Online Learning from Finite Training Sets and Robustness to Input Bias

Authors:
Peter Sollich;David Barber
Affiliations:
Department of Physics, University of Edinburgh, Edinburgh EH9 3JZ, U.K.;Real World Computing Partnership Theoretical Foundation, SNN, University of Nijmegen, 6525 EZ Nijmegen, The Netherlands
Venue:
Neural Computation
Year:
1998

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Abstract

We analyze online gradient descent learning from finite training sets at noninfinitesimal learning rates η . Exact results are obtained for the time-dependent generalization error of a simple model system: a linear network with a large number of weights N, trained on p = αN examples. This allows us to study in detail the effects of finite training set size α on, for example, the optimal choice of learning rate η. We also compare online and offline learning, for respective optimal settings of η at given final learning time. Online learning turns out to be much more robust to input bias and actually outperforms offline learning when such bias is present; for unbiased inputs, online and offline learning perform almost equally well.