# Adaptive Conformal Inference by Betting

arXiv: https://arxiv.org/abs/2412.19318 · HTML: https://mlsanity.com/paper/2412.19318/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 29 references that are in the map.
- First posted on arXiv 26 Dec 2024.

## Built on by (most cited first, 12 of 12)

- [Error-quantified Conformal Inference for Time Series](https://mlsanity.com/paper/2502.00818/) (2025)
- [Direct Prediction Set Minimization via Bilevel Conformal Classifier Training](https://mlsanity.com/paper/2506.06599/) (2025)
- [Optimistic Interior Point Methods for Sequential Hypothesis Testing by Betting](https://mlsanity.com/paper/2502.07774/) (2025)
- [Multi-model Online Conformal Prediction with Graph-Structured Feedback](https://mlsanity.com/paper/2506.20898/) (2025)
- [Conformal Prediction in The Loop: A Feedback-Based Uncertainty Model for Trajectory Optimization](https://mlsanity.com/paper/2510.16376/) (2025)
- [Distribution-informed Online Conformal Prediction](https://mlsanity.com/paper/2512.07770/) (2025)
- [ConformalShift: Targeted Event Reordering Against Adaptive ECG Monitoring](https://mlsanity.com/paper/2608.03628/) (2026)
- [Elements of Conformal Prediction](https://mlsanity.com/paper/2603.23923/) (2026)
- [CUSUM-Shaped Inference-Time Monitoring and Targeted Re-Decoding for Quantized Small Language Model Reasoning](https://mlsanity.com/paper/2607.20129/) (2026)
- [Adaptive Conformal Prediction for Quantum Machine Learning](https://mlsanity.com/paper/2511.18225/) (2025)
- [Parameter-Free and Group Conditional Online Conformal Prediction](https://mlsanity.com/paper/2606.00419/) (2026)
- [Calibrated e-CUSUM Decoding for Quantized Reasoning Models: Why Token Log-Probability Is the Wrong Observable for Decoding Monitors](https://mlsanity.com/paper/2607.11317/) (2026)

## Abstract (arXiv)

Conformal prediction is a valuable tool for quantifying predictive uncertainty of machine learning models. However, its applicability relies on the assumption of data exchangeability, a condition which is often not met in real-world scenarios. In this paper, we consider the problem of adaptive conformal inference without any assumptions about the data generating process. Existing approaches for adaptive conformal inference are based on optimizing the pinball loss using variants of online gradient descent. A notable shortcoming of such approaches is in their explicit dependence on and sensitivity to the choice of the learning rates. In this paper, we propose a different approach for adaptive conformal inference that leverages parameter-free online convex optimization techniques. We prove that our method controls long-term miscoverage frequency at a nominal level and demonstrate its convincing empirical performance without any need of performing cumbersome parameter tuning.