# Calibrated Regression Against An Adversary Without Regret

arXiv: https://arxiv.org/abs/2302.12196 · HTML: https://mlsanity.com/paper/2302.12196/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 30 references that are in the map.
- First posted on arXiv 23 Feb 2023.

## Builds on (most cited first, 9 of 9)

- [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)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Using Trusted Data to Train Deep Networks on Labels Corrupted by Severe Noise](https://mlsanity.com/paper/1802.05300/) (2018)
- [Calibrated and Sharp Uncertainties in Deep Learning via Density Estimation](https://mlsanity.com/paper/2112.07184/) (2021)
- [Calibrated Model-Based Deep Reinforcement Learning](https://mlsanity.com/paper/1906.08312/) (2019)
- [Online Minimax Multiobjective Optimization: Multicalibeating and Other Applications](https://mlsanity.com/paper/2108.03837/) (2021)

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

- [Calibeating Made Simple](https://mlsanity.com/paper/2603.22167/) (2026)
- [Calibrated Multi-Level Quantile Forecasting](https://mlsanity.com/paper/2512.23671/) (2025)
- [Online Sharp-Calibrated Bayesian Optimization](https://mlsanity.com/paper/2605.10572/) (2026)

## Abstract (arXiv)

We are interested in probabilistic prediction in online settings in which data does not follow a probability distribution. Our work seeks to achieve two goals: (1) producing valid probabilities that accurately reflect model confidence; and (2) ensuring that traditional notions of performance (e.g., high accuracy) still hold. We introduce online algorithms guaranteed to achieve these goals on arbitrary streams of data points, including data chosen by an adversary. Specifically, our algorithms produce forecasts that are (1) calibrated -- i.e., an 80% confidence interval contains the true outcome 80% of the time -- and (2) have low regret relative to a user-specified baseline model. We implement a post-hoc recalibration strategy that provably achieves these goals in regression; previous algorithms applied to classification or achieved (1) but not (2). In the context of Bayesian optimization, an online model-based decision-making task in which the data distribution shifts over time, our method yields accelerated convergence to improved optima.