# Simultaneous Blackwell Approachability and Applications to Multiclass Omniprediction

arXiv: https://arxiv.org/abs/2602.17577 · HTML: https://mlsanity.com/paper/2602.17577/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 47 references that are in the map.
- First posted on arXiv 19 Feb 2026.

## Builds on (most cited first, 26 of 26)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibration](https://mlsanity.com/paper/1910.12656/) (2019)
- [Calibrating Predictions to Decisions: A Novel Approach to Multi-Class Calibration](https://mlsanity.com/paper/2107.05719/) (2021)
- [Omnipredictors](https://mlsanity.com/paper/2109.05389/) (2021)
- [A Characterization of Multiclass Learnability](https://mlsanity.com/paper/2203.01550/) (2022)
- [Loss Minimization through the Lens of Outcome Indistinguishability](https://mlsanity.com/paper/2210.08649/) (2022)
- [U-Calibration: Forecasting for an Unknown Agent](https://mlsanity.com/paper/2307.00168/) (2023)
- [High-Dimensional Prediction for Sequential Decision Making](https://mlsanity.com/paper/2310.17651/) (2023)
- [Oracle Efficient Online Multicalibration and Omniprediction](https://mlsanity.com/paper/2307.08999/) (2023)
- [Near-Optimal Algorithms for Omniprediction](https://mlsanity.com/paper/2501.17205/) (2025)
- [Swap Agnostic Learning, or Characterizing Omniprediction via Multicalibration](https://mlsanity.com/paper/2302.06726/) (2023)
- [Online Minimax Multiobjective Optimization: Multicalibeating and Other Applications](https://mlsanity.com/paper/2108.03837/) (2021)
- [A Characterization of List Learnability](https://mlsanity.com/paper/2211.04956/) (2022)
- [The Sample Complexity of Learning Linear Predictors with the Squared Loss](https://mlsanity.com/paper/1406.5143/) (2014)
- [On Computationally Efficient Multi-Class Calibration](https://mlsanity.com/paper/2402.07821/) (2024)
- [Sample Efficient Omniprediction and Downstream Swap Regret for Non-Linear Losses](https://mlsanity.com/paper/2502.12564/) (2025)
- [From Fairness to Infinity: Outcome-Indistinguishable (Omni)Prediction in Evolving Graphs](https://mlsanity.com/paper/2411.17582/) (2024)
- [High dimensional online calibration in polynomial time](https://mlsanity.com/paper/2504.09096/) (2025)
- [High-Dimensional Calibration from Swap Regret](https://mlsanity.com/paper/2505.21460/) (2025)
- [Approachability in unknown games: Online learning meets multi-objective optimization](https://mlsanity.com/paper/1402.2043/) (2014)
- [The PAV algorithm optimizes binary proper scoring rules](https://mlsanity.com/paper/1304.2331/) (2013)
- [Omnipredicting Single-Index Models with Multi-Index Models](https://mlsanity.com/paper/2411.13083/) (2024)
- [Generalized and Unified Equivalences between Hardness and Pseudoentropy](https://mlsanity.com/paper/2507.05972/) (2025)
- [Calibration through the Lens of Indistinguishability](https://mlsanity.com/paper/2509.02279/) (2025)
- [Approachability with Constraints](https://mlsanity.com/paper/1712.00781/) (2017)

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

- [Testable and Actionable Calibration for Full Swap Regret](https://mlsanity.com/paper/2605.17749/) (2026)
- [Optimal Recalibration of an Online Predictor](https://mlsanity.com/paper/2607.19689/) (2026)
- [Fast Rates for Swap-Agnostic Learning of Proper Losses](https://mlsanity.com/paper/2607.28856/) (2026)

## Abstract (arXiv)

Omniprediction is a learning problem that requires suboptimality bounds for each of a family of losses L against a family of comparator predictors C. We initiate the study of omniprediction in a multiclass setting, where the comparator family C may be infinite. Our main result is an extension of the recent binary omniprediction algorithm of [OKK25] to the multiclass setting, with sample complexity (in statistical settings) or regret horizon (in online settings) ≈ varepsilon-(k+1), for varepsilon-omniprediction in a k-class prediction problem. En route to proving this result, we design a framework of potential broader interest for solving Blackwell approachability problems where multiple sets must simultaneously be approached via coupled actions.