Pearlmutter, Barak A. (2005) Bounds on Query Convergence. Working Paper. arXiv.

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Abstract

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 meets it. We further establish a bound on the total regret, E[ sum_{i=1..t} (x_i - x*)^2 ] >= O(sqrt(t)) These bounds may impose practical limitations on an agent's performance, as O(eps^-4) queries are made before the queries converge to x* with eps accuracy.

Item Type:	Monograph (Working Paper)
Additional Information:	Cite as: arXiv:cs/0511088 [cs.LG]
Keywords:	Bounds; Query Convergence;
Academic Unit:	Faculty of Science and Engineering > Computer Science
Item ID:	8163
Identification Number:	arXiv:cs/0511088 [cs.LG]
Depositing User:	Barak Pearlmutter
Date Deposited:	13 Apr 2017 14:21
Publisher:	arXiv
Funders:	Science Foundation Ireland (SFI)
URI:	https://arxiv.org
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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