Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal rates for zero-order convex optimization: the power of two
  function evaluations   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. We establish such results for both smooth and non-smooth
cases, sharpening previous analyses that suggested a worse dimension
dependence, and extend our results to the case of multiple ($m \ge 2$)
evaluations. We complement our algorithmic development with
information-theoretic lower bounds on the minimax convergence rate of such
problems, establishing the sharpness of our achievable results up to constant
(sometimes logarithmic) factors.

37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph