Fourier Representations for Black-Box Optimization over Categorical Variables

Optimization of real-world black-box functions defined over purely categorical variables is an active area research. In particular, optimization and design biological sequences with specific functional or structural properties have a profound impact in medicine, materials science, biotechnology. Standalone search algorithms, such as simulated annealing (SA) Monte Carlo tree (MCTS), are typically used for problems. order to improve the performance sample efficiency we propose use existing methods conjunction surrogate model evaluations variables. To this end, present two different representations, group-theoretic Fourier expansion abridged one-hot encoded Boolean expansion. learn consider settings update our model. First, utilize adversarial online regression setting where characters each representation considered experts their respective coefficients updated via exponential weight rule time black box evaluated. Second, Bayesian queries selected Thompson sampling posterior sparse (over proposed representation) regularized horseshoe prior. Numerical experiments synthetic benchmarks well RNA sequence problems demonstrate representational power methods, which achieve competitive superior compared state-of-the-art counterparts, while improving computation cost and/or efficiency, substantially.