Robust randomized optimization with k nearest neighbors

Henry Reeve, Ata Kaban

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Modern applications of machine learning typically require the tuning of a multitude of hyperparameters. With this motivation in mind, we consider the problem of optimization given a set of noisy function evaluations. We focus on robust optimization in which the goal is to find a point in the input space such that the function remains high when perturbed by an adversary within a given radius. Here we identify the minimax optimal rate for this problem, which turns out to be of order (n-λ/(2λ+1)), where n is the sample size and λ quantifies the smoothness of the function for a broad class of problems, including situations where the metric space is unbounded. The optimal rate is achieved (up to logarithmic factors) by a conceptually simple algorithm based on k-nearest neighbor regression.

Original languageEnglish
Pages (from-to)819-836
Number of pages18
JournalAnalysis and Applications
Issue number5
Publication statusPublished - 1 Sept 2019

Bibliographical note

(In Special Issue on Mathematics of Big Data: Deep Learning, Approximation and Optimization)


  • Optimisation for machine learning
  • metric spaces
  • non-parametric methods
  • Optimization for machine learning

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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