We present a low-regret, parameter-free algorithm for online portfolio selection aimed at tracking an external benchmark’s returns using the mean absolute deviation loss. The algorithm is based on a black-box reduction technique of Cutkosky and Orabona (2018), that combines coin-betting for magnitude learning and online gradient descent for direction learning. For the baseline comparator class of constantly rebalanced portfolios, we establish a regret bound of \(O(\sqrt{T})\) , where T is the time horizon. The main contribution is the extension of this method to compete against functional comparators from a reproducing kernel Hilbert space by using a random feature-based approximation. The method is illustrated by two computer experiments: one is testing it against a constantly rebalanced portfolio in a high-dimensional market, and another is evaluating the random feature-based approach in a single-asset, mean-reverting market.
