# Generalized Exponentiated Gradient Algorithms and Their Application to On-Line Portfolio Selection

arXiv: https://arxiv.org/abs/2406.00655 · HTML: https://mlsanity.com/paper/2406.00655/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 47 references that are in the map.
- First posted on arXiv 2 Jun 2024.

## Builds on (most cited first, 9 of 9)

- [Online Learning: A Comprehensive Survey](https://mlsanity.com/paper/1802.02871/) (2018)
- [Exponentiated Gradient Meets Gradient Descent](https://mlsanity.com/paper/1902.01903/) (2019)
- [Stochastic Mirror Descent: Convergence Analysis and Adaptive Variants via the Mirror Stochastic Polyak Stepsize](https://mlsanity.com/paper/2110.15412/) (2021)
- [Alpha-Beta Divergence For Variational Inference](https://mlsanity.com/paper/1805.01045/) (2018)
- [Boosting with Tempered Exponential Measures](https://mlsanity.com/paper/2306.05487/) (2023)
- [Convergence of the Exponentiated Gradient Method with Armijo Line Search](https://mlsanity.com/paper/1712.08480/) (2017)
- [Online Self-Concordant and Relatively Smooth Minimization, With Applications to Online Portfolio Selection and Learning Quantum States](https://mlsanity.com/paper/2210.00997/) (2022)
- [Exponentiated Gradient Exploration for Active Learning](https://mlsanity.com/paper/1408.2196/) (2014)
- [Inverse Reinforcement Learning With Constraint Recovery](https://mlsanity.com/paper/2305.08130/) (2023)

## Built on by (most cited first, 5 of 5)

- [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)
- [Mirror Descent Using the Tempesta Generalized Multi-parametric Logarithms](https://mlsanity.com/paper/2506.13984/) (2025)
- [The alpha-beta divergence for real and complex data](https://mlsanity.com/paper/2508.03272/) (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)

This paper introduces a novel family of generalized exponentiated gradient (EG) updates derived from an Alpha-Beta divergence regularization function. Collectively referred to as EGAB, the proposed updates belong to the category of multiplicative gradient algorithms for positive data and demonstrate considerable flexibility by controlling iteration behavior and performance through three hyperparameters: α, β, and the learning rate η. To enforce a unit l1 norm constraint for nonnegative weight vectors within generalized EGAB algorithms, we develop two slightly distinct approaches. One method exploits scale-invariant loss functions, while the other relies on gradient projections onto the feasible domain. As an illustration of their applicability, we evaluate the proposed updates in addressing the online portfolio selection problem (OLPS) using gradient-based methods. Here, they not only offer a unified perspective on the search directions of various OLPS algorithms (including the standard exponentiated gradient and diverse mean-reversion strategies), but also facilitate smooth interpolation and extension of these updates due to the flexibility in hyperparameter selection. Simulation results confirm that the adaptability of these generalized gradient updates can effectively enhance the performance for some portfolios, particularly in scenarios involving transaction costs.