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A framework is introduced for sequentially solving convex stochastic minimization problems, where the objective functions change slowly, in the sense that the distance between successive minimizers is bounded. The minimization problems are…
Bayesian Optimization with multi-objective acquisition functions such as q-Expected Hypervolume Improvement (qEHVI) requires efficient candidate optimization to maximize acquisition function values. Traditional approaches rely on continuous…
In this paper, we propose: (a) a restart schedule for an adaptive simulated annealer, and (b) parallel simulated annealing, with an adaptive and parameter-free annealing schedule. The foundation of our approach is the Modified Lam annealing…
Simulation is increasingly being used for generating large labelled datasets in many machine learning problems. Recent methods have focused on adjusting simulator parameters with the goal of maximising accuracy on a validation task, usually…
A new approach to the solution of boundary value problems within the so-called fictitious domain methods philosophy is proposed which avoids well known shortcomings of other fictitious domain methods, including the need to generate…
A framework previously introduced in [3] for solving a sequence of stochastic optimization problems with bounded changes in the minimizers is extended and applied to machine learning problems such as regression and classification. The…
Optimization problems with an auxiliary latent variable structure in addition to the main model parameters occur frequently in computer vision and machine learning. The additional latent variables make the underlying optimization task…
We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. The algorithm can be seen as an analogue of quantum annealing under the restriction of a product state space, where…
We discuss kinetic-based particle optimization methods and variable-sample strategies for problems where the cost function represents the expected value of a random mapping. Kinetic-based optimization methods rely on a consensus mechanism…
We propose and study a version of simulated annealing (SA) on continuous state spaces based on $(t,s)_R$-sequences. The parameter $R\in\bar{\mathbb{N}}$ regulates the degree of randomness of the input sequence, with the case $R=0$…
In this paper, a simulation-based method for the analysis and design of abstracted models for a stochastic hybrid system is proposed. The accuracy of a model is evaluated in terms of its capability to reproduce the system output for all the…
In this paper, we introduce a quantum-enhanced algorithm for simulation-based optimization. Simulation-based optimization seeks to optimize an objective function that is computationally expensive to evaluate exactly, and thus, is…
Minimax optimization has been central in addressing various applications in machine learning, game theory, and control theory. Prior literature has thus far mainly focused on studying such problems in the continuous domain, e.g.,…
A framework is introduced for solving a sequence of slowly changing optimization problems, including those arising in regression and classification applications, using optimization algorithms such as stochastic gradient descent (SGD). The…
Simulated annealing (SA) is a kind of relaxation method for finding equilibria of Hamiltonian systems. A set of evolution equations is solved with SA, which is derived from the original Hamiltonian system so that the energy of the system…
Given an energy potential on the Euclidian space, a piecewise deterministic Markov process is designed to sample the corresponding Gibbs measure. In dimension one an Eyring-Kramers formula is obtained for the exit time of the domain of a…
We present an algorithm for a class of statistical inference problems. The main idea is to reformulate the inference problem as an optimization procedure, based on the generation of surrogate (auxiliary) functions. This approach is…
Quantitative long-time entropic convergence and short-time regularization are established for an idealized Hamiltonian Monte Carlo chain which alternatively follows an Hamiltonian dynamics for a fixed time and then partially or totally…
An algorithm is proposed that enables the imposition of shape constraints on regression curves, without requiring the constraints to be written as closed-form expressions, nor assuming the functional form of the loss function. This…
We introduce a constraint-based framework for studying infinite qualitative simulations concerned with contingencies such as time, space, shape, size, abstracted into a finite set of qualitative relations. To define the simulations, we…