Sample Efficient Graph-Based Optimization with Noisy Observations

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Thanh Tan Nguyen, Ali Shameli, Yasin Abbasi-Yadkori, Anup Rao, Branislav Kveton ;
Proceedings of Machine Learning Research, PMLR 89:3333-3341, 2019.

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 advertising application.

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