Exploiting Random Walks for Learning

In this paper we consider an approach to passive learning. In contrast to the classical PAC model we do not assume that the examples are independently drawn according to an underlying distribution, but that they are generated by a time-driven process. We define deterministic and probabilistic learning models of this sort and investigate the relationships between them and with other models. The fact that successive examples are related can often be used to gain additional information similar to the information gained by membership queries. We show how this can be used to design on-line prediction algorithms. In particular, we present efficient algorithms for exactly identifying Boolean threshold functions and 2-term RSE, and for learning 2-term-DNF, when the examples are generated by a random walk on {0, 1}n.

[1]  Leslie G. Valiant,et al.  A theory of the learnable , 1984, STOC '84.

[2]  N. Littlestone.  Learning Quickly When Irrelevant Attributes Abound: A New Linear-Threshold Algorithm , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[3]  M. Kearns,et al.  Recent Results on Boolean Concept Learning , 1987 .

[4]  David Haussler,et al.  Predicting (0, 1)-functions on randomly drawn points , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[5]  David Haussler,et al.  Equivalence of models for polynomial learnability , 1988, COLT '88.

[6]  Nick Littlestone,et al.  From on-line to batch learning , 1989, COLT '89.

[7]  A Markovian extension of Valiant's learning model , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[8]  Ronald L. Graham,et al.  Asymptotic Analysis of a Random Walk on a Hypercube with Many Dimensions , 1990, Random Struct. Algorithms.

[9]  Avrim Blum.  Separating PAC and mistake-bound learning models over the Boolean domain (abstract) , 1990, COLT '90.

[10]  Hans Ulrich Simon,et al.  On learning ring-sum-expansions , 1990, COLT '90.

[11]  Peter L. Bartlett,et al.  Learning with a slowly changing distribution , 1992, COLT '92.

[12]  Manfred K. Warmuth,et al.  Some weak learning results , 1992, COLT '92.

[13]  Ronitt Rubinfeld,et al.  Efficient learning of typical finite automata from random walks , 1993, STOC.

[14]  Dharmendra S. Modha,et al.  Minimum complexity regression estimation with weakly dependent observations , 1996, IEEE Trans. Inf. Theory.

[15]  Marco C. Campi,et al.  Learning dynamical systems in a stationary environment , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[16]  Guy A. Dumont,et al.  Learning of nonlinear FIR models under uniform distribution , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[17]  Peter L. Bartlett,et al.  Estimation and Approximation Bounds for Gradient-Based Reinforcement Learning , 2000, J. Comput. Syst. Sci..