# Faster Recalibration of an Online Predictor via Approachability

arXiv: https://arxiv.org/abs/2310.17002 · HTML: https://mlsanity.com/paper/2310.17002/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 28 references that are in the map.
- First posted on arXiv 25 Oct 2023.

## Builds on (most cited first, 4 of 4)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Man is to Computer Programmer as Woman is to Homemaker? Debiasing Word Embeddings](https://mlsanity.com/paper/1607.06520/) (2016)
- [Online Minimax Multiobjective Optimization: Multicalibeating and Other Applications](https://mlsanity.com/paper/2108.03837/) (2021)
- ["Calibeating": Beating Forecasters at Their Own Game](https://mlsanity.com/paper/2209.04892/) (2022)

## Built on by (most cited first, 11 of 11)

- [Forecasting for Swap Regret for All Downstream Agents](https://mlsanity.com/paper/2402.08753/) (2024)
- [On the Distance from Calibration in Sequential Prediction](https://mlsanity.com/paper/2402.07458/) (2024)
- [Calibeating Made Simple](https://mlsanity.com/paper/2603.22167/) (2026)
- [Calibrated Probabilistic Forecasts for Arbitrary Sequences](https://mlsanity.com/paper/2409.19157/) (2024)
- [Computing Optimal Regularizers for Online Linear Optimization](https://mlsanity.com/paper/2410.17336/) (2024)
- [An Efficient Black-Box Reduction from Online Learning to Multicalibration, and a New Route to Phi-Regret Minimization](https://mlsanity.com/paper/2604.19592/) (2026)
- [Proper Calibeating](https://mlsanity.com/paper/2605.26703/) (2026)
- [Optimal Recalibration of an Online Predictor](https://mlsanity.com/paper/2607.19689/) (2026)
- [Efficient Opportunistic Approachability](https://mlsanity.com/paper/2602.21328/) (2026)
- [Blackwell Approachability and Gradient Equilibrium are Equivalent](https://mlsanity.com/paper/2606.27315/) (2026)
- [Fast Rates for Swap-Agnostic Learning of Proper Losses](https://mlsanity.com/paper/2607.28856/) (2026)

## Abstract (arXiv)

Predictive models in ML need to be trustworthy and reliable, which often at the very least means outputting calibrated probabilities. This can be particularly difficult to guarantee in the online prediction setting when the outcome sequence can be generated adversarially. In this paper we introduce a technique using Blackwell's approachability theorem for taking an online predictive model which might not be calibrated and transforming its predictions to calibrated predictions without much increase to the loss of the original model. Our proposed algorithm achieves calibration and accuracy at a faster rate than existing techniques arXiv:1607.03594 and is the first algorithm to offer a flexible tradeoff between calibration error and accuracy in the online setting. We demonstrate this by characterizing the space of jointly achievable calibration and regret using our technique.