Parameter-Free Convex Learning through Coin Betting

We present a new parameter-free algorithm for online linear optimization over any Hilbert space. It is theoretically optimal, with regret guarantees as good as with the best possible learning rate. The algorithm is simple and easy to implement. The analysis is given via the adversarial coin-betting game, Kelly betting and the Krichevsky-Trofimov estimator. Applications to obtain parameter-free convex optimization and machine learning algorithms are shown.