Optimal rates for zero-order convex optimization: the power of two function evaluations

7 Dec 2013John C. DuchiMichael I. JordanMartin J. WainwrightAndre Wibisono

We consider derivative-free algorithms for stochastic and non-stochastic convex optimization problems that use only function values rather than gradients. Focusing on non-asymptotic bounds on convergence rates, we show that if pairs of function values are available, algorithms for $d$-dimensional optimization that use gradient estimates based on random perturbations suffer a factor of at most $\sqrt{d}$ in convergence rate over traditional stochastic gradient methods... (read more)

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