Combinatorial Black-Box Optimization with Expert Advice
Aug 13, 20207 views
We consider the problem of black-box function optimization over,the Boolean hypercube. Despite the vast literature on black-box,function optimization over continuous domains, not much attention,has been paid to learning models for optimization over combinatorial domains until recently. However, the computational complexity,of the recently devised algorithms are prohibitive even for moderate numbers of variables; drawing one sample using the existing,algorithms is more expensive than a function evaluation for many,black-box functions of interest. To address this problem, we propose a computationally efficient model learning algorithm based on,multilinear polynomials and exponential weight updates. In the proposed algorithm, we alternate between simulated annealing with,respect to the current polynomial representation and updating the,weights using monomial experts’ advice. Numerical experiments,on various datasets in both unconstrained and sum-constrained,Boolean optimization indicate the competitive performance of the,proposed algorithm, while improving the computational time up to,several orders of magnitude compared to state-of-the-art algorithms,in the literature.