Sample Efficient Graph-Based Optimization with Noisy Observations

TL;DR

This paper investigates the sample complexity of optimizing functions on graphs with noisy data, introducing a convexity notion and demonstrating efficient algorithms like greedy and simulated annealing for near-optimal solutions.

Contribution

It introduces a new convexity concept for graph functions and analyzes the sample complexity of optimization algorithms under noise, applicable to classification and re-ranking tasks.

Findings

A variant of best-arm identification finds near-optimal solutions with queries independent of graph size.

Sample complexity bounds are established for simulated annealing on nearly convex functions with local minima.

Algorithms like greedy with restarts and simulated annealing are effective in practical graph-based problems.

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.