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THE GENERALIZATION ABILITY OF ONLINE ALGORITHMS
FOR DEPENDENT DATA
ABSTRACT:
We study the generalization performance of online learning algorithms trained on samples
coming from a dependent source of data. We show that the generalization error of any stable
online algorithm concentrates around its regret—an easily computable statistic of the online
performance of the algorithm—when the underlying ergodic process is - or -mixing.
We show high probability error bounds assuming the loss function is convex, and we also
establish sharp convergence rates and deviation bounds for strongly convex losses and several
linear prediction problems such as linear and logistic regression, least-squares SVM, and
boosting on dependent data.
Our results have straightforward applications to stochastic optimization with dependent data, and
our analysis requires only martingale convergence arguments; we need not rely on more
powerful statistical tools such as empirical process theory.