Quantifying Aleatoric and Epistemic Dynamics Uncertainty via Local Conformal Calibration

TL;DR

LUCCa introduces a conformal-prediction-based calibration that converts the aleatoric uncertainty of an approximate dynamics $ ilde{f}$ into probabilistically valid prediction regions for future states using a calibration set $D_{cal}$ and Split Conformal Prediction. It builds a local, adaptive scaling via LOCART by learning per-region factors $\\xi_k$ through a decision-tree partition of the transformed input $ar{X}$, and uses a Mahalanobis distance-based non-conformity measure to generate residuals. For the first planning step, a single scaling $\\xi$ calibrates the covariance so that the hyperellipsoid around the predicted next state contains at least $(1-\\alpha)$ of the true next states; LOCART provides regional refinements to reflect local predictive difficulty. Under a linear-Gaussian $ ilde{f}$ and a one-step feedback controller, LUCCa's first-step safety guarantee extends to multi-step planning, and empirical results on a double-integrator show improved probabilistic safety versus an uncalibrated baseline while maintaining planning performance.

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.