Optimum-statistical Collaboration Towards General and Efficient Black-box Optimization
This work addresses the challenge of efficient black-box optimization for machine learning and AI applications, offering a more general and effective approach compared to prior incremental methods.
The paper tackles the problem of black-box optimization by delineating the roles of resolution and statistical uncertainty, leading to a general algorithm framework called optimum-statistical collaboration. It results in a variance-adaptive algorithm, VHCT, which achieves rate-optimal regret bounds in theory and outperforms prior methods in experiments.
In this paper, we make the key delineation on the roles of resolution and statistical uncertainty in hierarchical bandits-based black-box optimization algorithms, guiding a more general analysis and a more efficient algorithm design. We introduce the \textit{optimum-statistical collaboration}, an algorithm framework of managing the interaction between optimization error flux and statistical error flux evolving in the optimization process. We provide a general analysis of this framework without specifying the forms of statistical error and uncertainty quantifier. Our framework and its analysis, due to their generality, can be applied to a large family of functions and partitions that satisfy different local smoothness assumptions and have different numbers of local optimums, which is much richer than the class of functions studied in prior works. Our framework also inspires us to propose a better measure of the statistical uncertainty and consequently a variance-adaptive algorithm \texttt{VHCT}. In theory, we prove the algorithm enjoys rate-optimal regret bounds under different local smoothness assumptions; in experiments, we show the algorithm outperforms prior efforts in different settings.