A Combinatorial Characterization of Supervised Online Learnability
Vinod Raman, Unique Subedi, Ambuj Tewari
TL;DR
This paper introduces the sequential minimax dimension, a new combinatorial measure that precisely characterizes the online learnability of hypothesis classes under bounded loss functions, unifying existing dimensions.
Contribution
It proposes a novel scale-sensitive combinatorial dimension that provides a tight characterization of online learnability and encompasses most existing dimensions.
Findings
Sequential minimax dimension characterizes online learnability.
It subsumes most existing combinatorial dimensions.
Provides a tight quantitative measure for online learnability.
Abstract
We study the online learnability of hypothesis classes with respect to arbitrary, but bounded loss functions. No characterization of online learnability is known at this level of generality. We give a new scale-sensitive combinatorial dimension, named the sequential minimax dimension, and show that it gives a tight quantitative characterization of online learnability. In addition, we show that the sequential minimax dimension subsumes most existing combinatorial dimensions in online learning theory.
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Taxonomy
TopicsAdvanced Bandit Algorithms Research · Machine Learning and Algorithms · Computability, Logic, AI Algorithms