This paper presents a new optimization methods that combines Bayesian optimization applied locally with concepts from MADS to provide nonlocal exploration. The main idea of the paper is to find an algorithm that is suitable for the range of functions that are slightly expensive, but not enough to require the sample efficiency of standard Bayesian optimization. The authors applied this method for maximum likelihood computations within the range of a 1 second. A standard critique to Bayesian optimization methods is that they are very expensive due to the fact that they rely on a surrogate model, like a Gaussian process that has a O(n 3) cost. The method presented in this paper (BADS) also rely on a GP.

Computational models in fields such as computational neuroscience are often evaluated via stochastic simulation or numerical approximation. Fitting these models implies a difficult optimization problem over complex, possibly noisy parameter landscapes. Bayesian optimization (BO) has been successfully applied to solving expensive black-box problems in engineering and machine learning. Here we explore whether BO can be applied as a general tool for model fitting. First, we present a novel hybrid BO algorithm, Bayesian adaptive direct search (BADS), that achieves competitive performance with an affordable computational overhead for the running time of typical models.