TY - JOUR
AU - Karabag, Mustafa O.
AU - Neary, Cyrus
AU - Topcu, Ufuk
PY - 2021/05/18
Y2 - 2022/05/24
TI - Smooth Convex Optimization Using Sub-Zeroth-Order Oracles
JF - Proceedings of the AAAI Conference on Artificial Intelligence
JA - AAAI
VL - 35
IS - 5
SE - AAAI Technical Track on Constraint Satisfaction and Optimization
DO -
UR - https://ojs.aaai.org/index.php/AAAI/article/view/16499
SP - 3815-3822
AB - We consider the problem of minimizing a smooth, Lipschitz, convex function over a compact, convex set using sub-zeroth-order oracles: an oracle that outputs the sign of the directional derivative for a given point and a given direction, an oracle that compares the function values for a given pair of points, and an oracle that outputs a noisy function value for a given point. We show that the sample complexity of optimization using these oracles is polynomial in the relevant parameters. The optimization algorithm that we provide for the comparator oracle is the first algorithm with a known rate of convergence that is polynomial in the number of dimensions. We also give an algorithm for the noisy-value oracle that incurs sublinear regret in the number of queries and polynomial regret in the number of dimensions.
ER -