# Conformal Prediction in The Loop: A Feedback-Based Uncertainty Model for Trajectory Optimization

arXiv: https://arxiv.org/abs/2510.16376 · HTML: https://mlsanity.com/paper/2510.16376/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 50 references that are in the map.
- First posted on arXiv 18 Oct 2025.

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

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [AgentFormer: Agent-Aware Transformers for Socio-Temporal Multi-Agent Forecasting](https://mlsanity.com/paper/2103.14023/) (2021)
- [Conformal Language Modeling](https://mlsanity.com/paper/2306.10193/) (2023)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Human Trajectory Forecasting in Crowds: A Deep Learning Perspective](https://mlsanity.com/paper/2007.03639/) (2020)
- [Safe Planning in Dynamic Environments using Conformal Prediction](https://mlsanity.com/paper/2210.10254/) (2022)
- [Conformal PID Control for Time Series Prediction](https://mlsanity.com/paper/2307.16895/) (2023)
- [Diverse Trajectory Forecasting with Determinantal Point Processes](https://mlsanity.com/paper/1907.04967/) (2019)
- [Sequential Predictive Conformal Inference for Time Series](https://mlsanity.com/paper/2212.03463/) (2022)
- [Conformal Prediction Under Feedback Covariate Shift for Biomolecular Design](https://mlsanity.com/paper/2202.03613/) (2022)
- [Adaptive Conformal Prediction for Motion Planning among Dynamic Agents](https://mlsanity.com/paper/2212.00278/) (2022)
- [Conformal Decision Theory: Safe Autonomous Decisions from Imperfect Predictions](https://mlsanity.com/paper/2310.05921/) (2023)
- [Conformal Prediction for Time Series with Modern Hopfield Networks](https://mlsanity.com/paper/2303.12783/) (2023)
- [Length Optimization in Conformal Prediction](https://mlsanity.com/paper/2406.18814/) (2024)
- [Conformal prediction for multi-dimensional time series by ellipsoidal sets](https://mlsanity.com/paper/2403.03850/) (2024)
- [Conformal Prediction Regions for Time Series using Linear Complementarity Programming](https://mlsanity.com/paper/2304.01075/) (2023)
- [Model-Based Diffusion for Trajectory Optimization](https://mlsanity.com/paper/2407.01573/) (2024)
- [Efficient and Differentiable Conformal Prediction with General Function Classes](https://mlsanity.com/paper/2202.11091/) (2022)
- [Conformal Validity Guarantees Exist for Any Data Distribution (and How to Find Them)](https://mlsanity.com/paper/2405.06627/) (2024)
- [Multi-Agent Reachability Calibration with Conformal Prediction](https://mlsanity.com/paper/2304.00432/) (2023)
- [Robots That Can See: Leveraging Human Pose for Trajectory Prediction](https://mlsanity.com/paper/2309.17209/) (2023)
- [Robust Yet Efficient Conformal Prediction Sets](https://mlsanity.com/paper/2407.09165/) (2024)
- [Conformal Predictive Safety Filter for RL Controllers in Dynamic Environments](https://mlsanity.com/paper/2306.02551/) (2023)
- [Adaptive Conformal Inference by Betting](https://mlsanity.com/paper/2412.19318/) (2024)
- [Multi-Source Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2405.09331/) (2024)
- [Conformalized Adaptive Forecasting of Heterogeneous Trajectories](https://mlsanity.com/paper/2402.09623/) (2024)
- [Wasserstein Distributionally Robust Motion Control for Collision Avoidance Using Conditional Value-at-Risk](https://mlsanity.com/paper/2001.04727/) (2020)
- [Safety-Critical Control with Uncertainty Quantification using Adaptive Conformal Prediction](https://mlsanity.com/paper/2407.03569/) (2024)

## Built on by (most cited first, 3 of 3)

- [Conformal Policy Control](https://mlsanity.com/paper/2603.02196/) (2026)
- [Counterfactual Online Conformal Prediction Under Adaptive Logging](https://mlsanity.com/paper/2609.30811/) (2026)
- [Multivariate conformal uncertainty propagation in multitask atomistic simulation: Successes and pitfalls](https://mlsanity.com/paper/2609.31384/) (2026)

## Abstract (arXiv)

Conformal Prediction (CP) is a powerful statistical machine learning tool to construct uncertainty sets with coverage guarantees, which has fueled its extensive adoption in generating prediction regions for decision-making tasks, e.g., Trajectory Optimization (TO) in uncertain environments. However, existing methods predominantly employ a sequential scheme, where decisions rely unidirectionally on the prediction regions, and consequently the information from decision-making fails to be fed back to instruct CP. In this paper, we propose a novel Feedback-Based CP (Fb-CP) framework for shrinking-horizon TO with a joint risk constraint over the entire mission time. Specifically, a CP-based posterior risk calculation method is developed by fully leveraging the realized trajectories to adjust the posterior allowable risk, which is then allocated to future times to update prediction regions. In this way, the information in the realized trajectories is continuously fed back to the CP, enabling attractive feedback-based adjustments of the prediction regions and a provable online improvement in trajectory performance. Furthermore, we theoretically prove that such adjustments consistently maintain the coverage guarantees of the prediction regions, thereby ensuring provable safety. Additionally, we develop a decision-focused iterative risk allocation algorithm with theoretical convergence analysis for allocating the posterior allowable risk which closely aligns with Fb-CP. Furthermore, we extend the proposed method to handle distribution shift. The effectiveness and superiority of the proposed method are demonstrated through benchmark experiments.