The Multi-Query Paradox in Zeroth-Order Optimization

Zeroth-order (ZO) optimization provides a powerful framework for problems where explicit gradients are unavailable and have to be approximated using only queries to function value. The prevalent single-query approach is simple, but suffers from high estimation variance, motivating a multi-query paradigm to improves estimation accuracy. This, however, creates a critical trade-off: under a fixed budget of queries (i.e. cost), queries per iteration and the total number of optimization iterations are inversely proportional to one another. How to best allocate this budget is a fundamental, under-explored question.