ﻻ يوجد ملخص باللغة العربية
In this paper, the problem of safe global maximization (it should not be confused with robust optimization) of expensive noisy black-box functions satisfying the Lipschitz condition is considered. The notion safe means that the objective function $f(x)$ during optimization should not violate a safety threshold, for instance, a certain a priori given value $h$ in a maximization problem. Thus, any new function evaluation (possibly corrupted by noise) must be performed at safe points only, namely, at points $y$ for which it is known that the objective function $f(y) > h$. The main difficulty here consists in the fact that the used optimization algorithm should ensure that the safety constraint will be satisfied at a point $y$ before evaluation of $f(y)$ will be executed. Thus, it is required both to determine the safe region $Omega$ within the search domain~$D$ and to find the global maximum within $Omega$. An additional difficulty consists in the fact that these problems should be solved in the presence of the noise. This paper starts with a theoretical study of the problem and it is shown that even though the objective function $f(x)$ satisfies the Lipschitz condition, traditional Lipschitz minorants and majorants cannot be used due to the presence of the noise. Then, a $delta$-Lipschitz framework and two algorithms using it are proposed to solve the safe global maximization problem. The first method determines the safe area within the search domain and the second one executes the global maximization over the found safe region. For both methods a number of theoretical results related to their functioning and convergence is established. Finally, numerical experiments confirming the reliability of the proposed procedures are performed.
We present mlrMBO, a flexible and comprehensive R toolbox for model-based optimization (MBO), also known as Bayesian optimization, which addresses the problem of expensive black-box optimization by approximating the given objective function through a
We propose a novel information-theoretic approach for Bayesian optimization called Predictive Entropy Search (PES). At each iteration, PES selects the next evaluation point that maximizes the expected information gained with respect to the global max
Langevin dynamics (LD) has been proven to be a powerful technique for optimizing a non-convex objective as an efficient algorithm to find local minima while eventually visiting a global minimum on longer time-scales. LD is based on the first-order La
In this work, we study the problem of global optimization in univariate loss functions, where we analyze the regret of the popular lower bounding algorithms (e.g., Piyavskii-Shubert algorithm). For any given time $T$, instead of the widely available
We propose a new distributed optimization algorithm for solving a class of constrained optimization problems in which (a) the objective function is separable (i.e., the sum of local objective functions of agents), (b) the optimization variables of di