Publications related to Linear Speedup In Saddle-Point Escape For Decentralized Non-Convex Optimization

BENIGN LANDSCAPES OF LOW-DIMENSIONAL RELAXATIONS FOR ORTHOGONAL SYNCHRONIZATION ON GENERAL GRAPHS

Orthogonal group synchronization is the problem of estimating n elements Z(1),& mldr;,Z(n) from the rxr orthogonal group given some relative measurements R-ij approximate to Z(i)Z(j)(-1). The least-squares formulation is nonconvex. To avoid its local minim ...

Siam Publications2024

The effect of smooth parametrizations on nonconvex optimization landscapes

Nicolas Boumal

We develop new tools to study landscapes in nonconvex optimization. Given one optimization problem, we pair it with another by smoothly parametrizing the domain. This is either for practical purposes (e.g., to use smooth optimization algorithms with good g ...

Springer Heidelberg2024

Augmented Lagrangian Methods for Provable and Scalable Machine Learning

Mehmet Fatih Sahin

Non-convex constrained optimization problems have become a powerful framework for modeling a wide range of machine learning problems, with applications in k-means clustering, large- scale semidefinite programs (SDPs), and various other tasks. As the perfor ...

EPFL2023

Safe Zeroth-Order Convex Optimization Using Quadratic Local Approximations

Giancarlo Ferrari Trecate, Maryam Kamgarpour, Yuning Jiang, Baiwei Guo

We address black-box convex optimization problems, where the objective and constraint functions are not explicitly known but can be sampled within the feasible set. The challenge is thus to generate a sequence of feasible points converging towards an optim ...

2023

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

End-to-End Learning for Stochastic Optimization: A Bayesian Perspective

Daniel Kuhn, Tobias Sutter, Yves Rychener

We develop a principled approach to end-to-end learning in stochastic optimization. First, we show that the standard end-to-end learning algorithm admits a Bayesian interpretation and trains a posterior Bayes action map. Building on the insights of this an ...

2023

Data-Driven Control and Optimization under Noisy and Uncertain Conditions

Baiwei Guo

Control systems operating in real-world environments often face disturbances arising from measurement noise and model mismatch. These factors can significantly impact the perfor- mance and safety of the system. In this thesis, we aim to leverage data to de ...

EPFL2023

A comprehensive review of digital twin-part 2: roles of uncertainty quantification and optimization, a battery digital twin, and perspectives

Olga Fink, Chao Hu, Sayan Ghosh

As an emerging technology in the era of Industry 4.0, digital twin is gaining unprecedented attention because of its promise to further optimize process design, quality control, health monitoring, decision- and policy-making, and more, by comprehensively m ...

SPRINGER2023

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

Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy

Nicolas Boumal

We consider the problem of provably finding a stationary point of a smooth function to be minimized on the variety of bounded-rank matrices. This turns out to be unexpectedly delicate. We trace the difficulty back to a geometric obstacle: On a nonsmooth se ...

SPRINGER HEIDELBERG2022

Linear Speedup In Saddle-Point Escape For Decentralized Non-Convex Optimization

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BENIGN LANDSCAPES OF LOW-DIMENSIONAL RELAXATIONS FOR ORTHOGONAL SYNCHRONIZATION ON GENERAL GRAPHS

The effect of smooth parametrizations on nonconvex optimization landscapes

Augmented Lagrangian Methods for Provable and Scalable Machine Learning

Safe Zeroth-Order Convex Optimization Using Quadratic Local Approximations

Universal and adaptive methods for robust stochastic optimization

End-to-End Learning for Stochastic Optimization: A Bayesian Perspective

Data-Driven Control and Optimization under Noisy and Uncertain Conditions

A comprehensive review of digital twin-part 2: roles of uncertainty quantification and optimization, a battery digital twin, and perspectives

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

Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy

BENIGN LANDSCAPES OF LOW-DIMENSIONAL RELAXATIONS FOR ORTHOGONAL SYNCHRONIZATION ON GENERAL GRAPHS

Augmented Lagrangian Methods for Provable and Scalable Machine Learning

The effect of smooth parametrizations on nonconvex optimization landscapes

Safe Zeroth-Order Convex Optimization Using Quadratic Local Approximations

Data-Driven Control and Optimization under Noisy and Uncertain Conditions

Universal and adaptive methods for robust stochastic optimization

End-to-End Learning for Stochastic Optimization: A Bayesian Perspective

A comprehensive review of digital twin-part 2: roles of uncertainty quantification and optimization, a battery digital twin, and perspectives

Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy

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