Optimistic Optimization of Gaussian Process Samples
This work addresses the computational limitations of Bayesian optimization for global optimization, offering a faster alternative that retains some of its functionality, which is incremental in bridging geometric and probabilistic search methods.
The paper tackled the problem of combining the conceptual advantages of Bayesian optimization with the computational efficiency of optimistic optimization by mapping kernels to dissimilarities, resulting in an algorithm with a run-time of up to O(N log N). It found that optimistic optimization is strongly preferable for stationary kernels on low-cost objectives, while Bayesian optimization performs better for strongly coupled models.
Bayesian optimization is a popular formalism for global optimization, but its computational costs limit it to expensive-to-evaluate functions. A competing, computationally more efficient, global optimization framework is optimistic optimization, which exploits prior knowledge about the geometry of the search space in form of a dissimilarity function. We investigate to which degree the conceptual advantages of Bayesian Optimization can be combined with the computational efficiency of optimistic optimization. By mapping the kernel to a dissimilarity, we obtain an optimistic optimization algorithm for the Bayesian Optimization setting with a run-time of up to $\mathcal{O}(N \log N)$. As a high-level take-away we find that, when using stationary kernels on objectives of relatively low evaluation cost, optimistic optimization can be strongly preferable over Bayesian optimization, while for strongly coupled and parametric models, good implementations of Bayesian optimization can perform much better, even at low evaluation cost. We argue that there is a new research domain between geometric and probabilistic search, i.e. methods that run drastically faster than traditional Bayesian optimization, while retaining some of the crucial functionality of Bayesian optimization.