Sample Efficient Graph-Based Optimization with Noisy Observations
Abstract
We study sample complexity of optimizing "hill-climbing friendly" functions defined on a graph under noisy observations. We define a notion of convexity, and we show that a variant of best-arm identification can find a near-optimal solution after a small number of queries that is independent of the size of the graph. For functions that have local minima and are nearly convex, we show a sample complexity for the classical simulated annealing under noisy observations. We show effectiveness of the greedy algorithm with restarts and the simulated annealing on problems of graph-based nearest neighbor classification as well as a web document re-ranking application.
Keywords
Cite
@article{arxiv.2006.02672,
title = {Sample Efficient Graph-Based Optimization with Noisy Observations},
author = {Tan Nguyen and Ali Shameli and Yasin Abbasi-Yadkori and Anup Rao and Branislav Kveton},
journal= {arXiv preprint arXiv:2006.02672},
year = {2020}
}
Comments
The first version of this paper appeared in AISTATS 2019. Thank to community feedback, some typos and a minor issue have been identified. Specifically, on page 4, column 2, line 18, the statement $\Delta_{1,s} \ge (1+m)^{S-1-s} \Delta_1$ is not valid, and in the proof of Theorem 2, "By Lemma 1" should be "By Definition 2". These problems are fixed in this updated version published here on arxiv