Efficient Online Large-Margin Classification via Dual Certificates
This work addresses online classification for optimization and learning applications, offering incremental improvements in theoretical guarantees and practical performance.
The paper tackles the problem of online classification by designing a translation-invariant algorithm based on the dual formulation of the maximum margin problem, resulting in improved mistake bounds and accuracy, with at most two mistakes per sequence in certain regimes compared to the perceptron's potential for arbitrarily many mistakes.
Online classification is a central problem in optimization, statistical learning and data science. Classical algorithms such as the perceptron offer efficient updates and finite mistake guarantees on linearly separable data, but they do not exploit the underlying geometric structure of the classification problem. We study the offline maximum margin problem through its dual formulation and use the resulting geometric insights to design a principled and efficient algorithm for the online setting. A key feature of our method is its translation invariance, inherited from the offline formulation, which plays a central role in its performance analysis. Our theoretical analysis yields improved mistake and margin bounds that depend only on translation-invariant quantities, offering stronger guarantees than existing algorithms under the same assumptions in favorable settings. In particular, we identify a parameter regime where our algorithm makes at most two mistakes per sequence, whereas the perceptron can be forced to make arbitrarily many mistakes. Our numerical study on real data further demonstrates that our method matches the computational efficiency of existing online algorithms, while significantly outperforming them in accuracy.