generalization and planning performance, especially in tasks with many objects or varying instance counts. Augmentations to handle asymmetric dynamics extend applicability beyond strictly symmetric OO settings, positioning OOCDM as a practical framework for scalable, causality-aware world models in RL.

Abstract

Causal dynamics models (CDMs) have demonstrated significant potential in addressing various challenges in reinforcement learning. To learn CDMs, recent studies have performed causal discovery to capture the causal dependencies among environmental variables. However, the learning of CDMs is still confined to small-scale environments due to computational complexity and sample efficiency constraints. This paper aims to extend CDMs to large-scale object-oriented environments, which consist of a multitude of objects classified into different categories. We introduce the Object-Oriented CDM (OOCDM) that shares causalities and parameters among objects belonging to the same class. Furthermore, we propose a learning method for OOCDM that enables it to adapt to a varying number of objects. Experiments on large-scale tasks indicate that OOCDM outperforms existing CDMs in terms of causal discovery, prediction accuracy, generalization, and computational efficiency.
Paper Structure (76 sections, 22 theorems, 106 equations, 11 figures, 14 tables, 3 algorithms)

This paper contains 76 sections, 22 theorems, 106 equations, 11 figures, 14 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related works
  3. Causality and Reinforcement Learning
  4. Object-Oriented Reinforcement Learning
  5. Relational Causal Discovery
  6. Preliminaries
  7. Notations
  8. Causal Dynamics Models
  9. Object-Oriented Markov Decision Process
  10. Method
  11. Object-Oriented Causal Graph
  12. Object-Oriented Causal Dynamics Model
  13. Object-Oriented Causal Discovery
  14. Model Learning
  15. Releasing Dynamic Symmetries
  16. ...and 61 more sections

Key Result

Theorem 3.2

Assuming that state variables transit independently, i.e. $p({\mathbf{S}}'|{\mathbf{S}}, {\mathbf{A}}) = \prod_{j=1}^{n_s} p({\textnormal{S}}_j'|{\mathbf{S}}, {\mathbf{A}})$, then the ground-truth causal graph ${\mathcal{G}}$ is bipartite. That is, all edges start in $({\mathbf{S}}, {\mathbf{A}})$ a for each ${\textnormal{X}}_i \in ({\mathbf{S}}, {\mathbf{A}})$ and $\ {\textnormal{S}}_j' \in {\mat

Figures (11)

  • Figure 1: An OOMDP for Starcraft with the causation symmetry.
  • Figure 2: The workflow overview.
  • Figure 3: The class-level causalities in Example \ref{['example:starcraft']}.
  • Figure 4: The illustration of $f_{C_1.V}(O_1.{\textnormal{V}}'|{\mathbf{S}}, {\mathbf{A}}; {\mathcal{G}})$.
  • Figure 5: The dense dynamics model and causal dynamics model for a simple kinetic system.
  • ...and 6 more figures

Theorems & Definitions (58)

  • Definition 3.1
  • Theorem 3.2: Causal discovery for CDMs
  • Example 3.3
  • Definition 4.2
  • Theorem 4.3
  • Definition 4.4
  • Definition 2.1: Markov Compatibility
  • Theorem 2.2: Existence of causal graphs
  • proof
  • Definition 2.3: Bayesian Network
  • ...and 48 more