AdaptNC: Adaptive Nonconformity Scores for Uncertainty-Aware Autonomous Systems in Dynamic Environments

Rigorous uncertainty quantification is essential for the safe deployment of autonomous systems in unconstrained environments. Conformal Prediction (CP) provides a distribution-free framework for this task, yet its standard formulations rely on exchangeability assumptions that are violated by the distribution shifts inherent in real-world robotics. Existing online CP methods maintain target coverage by adaptively scaling the conformal threshold, but typically employ a static nonconformity score function. We show that this fixed geometry leads to highly conservative, volume-inefficient prediction regions when environments undergo structural shifts. To address this, we propose \textbf{AdaptNC}, a framework for the joint online adaptation of both the nonconformity score parameters and the conformal threshold. AdaptNC leverages an adaptive reweighting scheme to optimize score functions, and introduces a replay buffer mechanism to mitigate the coverage instability that occurs during score transitions. We evaluate AdaptNC on diverse robotic benchmarks involving multi-agent policy changes, environmental changes and sensor degradation. Our results demonstrate that AdaptNC significantly reduces prediction region volume compared to state-of-the-art threshold-only baselines while maintaining target coverage levels.

💡 Research Summary

The paper tackles a fundamental limitation of existing online conformal prediction (CP) methods for autonomous systems operating under distribution shift. While prior work has focused on adaptively scaling the conformal quantile to preserve a target coverage level, it has kept the nonconformity score function fixed. A static score leads to overly conservative, high‑volume prediction regions when the environment’s underlying data distribution changes structurally, which in turn hampers downstream control and decision‑making.

AdaptNC (Adaptive Nonconformity Scores) is introduced as a unified framework that jointly adapts both the nonconformity score parameters θ_t and the conformal threshold q_{1‑α,t}. The method builds on the “distribution‑to‑any” CP (DtA CI) algorithm, which maintains a pool of k candidate adaptation rates γ_i and updates their weights w_{i,t} exponentially based on recent coverage errors. These expert weights provide a real‑time estimate of how quickly the data distribution is drifting.

The core of AdaptNC consists of three steps repeated at each time step t:

1. Conformal Threshold Update – Using the current expert weights, an averaged quantile \bar{α}t is computed and the corresponding quantile q{1‑\bar{α},D_t} is applied to the present score function. This step preserves the long‑run coverage guarantee proved in Theorem C.1, which bounds the gap between the estimated quantile and the unknown optimal quantile α*_t.

2. Score Parameter Adaptation – A history buffer H stores recent triples (X, Y, \hat Y). Each entry is re‑weighted by ω_t, a function of the expert weights and learning rates (Equation 4). The re‑weighted empirical distribution H_ω is then used to solve a volume‑minimization problem: minimize the Lebesgue volume of the set {y : s(X,y;θ) ≤ q_{1‑α,t}} subject to the weighted coverage constraint. Practically, the authors employ a two‑stage procedure: (a) kernel density estimation (KDE) on the weighted samples to locate high‑density regions covering 1‑α of the mass, and (b) fitting a convex template (e.g., an ellipsoid) around these regions, which defines the new nonconformity score. Gradient‑based optimization refines θ_t online.

3. Replay Mechanism – Changing the score function can cause an abrupt “coverage shock” because the distribution of scores shifts. To mitigate this, a replay buffer re‑processes a recent window of observations after each score update, recomputing scores and the quantile on the same data. This stabilizes coverage until the new score settles. The replay step is executed only every t_s steps to keep computational cost manageable.

The authors provide a theoretical analysis showing asymptotic convergence of both coverage and score parameters, assuming the distribution shift eventually decays.

Empirical evaluation spans three robotic benchmarks: (i) multi‑agent policy switches, (ii) environmental changes (indoor‑outdoor lighting, terrain), and (iii) sensor degradation (gradual loss of LiDAR range). Baselines include DtA CI, Adaptive Conformal Inference, and fixed‑score online CP. Across all scenarios, AdaptNC reduces the average prediction region volume by 20‑35 % while maintaining coverage within 1‑2 % of the 95 % target. Notably, in the sensor‑degradation experiment, the adaptive score quickly contracts the region around the remaining reliable measurements, preventing the dramatic volume blow‑up observed in baseline methods.

The paper also discusses practical considerations: the score‑adaptation step incurs extra computation (KDE, gradient updates), and performance is sensitive to the replay buffer size and adaptation interval t_s. For high‑dimensional outputs (e.g., images), convex templates may be insufficient, suggesting future work on richer, possibly non‑convex score families.

In summary, AdaptNC represents the first systematic approach that treats the nonconformity score as a mutable component in online CP under distribution shift. By coupling adaptive re‑weighting with a replay‑based stabilization, it delivers tighter, more informative uncertainty sets without sacrificing the rigorous coverage guarantees essential for safety‑critical autonomous systems.