Generalized Information Gathering Under Dynamics Uncertainty

2026-01-29

AI Summary

This work addresses the limited generality of existing active learning methods in unknown dynamical systems, which often rely on restrictive modeling assumptions. The authors propose a unified framework that explicitly models the causal dependencies among parameters, beliefs, and control actions, thereby decoupling information-gathering costs from specific system models. Central to this framework is a general information acquisition criterion based on Massey’s directed information, for which mutual information is shown to be a special case. Theoretical connections are established between this criterion and the information gain in linearized Bayesian estimation. By integrating causal modeling, directed information theory, Bayesian updating, and general-purpose planning, the approach is applicable to linear, nonlinear, and multi-agent systems. Experimental results demonstrate its broad applicability and provide a theoretical foundation for mutual information–driven active learning.

Technology Category

• Machine Learning: Active Learning
• Multiagent Systems: Multiagent Learning
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

An agent operating in an unknown dynamical system must learn its dynamics from observations. Active information gathering accelerates this learning, but existing methods derive bespoke costs for specific modeling choices: dynamics models, belief update procedures, observation models, and planners. We present a unifying framework that decouples these choices from the information-gathering cost by explicitly exposing the causal dependencies between parameters, beliefs, and controls. Using this framework, we derive a general information-gathering cost based on Massey's directed information that assumes only Markov dynamics with additive noise and is otherwise agnostic to modeling choices. We prove that the mutual information cost used in existing literature is a special case of our cost. Then, we leverage our framework to establish an explicit connection between the mutual information cost and information gain in linearized Bayesian estimation, thereby providing theoretical justification for mutual information-based active learning approaches. Finally, we illustrate the practical utility of our framework through experiments spanning linear, nonlinear, and multi-agent systems.

Problem

• information gathering
• dynamics uncertainty
• active learning
• Markov dynamics
• directed information

Innovation

• active information gathering
• directed information
• model-agnostic
• causal dependencies
• Bayesian estimation