Related papers: Sensitivity analysis of the maximal value function…
Non-smoothness at optimal points is a common phenomenon in many eigenvalue optimization problems. We consider two recent algorithms to minimize the largest eigenvalue of a Hermitian matrix dependent on one parameter, both proven to be…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective…
We study online convex optimization under stochastic sub-gradient observation faults, where we introduce adaptive algorithms with minimax optimal regret guarantees. We specifically study scenarios where our sub-gradient observations can be…
The main goal of this paper is to apply the machinery of variational analysis and generalized differentiation to study infinite horizon stochastic dynamic programming (DP) with discrete time in the Banach space setting without convexity…
This study explores the performance of the random Gaussian smoothing Zeroth-Order ExtraGradient (ZO-EG) scheme considering \Af{deterministic} min-max optimisation problems with possibly NonConvex-NonConcave (NC-NC) objective functions. We…
Regularization plays a key role in a variety of optimization formulations of inverse problems. A recurring theme in regularization approaches is the selection of regularization parameters, and their effect on the solution and on the optimal…
We study nonparametric change-point estimation from indirect noisy observations. Focusing on the white noise convolution model, we consider two classes of functions that are smooth apart from the change-point. We establish lower bounds on…
The softmax function is a ubiquitous component at the output of neural networks and increasingly in intermediate layers as well. This paper provides convex lower bounds and concave upper bounds on the softmax function, which are compatible…
The Frank-Wolfe (FW) method is a popular approach for solving optimization problems with structured constraints that arise in machine learning applications. In recent years, stochastic versions of FW have gained popularity, motivated by…
Maximizing high-dimensional, non-convex functions through noisy observations is a notoriously hard problem, but one that arises in many applications. In this paper, we tackle this challenge by modeling the unknown function as a sample from…
We study the problem of empirical minimization for variance-type functionals over functional classes. Sharp non-asymptotic bounds for the excess variance are derived under mild conditions. In particular, it is shown that under some…
This paper is concerned with the value function approach to multiobjective bilevel optimization which exploits a lower level frontier-type mapping in order to replace the hierarchical model of two interdependent multiobjective optimization…
Approximating a convex function by a polyhedral function that has a limited number of facets is a fundamental problem with applications in various fields, from mitigating the curse of dimensionality in optimal control to bi-level…
We provide three new proofs of the strong concavity of the dual function of some convex optimization problems. For problems with nonlinear constraints, we show that the the assumption of strong convexity of the objective cannot be weakened…
A fully stochastic second-order adaptive-regularization method for unconstrained nonconvex optimization is presented which never computes the objective-function value, but yet achieves the optimal $\mathcal{O}(\epsilon^{-3/2})$ complexity…
A theory of superefficiency and adaptation is developed under flexible performance measures which give a multiresolution view of risk and bridge the gap between pointwise and global estimation. This theory provides a useful benchmark for…
The key task of machine learning is to minimize the loss function that measures the model fit to the training data. The numerical methods to do this efficiently depend on the properties of the loss function. The most decisive among these…
Estimation of linear functionals from observed data is an important task in many subjects. Juditsky & Nemirovski [The Annals of Statistics 37.5A (2009): 2278-2300] propose a framework for non-parametric estimation of linear functionals in a…
We consider minimization of a smooth nonconvex function with inexact oracle access to gradient and Hessian (without assuming access to the function value) to achieve approximate second-order optimality. A novel feature of our method is that…
This work concerns the minimization of the pseudospectral abscissa of a matrix-valued function dependent on parameters analytically. The problem is motivated by robust stability and transient behavior considerations for a linear control…