Online Passive-Aggressive Algorithms
Koby Crammer, Ofer Dekel, Joseph Keshet, Shai Shalev-Shwartz and Yoram Singer
Technical Report, Leibniz Center
We present a family of online learning, margin based, algorithms for various prediction tasks. In particular we derive and analyze algorithms for binary and multiclass categorization, regression, uniclass prediction and sequence prediction. All of the algorithms we present can utilize kernel functions. The update steps of our different algorithms are all based on analytical solutions to simple constrained optimization problems. This unified view allows us to prove worst-case loss bounds for the different algorithms and for the various decision problems based on a single lemma. Our bounds on the cumulative loss of the algorithms are relative to the smallest loss that can be attained by any fixed hypothesis, and as such are applicable to both realizable and unrealizable settings. We demonstrate some of the merits of the proposed algorithms in a series of experiments with synthetic and real datasets.