Related papers: Safe global optimization of expensive noisy black-…

Topology optimization of frame structures under free-vibration eigenvalue constraints constitutes a challenging nonconvex polynomial optimization problem with disconnected feasible sets. In this article, we first formulate it as a…

Users of location-based services (LBSs) are highly vulnerable to privacy risks since they need to disclose, at least partially, their locations to benefit from these services. One possibility to limit these risks is to obfuscate the…

Zeroth-order optimization (ZO) algorithms have been recently used to solve black-box or simulation-based learning and control problems, where the gradient of the objective function cannot be easily computed but can be approximated using the…

Bayesian optimization and Lipschitz optimization have developed alternative techniques for optimizing black-box functions. They each exploit a different form of prior about the function. In this work, we explore strategies to combine these…

In this paper, the problem of estimating the level set of a black-box function from noisy and expensive evaluation queries is considered. A new algorithm for this problem in the Bayesian framework with a Gaussian Process (GP) prior is…

This paper introduces a relaxed noise calibration method to enhance data utility while attaining pufferfish privacy. This work builds on the existing $1$-Wasserstein (Kantorovich) mechanism by alleviating the existing overly strict…

Certified robustness is a desirable property for deep neural networks in safety-critical applications, and popular training algorithms can certify robustness of a neural network by computing a global bound on its Lipschitz constant.…

We consider Bayesian optimization of objective functions of the form $\rho[ F(x, W) ]$, where $F$ is a black-box expensive-to-evaluate function and $\rho$ denotes either the VaR or CVaR risk measure, computed with respect to the randomness…

In this paper, the problem of maximizing a black-box function $f:\mathcal{X} \to \mathbb{R}$ is studied in the Bayesian framework with a Gaussian Process (GP) prior. In particular, a new algorithm for this problem is proposed, and high…

We consider the problem of optimizing expensive black-box functions over discrete spaces (e.g., sets, sequences, graphs). The key challenge is to select a sequence of combinatorial structures to evaluate, in order to identify…

The graduated optimization approach is a method for finding global optimal solutions for nonconvex functions by using a function smoothing operation with stochastic noise. This paper makes three contributions regarding graduated…

In statistics, it is common to encounter multi-modal and non-smooth likelihood (or objective function) maximization problems, where the parameters have known upper and lower bounds. This paper proposes a novel derivative-free global…

Consensus based optimization is a derivative-free particles-based method for the solution of global optimization problems. Several versions of the method have been proposed in the literature, and different convergence results have been…

Motivated by a wide range of applications in data mining and machine learning, we consider the problem of maximizing a submodular function subject to supermodular cost constraints. In contrast to the well-understood setting of cardinality…

We have an $\m\x\n$ real-valued arbitrary matrix $A$ (e.g. a dictionary) with $\m<\n$ and data $d$ describing the sought-after object with the help of $A$. This work provides an in-depth analysis of the (local and global) minimizers of an…

Safe Bayesian optimization (BO) algorithms promise to find optimal control policies without knowing the system dynamics while at the same time guaranteeing safety with high probability. In exchange for those guarantees, popular algorithms…

We characterize the complexity of minimizing $\max_{i\in[N]} f_i(x)$ for convex, Lipschitz functions $f_1,\ldots, f_N$. For non-smooth functions, existing methods require $O(N\epsilon^{-2})$ queries to a first-order oracle to compute an…

We investigate the convergence properties of a class of iterative algorithms designed to minimize a potentially non-smooth and noisy objective function, which may be algebraically intractable and whose values may be obtained as the output…

Bayesian optimisation is a powerful tool to solve expensive black-box problems, but fails when the stationary assumption made on the objective function is strongly violated, which is the case in particular for ill-conditioned or…

It was recently shown in [http://arxiv.org/abs/1207.5518] that revenue optimization can be computationally efficiently reduced to welfare optimization in all multi-dimensional Bayesian auction problems with arbitrary (possibly…