# An Axiomatic Approach to Loss Aggregation and an Adapted Aggregating Algorithm

arXiv: https://arxiv.org/abs/2406.02292 · HTML: https://mlsanity.com/paper/2406.02292/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 25 references that are in the map.
- First posted on arXiv 4 Jun 2024.

## Builds on (most cited first, 7 of 7)

- [Fairness risk measures](https://mlsanity.com/paper/1901.08665/) (2019)
- [On-Demand Sampling: Learning Optimally from Multiple Distributions](https://mlsanity.com/paper/2210.12529/) (2022)
- [The fundamental nature of the log loss function](https://mlsanity.com/paper/1502.06254/) (2015)
- [Risk Measures and Upper Probabilities: Coherence and Stratification](https://mlsanity.com/paper/2206.03183/) (2022)
- [The Geometry and Calculus of Losses](https://mlsanity.com/paper/2209.00238/) (2022)
- [From Proper Scoring Rules to Max-Min Optimal Forecast Aggregation](https://mlsanity.com/paper/2102.07081/) (2021)
- [The Geometry of Mixability](https://mlsanity.com/paper/2302.11905/) (2023)

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

- [Adaptive Rigor in AI System Evaluation using Temperature-Controlled Verdict Aggregation via Generalized Power Mean](https://mlsanity.com/paper/2604.08595/) (2026)

## Abstract (arXiv)

Supervised learning has gone beyond the expected risk minimization framework. Central to most of these developments is the introduction of more general aggregation functions for losses incurred by the learner. In this paper, we turn towards online learning under expert advice. Via easily justified assumptions we characterize a set of reasonable loss aggregation functions as quasi-sums. Based upon this insight, we suggest a variant of the Aggregating Algorithm tailored to these more general aggregation functions. This variant inherits most of the nice theoretical properties of the AA, such as recovery of Bayes' updating and a time-independent bound on quasi-sum regret. Finally, we argue that generalized aggregations express the attitude of the learner towards losses.