GeoAdaLer: Geometric Insights into Adaptive Stochastic Gradient Descent Algorithms

TL;DR

GeoAdaLer introduces a geometrically motivated adaptive stochastic gradient descent method that enhances interpretability and performance in complex optimization landscapes, addressing longstanding mysteries in adaptive optimization geometry.

Contribution

The paper presents GeoAdaLer, a new adaptive optimization algorithm based on geometric insights, extending adaptive learning techniques with improved interpretability and effectiveness.

Findings

GeoAdaLer outperforms traditional methods in complex tasks.

The geometric approach improves convergence stability.

Enhanced interpretability of adaptive optimization processes.

Abstract

The Adam optimization method has achieved remarkable success in addressing contemporary challenges in stochastic optimization. This method falls within the realm of adaptive sub-gradient techniques, yet the underlying geometric principles guiding its performance have remained shrouded in mystery, and have long confounded researchers. In this paper, we introduce GeoAdaLer (Geometric Adaptive Learner), a novel adaptive learning method for stochastic gradient descent optimization, which draws from the geometric properties of the optimization landscape. Beyond emerging as a formidable contender, the proposed method extends the concept of adaptive learning by introducing a geometrically inclined approach that enhances the interpretability and effectiveness in complex optimization scenarios