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We prove that every online learnable class of functions of Littlestonedimension $d$ admits a learning algorithm with finite information complexity.Towards this end, we use the notion of a globally stable algorithm. Generally,the information complexity of such a globally stable algorithm is large yetfinite, roughly exponential in $d$. We also show there is room for improvement;for a canonical online learnable class, indicator functions of affine subspacesof dimension $d$, the information complexity can be upper boundedlogarithmically in $d$.

Finite Littlestone Dimension Implies Finite Information Complexity