• Corpus ID: 16018339

Bounds on Query Convergence

@article{Pearlmutter2005BoundsOQ,
  title={Bounds on Query Convergence},
  author={Barak A. Pearlmutter},
  journal={ArXiv},
  year={2005},
  volume={abs/cs/0511088}
}
The problem of finding an optimum using noisy evaluations of a smooth cost function arises in many contexts, including economics, business, medicine, experiment design, and foraging theory. We derive an asymptotic bound E[ (x_t - x*)^2 ] >= O(1/sqrt(t)) on the rate of convergence of a sequence (x_0, x_1, >...) generated by an unbiased feedback process observing noisy evaluations of an unknown quadratic function maximised at x*. The bound is tight, as the proof leads to a simple algorithm which… 

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