Abstract
We describe the optimization algorithm implemented in the open-source derivative-free solver RBFOpt. The algorithm is based on the radial basis function method of Gutmann and the metric stochastic response surface method of Regis and Shoemaker. We propose several modifications aimed at generalizing and improving these two algorithms: (i) the use of an extended space to represent categorical variables in unary encoding; (ii) a refinement phase to locally improve a candidate solution; (iii) interpolation models without the unisolvence condition, to both help deal with categorical variables, and initiate the optimization before a uniquely determined model is possible; (iv) a master-worker framework to allow asynchronous objective function evaluations in parallel. Numerical experiments show the effectiveness of these ideas.
Highlights
An optimization problem without any structural information on the objective function or the constraints, but for which we have the ability to evaluate them at given points, is called a black-box problem
The area of derivative-free optimization is dedicated to the study of optimization algorithms that do not rely on computing the partial derivatives of the objective function, and it is naturally applied to black-box problems
The algorithm uses the surrogate model to determine the point at which the objective function should be evaluated; this decision is based on criteria first introduced in [16, 33], together with the modifications discussed in [10]. We generalize these approaches in multiple ways, the most notable of which are: (i) We introduce a surrogate model defined in an extended space, mapping categorical variables to their unary encoding, and showing that all steps of the optimization algorithm can be performed in a natural way in either the original or the extended space
Summary
An optimization problem without any structural information on the objective function or the constraints, but for which we have the ability to evaluate them at given points, is called a black-box problem. This paper discusses the implementation of a global derivative-free optimization algorithm that is aimed at black-box problems with expensive objective function evaluations. We remark that RBFOpt is designed for deterministic black-box optimization problems, rather than hyperparameter optimization problems where the result of each objective evaluation is typically a sample from a random variable; we can use RBFOpt by fixing the dataset and the random seed used to train the classifier, thereby making the objective function deterministic This runs the risk of overfitting, as RBFOpt only observes one realization of a generalization error estimator, but in practice it can be an acceptable tradeoff.
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