On-line Prediction and Conversion Strategies

We study the problem of deterministically predicting boolean valuesby combining the boolean predictions of several experts.Previous on-line algorithms for this problem predict with the weightedmajority of the experts' predictions.These algorithms give each expert an exponential weight βmwhere β is a constant in [0,1) and m is the number of mistakesmade by the expert in the past. We show that it is better to usesums of binomials as weights.In particular, we present a deterministic algorithmusing binomial weights that has a better worst case mistake bound than thebest deterministic algorithm using exponential weights.The binomial weights naturally arise from a version space argument.We also show how both exponential and binomial weighting schemes can beused to make prediction algorithms robust against noise.

[1]  H. Chernoff.  A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations , 1952 .

[2]  W. W. Peterson,et al.  Error-Correcting Codes. , 1962 .

[3]  S. Ulam,et al.  Adventures of a Mathematician , 2019, Mathematics: People · Problems · Results.

[4]  Tom M. Mitchell,et al.  Version Spaces: A Candidate Elimination Approach to Rule Learning , 1977, IJCAI.

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

[6]  Dana Angluin,et al.  Queries and concept learning , 1988, Machine Learning.

[7]  Vladimir Vovk,et al.  Aggregating strategies , 1990, COLT '90.

[8]  N. Littlestone.  Mistake bounds and logarithmic linear-threshold learning algorithms , 1990 .

[9]  Javed A. Aslam,et al.  Searching in the presence of linearly bounded errors , 1991, STOC '91.

[10]  Philip M. Long,et al.  On-line learning of linear functions , 1991, STOC '91.

[11]  Noga Alon,et al.  The Probabilistic Method , 2015, Fundamentals of Ramsey Theory.

[12]  Joel H. Spencer,et al.  Ulam's Searching Game with a Fixed Number of Lies , 1992, Theor. Comput. Sci..

[13]  David Haussler,et al.  How to use expert advice , 1993, STOC.

[14]  Manfred K. Warmuth,et al.  Using experts for predicting continuous outcomes , 1994, European Conference on Computational Learning Theory.

[15]  Philip M. Long,et al.  Worst-case quadratic loss bounds for a generalization of the Widrow-Hoff rule , 1993, COLT '93.

[16]  Manfred K. Warmuth,et al.  The Weighted Majority Algorithm , 1994, Inf. Comput..

[17]  Philip M. Long,et al.  Simulating access to hidden information while learning , 1994, STOC '94.

[18]  Philip M. Long,et al.  Worst-case quadratic loss bounds for prediction using linear functions and gradient descent , 1996, IEEE Trans. Neural Networks.

[19]  Ehl Emile Aarts,et al.  Simulated annealing and Boltzmann machines , 2003 .

[20]  Philip M. Long,et al.  Structural Results About On-line Learning Models With and Without Queries , 1999, Machine Learning.

[21]  黄岩.  How to use , 2020, Biological Chirality.

[22]  F. Lemmermeyer.  Error-correcting Codes , 2005 .