A General Online Algorithm for Optimizing Complex Performance Metrics
This work addresses the problem of optimizing complex metrics in online classification for machine learning practitioners, representing a novel extension from batch to online settings.
The paper tackles the challenge of optimizing non-decomposable performance metrics like F-measure in online learning, introducing a general algorithm that achieves O(ln n / n) regret for concave and smooth metrics and demonstrates efficiency in empirical studies.
We consider sequential maximization of performance metrics that are general functions of a confusion matrix of a classifier (such as precision, F-measure, or G-mean). Such metrics are, in general, non-decomposable over individual instances, making their optimization very challenging. While they have been extensively studied under different frameworks in the batch setting, their analysis in the online learning regime is very limited, with only a few distinguished exceptions. In this paper, we introduce and analyze a general online algorithm that can be used in a straightforward way with a variety of complex performance metrics in binary, multi-class, and multi-label classification problems. The algorithm's update and prediction rules are appealingly simple and computationally efficient without the need to store any past data. We show the algorithm attains $\mathcal{O}(\frac{\ln n}{n})$ regret for concave and smooth metrics and verify the efficiency of the proposed algorithm in empirical studies.