Lower Bounds For Gradient-Free Convex Optimization And Convex-Concave Saddle-Point Problems
We study the query complexity of optimization with exact scalar-value information. For globally $L$-smooth convex functions on $\mathbb R^d$ with a minimizer in a Euclidean ball of radius $R$, we prove the lower bound $\Omega(d\min\{d,\sqrt{LR^2/\varepsilon}\})$ for adaptive randomized algorithms in the stated accuracy...