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In this paper, we propose a proximal gradient method and an accelerated proximal gradient method for solving composite optimization problems, where the objective function is the sum of a smooth and a convex, possibly nonsmooth, function. We…
We introduce and test an algorithm that adaptively estimates large deviation functions characterizing the fluctuations of additive functionals of Markov processes in the long-time limit. These functions play an important role for predicting…
Existing approaches to sample size calculations for developing clinical prediction models have focused on ensuring that the expected value of a chosen performance measure meets a pre-specified target. For example, to limit…
We here adapt an extended version of the adaptive cubic regularisation method with dynamic inexact Hessian information for nonconvex optimisation in [3] to the stochastic optimisation setting. While exact function evaluations are still…
Stochastic gradient algorithms are the main focus of large-scale optimization problems and led to important successes in the recent advancement of the deep learning algorithms. The convergence of SGD depends on the careful choice of…
Improving efficiency of importance sampler is at the center of research in Monte Carlo methods. While adaptive approach is usually difficult within the Markov Chain Monte Carlo framework, the counterpart in importance sampling can be…
This paper presents two stochastic model predictive control methods for linear time-invariant systems subject to unbounded additive uncertainties. The new methods are developed by formulating the chance constraints into deterministic form,…
We revisit the sample average approximation (SAA) approach for non-convex stochastic programming. We show that applying the SAA approach to problems with expected value equality constraints does not necessarily result in asymptotic…
Stochastic Model Predictive Control has proved to be an efficient method to plan trajectories in uncertain environments, e.g., for autonomous vehicles. Chance constraints ensure that the probability of collision is bounded by a predefined…
This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently…
We propose a novel method for sampling and optimization tasks based on a stochastic interacting particle system. We explain how this method can be used for the following two goals: (i) generating approximate samples from a given target…
The scenario-based optimization approach (`scenario approach') provides an intuitive way of approximating the solution to chance-constrained optimization programs, based on finding the optimal solution under a finite number of sampled…
Stochastic gradient methods (SGMs) have been widely used for solving stochastic optimization problems. A majority of existing works assume no constraints or easy-to-project constraints. In this paper, we consider convex stochastic…
In this paper, a novel method to adaptively approximate the solution to stochastic differential equations, which is based on compressive sampling and sparse recovery, is introduced. The proposed method consider the problem of sparse…
We propose a new, more general approach to the design of stochastic gradient-based optimization methods for machine learning. In this new framework, optimizers assume access to a batch of gradient estimates per iteration, rather than a…
In this paper, we consider convex stochastic optimization problems arising in machine learning applications (e.g., risk minimization) and mathematical statistics (e.g., maximum likelihood estimation). There are two main approaches to solve…
We present a new method for stochastic shape optimisation of engineering structures. The method generalises an existing deterministic scheme, in which the structure is represented and evolved by a level-set method coupled with mathematical…
An algorithm is said to be adaptive to a certain parameter (of the problem) if it does not need a priori knowledge of such a parameter but performs competitively to those that know it. This dissertation presents our work on adaptive…
Stochastic Gradient Descent (SGD) with gradient clipping is a powerful technique for enabling differentially private optimization. Although prior works extensively investigated clipping with a constant threshold, private training remains…
In this work we are interested in stochastic particle methods for multi-objective optimization. The problem is formulated using parametrized, single-objective sub-problems which are solved simultaneously. To this end a consensus based…