Finite-sample performance guarantees for one-dimensional stochastic root finding

Authors:
Samuel M. T. Ehrlichman;Shane G. Henderson
Affiliations:
Cornell University, Ithaca, NY;Cornell University, Ithaca, NY
Venue:
Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come
Year:
2007

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Abstract

We study the one-dimensional root finding problem for increasing convex functions. We give gradient-free algorithms for both exact and inexact (stochastic) function evaluations. For the stochastic case, we supply a probabilistic convergence guarantee in the spirit of selection-of-the-best methods. A worst-case bound on the work performed by the algorithm shows an improvement over naïve stochastic bisection.