# Generalized Information Gathering Under Dynamics Uncertainty

arXiv: https://arxiv.org/abs/2601.21988 · HTML: https://mlsanity.com/paper/2601.21988/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 63 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Builds on (most cited first, 30 of 32)

- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Efficient and Modular Implicit Differentiation](https://mlsanity.com/paper/2105.15183/) (2021)
- [Modern Bayesian Experimental Design](https://mlsanity.com/paper/2302.14545/) (2023)
- [Sample-efficient Cross-Entropy Method for Real-time Planning](https://mlsanity.com/paper/2008.06389/) (2020)
- [A Comparative Survey of Deep Active Learning](https://mlsanity.com/paper/2203.13450/) (2022)
- [Variational Bayesian Last Layers](https://mlsanity.com/paper/2404.11599/) (2024)
- [Meta-Learning Priors for Efficient Online Bayesian Regression](https://mlsanity.com/paper/1807.08912/) (2018)
- [Active Learning of Dynamics for Data-Driven Control Using Koopman Operators](https://mlsanity.com/paper/1906.05194/) (2019)
- [Optimistic Active Exploration of Dynamical Systems](https://mlsanity.com/paper/2306.12371/) (2023)
- [Actively Learning Gaussian Process Dynamics](https://mlsanity.com/paper/1911.09946/) (2019)
- [Active Learning in Robotics: A Review of Control Principles](https://mlsanity.com/paper/2106.13697/) (2021)
- [Online Natural Gradient as a Kalman Filter](https://mlsanity.com/paper/1703.00209/) (2017)
- [Stochastic Dynamic Games in Belief Space](https://mlsanity.com/paper/1909.06963/) (2019)
- [Safe Active Dynamics Learning and Control: A Sequential Exploration-Exploitation Framework](https://mlsanity.com/paper/2008.11700/) (2020)
- [TorchOpt: An Efficient Library for Differentiable Optimization](https://mlsanity.com/paper/2211.06934/) (2022)
- [Active Uncertainty Reduction for Safe and Efficient Interaction Planning: A Shielding-Aware Dual Control Approach](https://mlsanity.com/paper/2302.00171/) (2023)
- [Safe Active Learning for Time-Series Modeling with Gaussian Processes](https://mlsanity.com/paper/2402.06276/) (2024)
- [Learning to Play Trajectory Games Against Opponents with Unknown Objectives](https://mlsanity.com/paper/2211.13779/) (2022)
- [Dual Control for Approximate Bayesian Reinforcement Learning](https://mlsanity.com/paper/1510.03591/) (2015)
- [Active Learning with Dual Model Predictive Path-Integral Control for Interaction-Aware Autonomous Highway On-ramp Merging](https://mlsanity.com/paper/2310.07840/) (2023)
- [Auto-Encoding Bayesian Inverse Games](https://mlsanity.com/paper/2402.08902/) (2024)
- [First, Learn What You Don't Know: Active Information Gathering for Driving at the Limits of Handling](https://mlsanity.com/paper/2411.00107/) (2024)
- [Active Probing and Influencing Human Behaviors Via Autonomous Agents](https://mlsanity.com/paper/2304.11817/) (2023)
- [Dual Control for Interactive Autonomous Merging with Model Predictive Diffusion](https://mlsanity.com/paper/2502.09918/) (2025)
- [Smooth Information Gathering in Two-Player Noncooperative Games](https://mlsanity.com/paper/2404.00733/) (2024)
- [A Unified Framework for Robots that Influence Humans over Long-Term Interaction](https://mlsanity.com/paper/2503.14633/) (2025)
- [Online Competitive Information Gathering for Partially Observable Trajectory Games](https://mlsanity.com/paper/2506.01927/) (2025)
- [Active Probing with Multimodal Predictions for Motion Planning](https://mlsanity.com/paper/2507.09822/) (2025)
- [Optimization Outperforms Unscented Techniques for Nonlinear Smoothing](https://mlsanity.com/paper/2510.03846/) (2025)

## Abstract (arXiv)

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.