Online Learning for Loss Functions with Memory and Applications to Statistical Arbitrage

In many online learning scenarios the loss functions are not memoryless, but rather depend on history. Our first contribution is a complete characterizat ion of sufficient and necessary conditions for learning with memory, accompanied with a novel algorithm fo r this framework that attains the optimal O( √ T )-regret. This improves previous online learning algorithm s that guaranteed O(T ) regret and required more stringent conditions. As an application of th e new technique, we address the classical problem in finance of constructing mean reverting portfolio s. We design an efficient online learning algorithm for this problem, and provide guarantees for its p erformance. We complement our theoretical findings with an empirical study that verifies our theoretica l results on financial data.