Publications related to STORM+: Fully Adaptive SGD with Momentum for Nonconvex Optimization

Residual-based attention in physics-informed neural networks

Nikolaos Stergiopoulos, Sokratis Anagnostopoulos

Driven by the need for more efficient and seamless integration of physical models and data, physics -informed neural networks (PINNs) have seen a surge of interest in recent years. However, ensuring the reliability of their convergence and accuracy remains ...

Lausanne2024

Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

Nicolas Henri Bernard Flammarion, Hristo Georgiev Papazov, Scott William Pesme

In this work, we investigate the effect of momentum on the optimisation trajectory of gradient descent. We leverage a continuous-time approach in the analysis of momentum gradient descent with step size

\gamma

and momentum parameter

\beta

that allows u ...

2024

On the Generalization of Stochastic Gradient Descent with Momentum

Volkan Cevher, Kimon Antonakopoulos

While momentum-based accelerated variants of stochastic gradient descent (SGD) are widely used when training machine learning models, there is little theoretical understanding on the generalization error of such methods. In this work, we first show that th ...

Brookline2024

Universal and adaptive methods for robust stochastic optimization

Ali Kavis

Within the context of contemporary machine learning problems, efficiency of optimization process depends on the properties of the model and the nature of the data available, which poses a significant problem as the complexity of either increases ad infinit ...

EPFL2023

Contextual Stochastic Bilevel Optimization

Daniel Kuhn, Andreas Krause, Yifan Hu, Jie Wang

We introduce contextual stochastic bilevel optimization (CSBO) -- a stochastic bilevel optimization framework with the lower-level problem minimizing an expectation conditioned on some contextual information and the upper-level decision variable. This fram ...

2023

Phenomenological theory of variational quantum ground-state preparation

Ivano Tavernelli, Giuseppe Carleo

The variational approach is a cornerstone of computational physics, considering both conventional and quantum computing computational platforms. The variational quantum eigensolver algorithm aims to prepare the ground state of a Hamiltonian exploiting para ...

College Pk2023

Fast Adversarial Training With Adaptive Step Size

Sabine Süsstrunk, Mathieu Salzmann, Chen Liu, Zhuoyi Huang, Yong Zhang, Jue Wang

While adversarial training and its variants have shown to be the most effective algorithms to defend against adversarial attacks, their extremely slow training process makes it hard to scale to large datasets like ImageNet. The key idea of recent works to ...

Piscataway2023

The statistical complexity of early-stopped mirror descent

Tomas Vaskevicius, Varun Kanade

Recently there has been a surge of interest in understanding implicit regularization properties of iterative gradient-based optimization algorithms. In this paper, we study the statistical guarantees on the excess risk achieved by early-stopped unconstrain ...

Oxford2023

Phase diagram of Stochastic Gradient Descent in high-dimensional two-layer neural networks

Florent Gérard Krzakala, Lenka Zdeborová, Ludovic Théo Stephan, Bruno Loureiro

Despite the non-convex optimization landscape, over-parametrized shallow networks are able to achieve global convergence under gradient descent. The picture can be radically different for narrow net-works, which tend to get stuck in badly-generalizing loca ...

2022

ADAGRAD Avoids Saddle Points

Kimon Antonakopoulos, Xiao Wang

Adaptive first-order methods in optimization are prominent in machine learning and data science owing to their ability to automatically adapt to the landscape of the function being optimized. However, their convergence guarantees are typically stated in te ...

JMLR-JOURNAL MACHINE LEARNING RESEARCH2022

STORM+: Fully Adaptive SGD with Momentum for Nonconvex Optimization

Graph Chatbot

Chat with Graph Search

Residual-based attention in physics-informed neural networks

Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

On the Generalization of Stochastic Gradient Descent with Momentum

Universal and adaptive methods for robust stochastic optimization

Contextual Stochastic Bilevel Optimization

Phenomenological theory of variational quantum ground-state preparation

Fast Adversarial Training With Adaptive Step Size

The statistical complexity of early-stopped mirror descent

Phase diagram of Stochastic Gradient Descent in high-dimensional two-layer neural networks

ADAGRAD Avoids Saddle Points

Universal and adaptive methods for robust stochastic optimization

The statistical complexity of early-stopped mirror descent

Fast Adversarial Training With Adaptive Step Size

Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

Contextual Stochastic Bilevel Optimization

On the Generalization of Stochastic Gradient Descent with Momentum

Residual-based attention in physics-informed neural networks

Phase diagram of Stochastic Gradient Descent in high-dimensional two-layer neural networks

ADAGRAD Avoids Saddle Points

Phenomenological theory of variational quantum ground-state preparation