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In the recent years, a number of parameter-free algorithms have beendeveloped for online linear optimization over Hilbert spaces and for learningwith expert advice. These algorithms achieve optimal regret bounds that dependon the unknown competitors, without having to tune the learning rates withoracle choices.  We present a new intuitive framework to design parameter-free algorithms for\emph{both} online linear optimization over Hilbert spaces and for learningwith expert advice, based on reductions to betting on outcomes of adversarialcoins. We instantiate it using a betting algorithm based on theKrichevsky-Trofimov estimator. The resulting algorithms are simple, with noparameters to be tuned, and they improve or match previous results in terms ofregret guarantee and per-round complexity.

Coin Betting and Parameter-Free Online Learning