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On-line learning with malicious noise and the closure algorithm

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Abstract

We investigate a variant of the on-line learning model for classes of \0,1\-valued functions (concepts) in which the labels of a certain amount of the input instances are corrupted by adversarial noise. We propose an extension of a general learning strategy, known as “Closure Algorithm”, to this noise model, and show a worst-case mistake bound of m + (d+1)K for learning an arbitrary intersection-closed concept class C, where K is the number of noisy labels, d is a combinatorial parameter measuring C's complexity, and m is the worst-case mistake bound of the Closure Algorithm for learning C in the noise-free model. For several concept classes our extended Closure Algorithm is efficient and can tolerate a noise rate up to the information-theoretic upper bound. Finally, we show how to efficiently turn any algorithm for the on-line noise model into a learning algorithm for the PAC model with malicious noise.

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Authors and Affiliations

  1. IGI, Graz University of Technology, Klosterwiesgasse 32/2, A-8010, Graz, Austria

    Peter Auer

  2. DSI, University of Milan, Via Comelico 39, I-20135, Milano, Italy

    Nicolò Cesa-Bianchi

Authors
  1. Peter Auer
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  2. Nicolò Cesa-Bianchi
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Auer, P., Cesa-Bianchi, N. On-line learning with malicious noise and the closure algorithm. Annals of Mathematics and Artificial Intelligence 23, 83–99 (1998). https://doi.org/10.1023/A:1018960107028

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