Publications related to Iterative minimization of H2 control performance criteria

On the Generalization of Stochastic Gradient Descent with Momentum

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

Stochastic Second-Order Methods Improve Best-Known Sample Complexity of SGD for Gradient-Dominated Function

Patrick Thiran, Negar Kiyavash, Saber Salehkaleybar

We study the performance of Stochastic Cubic Regularized Newton (SCRN) on a class of functions satisfying gradient dominance property with

1\le\alpha\le2

which holds in a wide range of applications in machine learning and signal processing. This conditio ...

NeurIPS2022

Faster One-Sample Stochastic Conditional Gradient Method for Composite Convex Minimization

Volkan Cevher, Alp Yurtsever, Maria-Luiza Vladarean

We propose a stochastic conditional gradient method (CGM) for minimizing convex finitesum objectives formed as a sum of smooth and non-smooth terms. Existing CGM variants for this template either suffer from slow convergence rates, or require carefully inc ...

2022

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

Large Steps in Inverse Rendering of Geometry

Wenzel Alban Jakob, Baptiste Alexandre Marie Philippe Claude Nicolet

Inverse reconstruction from images is a central problem in many scientific and engineering disciplines. Recent progress on differentiable rendering has led to methods that can efficiently differentiate the full process of image formation with respect to mi ...

ASSOC COMPUTING MACHINERY2021

STORM+: Fully Adaptive SGD with Momentum for Nonconvex Optimization

Volkan Cevher, Ali Kavis

In this work we investigate stochastic non-convex optimization problems wherethe objective is an expectation over smooth loss functions, and the goal is to find an approximate stationary point. The most popular approach to handling such problems is varianc ...

2021

Distributed Learning in Non-Convex Environments-Part I: Agreement at a Linear Rate

Ali H. Sayed, Stefan Vlaski

Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, there has been increasing interest in understanding the behavior of gradient-descent algorithms in non-convex environments. Most available wor ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021

Complexity analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

Fabio Nobile, Sebastian Krumscheid, Matthieu Claude Martin

We consider the numerical approximation of an optimal control problem for an elliptic Partial Differential Equation (PDE) with random coefficients. Specifically, the control function is a deterministic, distributed forcing term that minimizes the expected ...

2021

Implicit Bias of SGD for Diagonal Linear Networks: a Provable Benefit of Stochasticity

Nicolas Henri Bernard Flammarion, Scott William Pesme, Loucas Pillaud-Vivien

Understanding the implicit bias of training algorithms is of crucial importance in order to explain the success of overparametrised neural networks. In this paper, we study the dynamics of stochastic gradient descent over diagonal linear networks through i ...

2021

Iterative minimization of H2 control performance criteria

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On the Generalization of Stochastic Gradient Descent with Momentum

Universal and adaptive methods for robust stochastic optimization

Stochastic Second-Order Methods Improve Best-Known Sample Complexity of SGD for Gradient-Dominated Function

Faster One-Sample Stochastic Conditional Gradient Method for Composite Convex Minimization

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

Large Steps in Inverse Rendering of Geometry

STORM+: Fully Adaptive SGD with Momentum for Nonconvex Optimization

Distributed Learning in Non-Convex Environments-Part I: Agreement at a Linear Rate

Complexity analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

Implicit Bias of SGD for Diagonal Linear Networks: a Provable Benefit of Stochasticity

Universal and adaptive methods for robust stochastic optimization

On the Generalization of Stochastic Gradient Descent with Momentum

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

STORM+: Fully Adaptive SGD with Momentum for Nonconvex Optimization

Complexity analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

Stochastic Second-Order Methods Improve Best-Known Sample Complexity of SGD for Gradient-Dominated Function

Distributed Learning in Non-Convex Environments-Part I: Agreement at a Linear Rate

Faster One-Sample Stochastic Conditional Gradient Method for Composite Convex Minimization

Large Steps in Inverse Rendering of Geometry

Implicit Bias of SGD for Diagonal Linear Networks: a Provable Benefit of Stochasticity