TL;DR
This paper introduces Graph Controllable Embeddings (GCE), a novel framework that uses Hilbert space embeddings and graph neural networks to model and control stochastic multi-object systems with varying interactions and topologies.
Contribution
GCE is a general, scalable framework that combines RKHS embeddings, mean field approximation, and GNNs to effectively model and control complex stochastic multi-object dynamics.
Findings
GCE outperforms existing embedding methods in experiments.
GCE generalizes to unseen topologies with limited data.
GCE enables effective control in physical, robotic, and power grid systems.
Abstract
This paper studies how to achieve accurate modeling and effective control in stochastic nonlinear dynamics with multiple interacting objects. However, non-uniform interactions and random topologies make this task challenging. We address these challenges by proposing \textit{Graph Controllable Embeddings} (GCE), a general framework to learn stochastic multi-object dynamics for linear control. Specifically, GCE is built on Hilbert space embeddings, allowing direct embedding of probability distributions of controlled stochastic dynamics into a reproducing kernel Hilbert space (RKHS), which enables linear operations in its RKHS while retaining nonlinear expressiveness. We provide theoretical guarantees on the existence, convergence, and applicability of GCE. Notably, a mean field approximation technique is adopted to efficiently capture inter-object dependencies and achieve provably low…
Peer Reviews
Decision·ICLR 2026 Poster
1. The idea is novel. It leverages the linear properties of RKHS to map originally complex nonlinear stochastic dynamics into RKHS, converting them into linear relationships. This further enables the adaptation of mature linear control methods, effectively overcoming the traditional challenges of nonlinear stochastic control for multi-body systems. 2. The theoretical analysis is detailed and comprehensive. Rigorous derivations are provided for aspects including the existence and convergence of t
1. Regarding the theoretical analysis in this paper, although convergence and consistency are mentioned as a key contribution in the Introduction section, multi-step approximate derivations (such as Equation (6) only using first-order approximation and adaptive mean field approximation) may undermine the aforementioned theoretical characteristics, leading to a significant deviation between practical implementation and theoretical guarantees. 2. Regarding scalability and generalization, although
The paper's contribution is well-supported by its technical components. The proposed framework is built upon the established theory of Kernel Bayes' Rule and provides a principled way to unify several graph-based embedding approaches under a single lens. Its core technical contribution is the introduction of a mean-field approximation to model adaptive, non-uniform interactions, which addresses a specific, documented limitation of prior methods like CKO. The paper includes theoretical proofs for
- The most efficient and recommended model variant, `Hom+Mean`, relies on a strong homogeneity assumption where all objects share the same underlying dynamics operator $C_{O|H}$. This may limit its applicability to highly heterogeneous multi-agent systems, where different types of agents (e.g., a mix of ground robots and aerial drones) possess fundamentally different transition models. The experiments, while strong, do not feature such a deeply heterogeneous environment to test this boundary. -
* The paper is exceptionally clear and well-written. It provides a strong motivation by precisely identifying the limitations of existing deterministic and non-controllable methods. The proposed framework is derived logically, making the theoretical foundations accessible. * The work is built on a strong theoretical foundation. It provides a principled framework for stochastic multi-object control by extending Hilbert space embeddings (RKHS) to handle probability distributions of system dynamic
* The "homogeneity" assumption, which uses a single shared operator for history dynamics, appears to contradict its application to environments with explicitly heterogeneous object types (like 'Soft' and 'Rope'). It is unclear how one operator can model the distinct dynamics of different object types. * The scalability claims are weakened by the model's design. While the mean-field approximation reduces the history term's complexity, the action term remains dense and scales quadratically with t
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
