# Efficient Sequential Calibration with O(T2/3-ε) Error Bound

arXiv: https://arxiv.org/abs/2607.12928 · HTML: https://mlsanity.com/paper/2607.12928/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 15 references that are in the map.
- First posted on arXiv 14 Jul 2026.

## Builds on (most cited first, 5 of 5)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Stronger Calibration Lower Bounds via Sidestepping](https://mlsanity.com/paper/2012.03454/) (2020)
- [Breaking the T2/3 Barrier for Sequential Calibration](https://mlsanity.com/paper/2406.13668/) (2024)
- [Calibrated Forecasts: The Minimax Proof](https://mlsanity.com/paper/2209.05863/) (2022)

## Built on by (most cited first, 1 of 1)

- [Explicit Asymptotic Bounds for Sequential Calibration Beyond T2/3](https://mlsanity.com/paper/2610.07623/) (2026)

## Abstract (arXiv)

We study the online binary sequential calibration problem. A recent breakthrough by citetdagan2024breaking overcomes the classical (T2/3) barrier for calibration error. Building on this result, we present an efficient randomized forecaster that achieves an expected calibration error (O(T2/3-varepsilon)) for some constant (varepsilon>0). Our forecaster combines the textscSPR-Calibration procedure citepdagan2024breaking with an outer Blackwell-style correction layer. The textscSPR-Calibration procedure controls calibration with respect to a surrogate sequence of conditional-mean estimates, while the correction layer controls the additional error incurred when these surrogates are used to approximate the true outcomes. The analysis decomposes the total calibration error into the surrogate calibration error and the residual discrepancy between the surrogate sequence and the true outcomes. The former is bounded by the textscSPR-Calibration guarantee in citetdagan2024breaking, and the latter is controlled using a quadratic potential argument together with the sparsity of the textscSPR-Calibration forecaster.