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We study sample complexity of optimizing "hill-climbing friendly" functionsdefined 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-optimalsolution after a small number of queries that is independent of the size of thegraph. For functions that have local minima and are nearly convex, we show asample complexity for the classical simulated annealing under noisyobservations. We show effectiveness of the greedy algorithm with restarts andthe simulated annealing on problems of graph-based nearest neighborclassification as well as a web document re-ranking application.

Sample Efficient Graph-Based Optimization with Noisy Observations