Optimistic Tree Searches for Combinatorial Black-Box Optimization

The optimization of combinatorial black-box functions is pervasive in computer science and engineering. However, the combinatorial explosion of the search space and lack of natural ordering pose significant challenges for current techniques from a theoretical and practical perspective, and require new algorithmic ideas. In this paper, we propose to adapt the recent advances in tree searches and partitioning techniques to design and analyze novel black-box combinatorial solvers. A first contribution is the analysis of a first tree-search algorithm called Optimistic Lipschitz Tree Search (OLTS) which assumes the Lipschitz constant of the function to be known. Linear convergence rates are provided for this algorithm under specific conditions, improving upon the logarithmic rates of baselines.