Geometry of Uncertainty: Learning Metric Spaces for Multimodal State Estimation in RL

2026-02-12

AI Summary

This work addresses the core challenge in reinforcement learning of accurately estimating environmental states from high-dimensional, multimodal, and noisy observations. It proposes a geometric representation of uncertainty that obviates the need for explicit noise modeling or prior assumptions about noise distributions. By constructing a structured latent space where distances between states correspond to the minimum number of actions required to transition between them, the method embeds state-transition dynamics directly into the metric geometry of the space. A multimodal latent transition model, coupled with an inverse-distance-weighted sensor fusion mechanism, enables adaptive integration of heterogeneous perceptual inputs. Empirical results demonstrate that this approach significantly improves state estimation accuracy and agent decision-making performance across diverse multimodal reinforcement learning tasks, while exhibiting enhanced robustness to observation noise.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Multimodal Learning
• Reasoning under Uncertainty: Uncertainty Representations

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG

Abstract

Estimating the state of an environment from high-dimensional, multimodal, and noisy observations is a fundamental challenge in reinforcement learning (RL). Traditional approaches rely on probabilistic models to account for the uncertainty, but often require explicit noise assumptions, in turn limiting generalization. In this work, we contribute a novel method to learn a structured latent representation, in which distances between states directly correlate with the minimum number of actions required to transition between them. The proposed metric space formulation provides a geometric interpretation of uncertainty without the need for explicit probabilistic modeling. To achieve this, we introduce a multimodal latent transition model and a sensor fusion mechanism based on inverse distance weighting, allowing for the adaptive integration of multiple sensor modalities without prior knowledge of noise distributions. We empirically validate the approach on a range of multimodal RL tasks, demonstrating improved robustness to sensor noise and superior state estimation compared to baseline methods. Our experiments show enhanced performance of an RL agent via the learned representation, eliminating the need of explicit noise augmentation. The presented results suggest that leveraging transition-aware metric spaces provides a principled and scalable solution for robust state estimation in sequential decision-making.

Problem

• state estimation
• multimodal observations
• sensor noise
• uncertainty
• reinforcement learning

Innovation

• metric space
• multimodal state estimation
• uncertainty geometry
• sensor fusion
• latent transition model