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math.OC2026

Curvature-Scaled Sharpness-Aware Minimization: Convergence Beyond Smoothness

Dimitris Oikonomou, Nicolas Loizou

Sharpness-Aware Minimization (SAM) has established itself as a widely used method for training deep neural networks. Despite its popularity, existing convergence guarantees for SAM…

math.OC2026

Adaptive Sharpness-Aware Minimization with a Polyak-type Step size: A Theory-Grounded Scheduler

Dimitris Oikonomou, Nicolas Loizou

Sharpness-Aware Minimization (SAM) has established itself as a powerful and widely adopted optimizer for training machine learning models. By explicitly minimizing the sharpness of…

math.OC2025

Safeguarded Stochastic Polyak Step Sizes for Non-smooth Optimization: Robust Performance Without Small (Sub)Gradients

Dimitris Oikonomou, Nicolas Loizou

The stochastic Polyak step size (SPS) has proven to be a promising choice for stochastic gradient descent (SGD), delivering competitive performance relative to state-of-the-art met…

math.OC2025

Sharpness-Aware Minimization: General Analysis and Improved Rates

Dimitris Oikonomou, Nicolas Loizou

Sharpness-Aware Minimization (SAM) has emerged as a powerful method for improving generalization in machine learning models by minimizing the sharpness of the loss landscape. Howev…

math.OC2024

Stochastic Polyak Step-sizes and Momentum: Convergence Guarantees and Practical Performance

Dimitris Oikonomou, Nicolas Loizou

Stochastic gradient descent with momentum, also known as Stochastic Heavy Ball method (SHB), is one of the most popular algorithms for solving large-scale stochastic optimization p…