Exponentiated Gradient versus Gradient Descent for Linear Predictors

We consider two algorithms for on-line prediction based on a linear model. The algorithms are the well-known gradient descent (GD) algorithm and a new algorithm, which we call EG ±. They both maintain a weight vector using simple updates. For the GD algorithm, the update is based on subtracting the...

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Bibliographic Details
Published in:Information and computation Vol. 132; no. 1; pp. 1 - 63
Main Authors: Kivinen, Jyrki, Warmuth, Manfred K.
Format: Journal Article
Language:English
Published: San Diego, CA Elsevier Inc 10.01.1997
Elsevier
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Artificial intelligence
Computer science; control theory; systems
Exact sciences and technology
Learning and adaptive systems
Theoretical computing
Learning
Linear prediction
Algorithms
Gradient method
Descent method
On line processing
ISSN:0890-5401, 1090-2651
Online Access:Get full text
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Summary:We consider two algorithms for on-line prediction based on a linear model. The algorithms are the well-known gradient descent (GD) algorithm and a new algorithm, which we call EG ±. They both maintain a weight vector using simple updates. For the GD algorithm, the update is based on subtracting the gradient of the squared error made on a prediction. The EG ±algorithm uses the components of the gradient in the exponents of factors that are used in updating the weight vector multiplicatively. We present worst-case loss bounds for EG ±and compare them to previously known bounds for the GD algorithm. The bounds suggest that the losses of the algorithms are in general incomparable, but EG ±has a much smaller loss if only few components of the input are relevant for the predictions. We have performed experiments which show that our worst-case upper bounds are quite tight already on simple artificial data.
ISSN:0890-5401
1090-2651
DOI:10.1006/inco.1996.2612