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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 $Ω(d\min\{d,\sqrt{LR^2/\varepsilon}\})$ for adaptive randomized algorithms in the
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