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This investigation seeks to establish the practicality of numerical frame approximations. Specifically, it develops a new method to approximate the inverse frame operator and analyzes its convergence properties. It is established that…

In this paper, we propose and analyze a trust-region model-based algorithm for solving unconstrained stochastic optimization problems. Our framework utilizes random models of an objective function $f(x)$, obtained from stochastic…

Building upon our earlier work of a martingale approach to global optimization, a powerful stochastic search scheme for the global optimum of cost functions is proposed on the basis of change of measures on the states that evolve as…

We consider minimizing functions for which it is expensive to compute the (possibly stochastic) gradient. Such functions are prevalent in reinforcement learning, imitation learning and adversarial training. Our target optimization framework…

We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits the…

We consider robust optimization problems, where the goal is to optimize in the worst case over a class of objective functions. We develop a reduction from robust improper optimization to Bayesian optimization: given an oracle that returns…

We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.…

When artificial neural networks have demonstrated exceptional practical success in a variety of domains, investigations into their theoretical characteristics, such as their approximation power, statistical properties, and generalization…

Bayesian Optimisation (BO) methods seek to find global optima of objective functions which are only available as a black-box or are expensive to evaluate. Such methods construct a surrogate model for the objective function, quantifying the…

We consider unconstrained stochastic optimization problems with no available gradient information. Such problems arise in settings from derivative-free simulation optimization to reinforcement learning. We propose an adaptive sampling…

Bayesian optimization has become a fundamental global optimization algorithm in many problems where sample efficiency is of paramount importance. Recently, there has been proposed a large number of new applications in fields such as…

We revisit the optimization from samples (OPS) model, which studies the problem of optimizing objective functions directly from the sample data. Previous results showed that we cannot obtain a constant approximation ratio for the maximum…

Chemical space is so large that brute force searches for new interesting molecules are infeasible. High-throughput virtual screening via computer cluster simulations can speed up the discovery process by collecting very large amounts of…

Bayesian optimization (BO) has become a powerful tool for solving simulation-based engineering optimization problems thanks to its ability to integrate physical and mathematical understandings, consider uncertainty, and address the…

In many domains, scientists build complex simulators of natural phenomena that encode their hypotheses about the underlying processes. These simulators can be deterministic or stochastic, fast or slow, constrained or unconstrained, and so…

Bayesian optimization is a powerful global optimization technique for expensive black-box functions. One of its shortcomings is that it requires auxiliary optimization of an acquisition function at each iteration. This auxiliary…

Existing work on data-driven optimization focuses on problems in static environments, but little attention has been paid to problems in dynamic environments. This paper proposes a data-driven optimization algorithm to deal with the…

Bayesian optimization is a sequential method for minimizing objective functions that are expensive to evaluate and about which few assumptions can be made. By using all gathered data to train a Gaussian process model for the function and…

When planning motions in a configuration space that has underlying symmetries (e.g. when manipulating one or multiple symmetric objects), the ideal planning algorithm should take advantage of those symmetries to produce shorter…

In this chapter, we discuss recent work on learning sparse approximations to high-dimensional functions on data, where the target functions may be scalar-, vector- or even Hilbert space-valued. Our main objective is to study how the…