Bayesian online learning for online portfolio selection

We propose a novel family of Bayesian learning algorithms for online portfolio selection that overcome many of the shortcomings of traditional techniques, including selection bias (the failure to cover a broad universe of assets), data-snooping bias (the risk that a trading strategy's performance on past data is inflated due to hyperparameter overfitting) and a lack of robustness to transaction costs. As the basis for this novel family, we develop a Bayesian treatment of the online passive-aggressive and gradient descent algorithms, some of the most popular algorithms in the literature. Our approach starts from a probabilistic interpretation of the underlying objective functions and enables uncertainty modelling, probabilistic predictions as well as automatic, data-dependent hyperparameter tuning. We conclude by testing our proposals on real-world financial data. We further benchmark our framework on a wide range of canonical test problems, over which it achieves a significant improvement on its competitors. Beyond online portfolio selection, our algorithms contribute to the theory of adaptive gradient methods by equipping these with uncertainty estimates and a self-tuning mechanism for the learning rate parameter, which constitutes a major milestone in the area of Bayesian inference for neural networks.