Generalized Information Gathering Under Dynamics Uncertainty

TL;DR

This paper introduces a unified framework for active information gathering in unknown dynamical systems, using Massey's directed information to create a general, model-agnostic cost function that connects to existing mutual information methods and is validated through diverse experiments.

Contribution

A unifying, model-agnostic framework for information gathering costs in dynamical systems, linking mutual information and information gain, with theoretical proofs and practical experiments.

Findings

Mutual information cost is a special case of the proposed Massey's directed information cost.

The framework provides theoretical justification for mutual information-based active learning.

Experiments demonstrate effectiveness across linear, nonlinear, and multi-agent systems.

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.