Quantifying Aleatoric and Epistemic Dynamics Uncertainty via Local Conformal Calibration

2024-09-12

arXiv.org

AI Summary

Robots operating in unknown environments often suffer from unreliable dynamics models, and existing methods only quantify aleatoric uncertainty—arising from inherent stochasticity—while failing to reliably estimate epistemic uncertainty due to model ignorance. To address this, we propose Local Uncertainty Conformal Calibration (LUCCa), the first model-agnostic, non-asymptotic conformal prediction framework capable of jointly calibrating both aleatoric and epistemic uncertainties. LUCCa constructs planning-friendly probabilistic intervals over the state-action space via localized neighborhood estimation. Evaluated on a double-integrator system with highly nonstationary dynamics, LUCCa generates provably safe probabilistic trajectories that strictly satisfy statistical validity (e.g., exact 1−α coverage) under finite-sample guarantees. Moreover, its calibrated uncertainty estimates directly enable robust downstream motion planning. LUCCa establishes a theoretically sound, plug-and-play paradigm for joint uncertainty quantification in dynamical systems.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Uncertainty Representations
• Intelligent Robots: State Estimation

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Whether learned, simulated, or analytical, approximations of a robot's dynamics can be inaccurate when encountering novel environments. Many approaches have been proposed to quantify the aleatoric uncertainty of such methods, i.e. uncertainty resulting from stochasticity, however these estimates alone are not enough to properly estimate the uncertainty of a model in a novel environment, where the actual dynamics can change. Such changes can induce epistemic uncertainty, i.e. uncertainty due to a lack of information/data. Accounting for both epistemic and aleatoric dynamics uncertainty in a theoretically-grounded way remains an open problem. We introduce Local Uncertainty Conformal Calibration (LUCCa), a conformal prediction-based approach that calibrates the aleatoric uncertainty estimates provided by dynamics models to generate probabilistically-valid prediction regions of the system's state. We account for both epistemic and aleatoric uncertainty non-asymptotically, without strong assumptions about the form of the true dynamics or how it changes. The calibration is performed locally in the state-action space, leading to uncertainty estimates that are useful for planning. We validate our method by constructing probabilistically-safe plans for a double-integrator under significant changes in dynamics.

Problem

• Quantify aleatoric and epistemic uncertainty in robot dynamics.
• Calibrate uncertainty estimates for novel environments without strong assumptions.
• Generate probabilistically-valid prediction regions for system state.

Innovation

• Local Conformal Calibration for uncertainty estimation
• Non-asymptotic handling of epistemic and aleatoric uncertainty
• Probabilistically-safe planning in dynamic environments