Publications related to Continuity Properties of Law-Invariant (Quasi-)Convex Risk Functions on L∞

Stability of Image-Reconstruction Algorithms

Michaël Unser, Sebastian Jonas Neumayer, Pol del Aguila Pla

Robustness and stability of image-reconstruction algorithms have recently come under scrutiny. Their importance to medical imaging cannot be overstated. We review the known results for the topical variational regularization strategies ( ℓ2 and ℓ1 regulariz ...

2023

Gradient-based optimisation of the conditional-value-at-risk using the multi-level Monte Carlo method

Fabio Nobile, Sundar Subramaniam Ganesh

In this work, we tackle the problem of minimising the Conditional-Value-at-Risk (CVaR) of output quantities of complex differential models with random input data, using gradient-based approaches in combination with the Multi-Level Monte Carlo (MLMC) method ...

2022

A first-order primal-dual method with adaptivity to local smoothness

Volkan Cevher, Maria-Luiza Vladarean

We consider the problem of finding a saddle point for the convex-concave objective

\min_x \max_y f(x) + \langle Ax, y\rangle - g^*(y)

, where

f

is a convex function with locally Lipschitz gradient and

g

is convex and possibly non-smooth. We propose an ...

2021

Convex optimization in sums of Banach spaces

Michaël Unser, Shayan Aziznejad

We characterize the solution of a broad class of convex optimization problems that address the reconstruction of a function from a finite number of linear measurements. The underlying hypothesis is that the solution is decomposable as a finite sum of compo ...

2021

Adaptive Gradient Descent without Descent

Konstantin Mishchenko

We present a strikingly simple proof that two rules are sufficient to automate gradient descent: 1) don’t increase the stepsize too fast and 2) don’t overstep the local curvature. No need for functional values, no line search, no information about the func ...

2020

A Multi-Agent Primal-Dual Strategy for Composite Optimization over Distributed Features

Ali H. Sayed, Sulaiman A S A E Alghunaim, Ming Yan

This work studies multi-agent sharing optimization problems with the objective function being the sum of smooth local functions plus a convex (possibly non-smooth) function coupling all agents. This scenario arises in many machine learning and engineering ...

IEEE2020

On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems

Volkan Cevher, Ali Kavis, Shaul Nadav Hallak

This paper analyzes the trajectories of stochastic gradient descent (SGD) to help understand the algorithm’s convergence properties in non-convex problems. We first show that the sequence of iterates generated by SGD remains bounded and converges with prob ...

2020

Stochastic Frank-Wolfe for Composite Convex Minimization

Volkan Cevher, Alp Yurtsever

A broad class of convex optimization problems can be formulated as a semidefinite program (SDP), minimization of a convex function over the positive-semidefinite cone subject to some affine constraints. The majority of classical SDP solvers are designed fo ...

2019

Discrete-time regional pole-placement using convex approximations: Theory and application to a boost converter

Emilio Maddalena

The problem of allocating the closed-loop poles of linear systems in specific regions of the complex plane defined by discrete time-domain requirements is addressed. The resulting non-convex set is inner-approximated by a convex region described with linea ...

2019

Optimistic Distributionally Robust Optimization for Nonparametric Likelihood Approximation

Daniel Kuhn, Viet Anh Nguyen, Soroosh Shafieezadeh Abadeh, Wolfram Wiesemann

The likelihood function is a fundamental component in Bayesian statistics. However, evaluating the likelihood of an observation is computationally intractable in many applications. In this paper, we propose a non-parametric approximation of the likelihood ...

2019

Continuity Properties of Law-Invariant (Quasi-)Convex Risk Functions on L∞

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Stability of Image-Reconstruction Algorithms

Gradient-based optimisation of the conditional-value-at-risk using the multi-level Monte Carlo method

A first-order primal-dual method with adaptivity to local smoothness

Convex optimization in sums of Banach spaces

Adaptive Gradient Descent without Descent

A Multi-Agent Primal-Dual Strategy for Composite Optimization over Distributed Features

On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems

Stochastic Frank-Wolfe for Composite Convex Minimization

Discrete-time regional pole-placement using convex approximations: Theory and application to a boost converter

Optimistic Distributionally Robust Optimization for Nonparametric Likelihood Approximation

Stability of Image-Reconstruction Algorithms

A Multi-Agent Primal-Dual Strategy for Composite Optimization over Distributed Features

Convex optimization in sums of Banach spaces

Stochastic Frank-Wolfe for Composite Convex Minimization

Optimistic Distributionally Robust Optimization for Nonparametric Likelihood Approximation

Gradient-based optimisation of the conditional-value-at-risk using the multi-level Monte Carlo method

On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems

Discrete-time regional pole-placement using convex approximations: Theory and application to a boost converter

Adaptive Gradient Descent without Descent

A first-order primal-dual method with adaptivity to local smoothness