Finite-sample performance guarantees for one-dimensional stochastic root finding. Ehrlichman, S. M. T. & Henderson, S. G. In Henderson, S. G., Biller, B., Hsieh, M., Shortle, J., Tew, J. D., & Barton, R. R., editors, Proceedings of the 2007 Winter Simulation Conference, pages 313–321, Piscataway, New Jersey, 2007. IEEE.
Finite-sample performance guarantees for one-dimensional stochastic root finding [pdf]Paper  abstract   bibtex   
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 naive stochastic bisection.

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