# Optimal Binary Classifier Aggregation for General Losses

arXiv: https://arxiv.org/abs/1510.00452 · HTML: https://mlsanity.com/paper/1510.00452/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Oct 2015.

## Built on by (most cited first, 6 of 6)

- [Learning from Multiple Noisy Partial Labelers](https://mlsanity.com/paper/2106.04530/) (2021)
- [Minimax risk classifiers with 0-1 loss](https://mlsanity.com/paper/2201.06487/) (2022)
- [Entropy, concentration, and learning: a statistical mechanics primer](https://mlsanity.com/paper/2409.18630/) (2024)
- [An Adaptive Method for Weak Supervision with Drifting Data](https://mlsanity.com/paper/2306.01658/) (2023)
- [Convergence Behavior of an Adversarial Weak Supervision Method](https://mlsanity.com/paper/2405.16013/) (2024)
- [Reliable Programmatic Weak Supervision with Confidence Intervals for Label Probabilities](https://mlsanity.com/paper/2508.03896/) (2025)

## Abstract (arXiv)

We address the problem of aggregating an ensemble of predictors with known loss bounds in a semi-supervised binary classification setting, to minimize prediction loss incurred on the unlabeled data. We find the minimax optimal predictions for a very general class of loss functions including all convex and many non-convex losses, extending a recent analysis of the problem for misclassification error. The result is a family of semi-supervised ensemble aggregation algorithms which are as efficient as linear learning by convex optimization, but are minimax optimal without any relaxations. Their decision rules take a form familiar in decision theory -- applying sigmoid functions to a notion of ensemble margin -- without the assumptions typically made in margin-based learning.