# Boosting with Tempered Exponential Measures

arXiv: https://arxiv.org/abs/2306.05487 · HTML: https://mlsanity.com/paper/2306.05487/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 39 references that are in the map.
- First posted on arXiv 8 Jun 2023.

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

- [Boosting Simple Learners](https://mlsanity.com/paper/2001.11704/) (2020)
- [Being Properly Improper](https://mlsanity.com/paper/2106.09920/) (2021)
- [Clustering above Exponential Families with Tempered Exponential Measures](https://mlsanity.com/paper/2211.02765/) (2022)
- [Boosting with the Logistic Loss is Consistent](https://mlsanity.com/paper/1305.2648/) (2013)

## Built on by (most cited first, 8 of 8)

- [Generalized Exponentiated Gradient Algorithms and Their Application to On-Line Portfolio Selection](https://mlsanity.com/paper/2406.00655/) (2024)
- [Optimal Transport with Tempered Exponential Measures](https://mlsanity.com/paper/2309.04015/) (2023)
- [Mirror Descent and Novel Exponentiated Gradient Algorithms Using Trace-Form Entropies and Deformed Logarithms](https://mlsanity.com/paper/2503.08748/) (2025)
- [Generalized Euler Logarithm and its Applications in Machine Learning: Natural Gradient, Backpropagation, Generalized EG, Mirror Descent and OLPS](https://mlsanity.com/paper/2502.17500/) (2025)
- [The Tempered Hilbert Simplex Distance and Its Application To Non-linear Embeddings of TEMs](https://mlsanity.com/paper/2311.13459/) (2023)
- [Tempered Calculus for ML: Application to Hyperbolic Model Embedding](https://mlsanity.com/paper/2402.04163/) (2024)
- [DPO Unchained: Your Training Algorithm is Secretly Disentangled in Human Choice Theory (and its Loss' Convexity is Dispensable)](https://mlsanity.com/paper/2507.07855/) (2025)
- [Group Entropies and Mirror Duality: A Class of Flexible Mirror Descent Updates for Machine Learning](https://mlsanity.com/paper/2603.08651/) (2026)

## Abstract (arXiv)

One of the most popular ML algorithms, AdaBoost, can be derived from the dual of a relative entropy minimization problem subject to the fact that the positive weights on the examples sum to one. Essentially, harder examples receive higher probabilities. We generalize this setup to the recently introduced it tempered exponential measures (TEMs) where normalization is enforced on a specific power of the measure and not the measure itself. TEMs are indexed by a parameter t and generalize exponential families (t=1). Our algorithm, t-AdaBoost, recovers AdaBoost~as a special case (t=1). We show that t-AdaBoost retains AdaBoost's celebrated exponential convergence rate when t∈ [0,1) while allowing a slight improvement of the rate's hidden constant compared to t=1. t-AdaBoost partially computes on a generalization of classical arithmetic over the reals and brings notable properties like guaranteed bounded leveraging coefficients for t∈ [0,1). From the loss that t-AdaBoost minimizes (a generalization of the exponential loss), we show how to derive a new family of it tempered losses for the induction of domain-partitioning classifiers like decision trees. Crucially, strict properness is ensured for all while their boosting rates span the full known spectrum. Experiments using t-AdaBoost+trees display that significant leverage can be achieved by tuning t.