PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

An Optimal Anytime Estimator Algorithm
Ricard Gavaldà
(2004) Technical Report. Departament de Llenguatges i Sistemes Informatics, UPC, Barcelona, Spain.

Abstract

In many applications a key step is estimating some unknown quantity X from a sequence of trials, each having expected value X. Optimal algorithms are known when the task is to estimate X within a multiplicative factor of e, for an e<1 given in advance. In this paper we consider <i>anytime</i> approximation algorithms, i.e., algorithms that must give a reliable approximation after each trial, and whose approximations have to be increasingly accurate as the number of trials grows. We give an anytime algorithm for this task when the only a-priori known property of X is its range, and show that it is asymptotically optimal in some cases, in the sense that no correct anytime algorithm can give asymptotically better approximations. The key ingredient is a new large deviation bound for the supremum of the deviations in an infinite sequence of trials, which can be seen as a non-limit analog of the classical Law of the Iterated Logarithm.

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EPrint Type:Monograph (Technical Report)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:930
Deposited By:Ricard Gavaldà
Deposited On:07 January 2005