Optimal tradeoff between zeroth-order queries and projection or LMO complexity

Determine the optimal tradeoff between function-value query complexity and projection or linear-minimization-oracle complexity for the zeroth-order constrained nonsmooth nonconvex optimization algorithms analyzed in the paper.

Background

The zeroth-order projection-based and projection-free algorithms achieve optimal dependence on the dimension and stationarity parameters in function-value query complexity. However, their computational costs, measured by the number of projections or linear minimization oracle (LMO) calls, can be substantially larger. Averaging independent two-point gradient estimators reduces the dimension dependence of these computational costs while preserving query complexity, but the resulting query–computation balance is not characterized optimally.