Mixability made efficient: Fast online multiclass logistic regression

• URL: http://arxiv.org/abs/2110.03960v1
• Date: Fri, 8 Oct 2021 08:22:05 GMT
• Title: Mixability made efficient: Fast online multiclass logistic regression
• Authors: R\'emi J\'ez\'equel (SIERRA), Pierre Gaillard (Thoth), Alessandro Rudi (SIERRA)
• Abstract summary: We show that mixability can be a powerful tool to obtain algorithms with optimal regret. The resulting methods often suffer from high computational complexity which has reduced their practical applicability.
• Score: 68.8204255655161
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Mixability has been shown to be a powerful tool to obtain algorithms with optimal regret. However, the resulting methods often suffer from high computational complexity which has reduced their practical applicability. For example, in the case of multiclass logistic regression, the aggregating forecaster (Foster et al. (2018)) achieves a regret of $O(\log(Bn))$ whereas Online Newton Step achieves $O(e^B\log(n))$ obtaining a double exponential gain in $B$ (a bound on the norm of comparative functions). However, this high statistical performance is at the price of a prohibitive computational complexity $O(n^{37})$.

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