Efficient Online Learning with Memory via Frank-Wolfe Optimization: Algorithms with Bounded Dynamic Regret and Applications to Control

Projection operations are a typical computation bottleneck in online learning. In this paper, we enable projection-free online learning within the framework of Online Convex Optimization with Memory (OCO-M) -- OCO-M captures how the history of decisions affects the current outcome by allowing the online learning loss functions to depend on both current and past decisions. Particularly, we introduce the first projection-free meta-base learning algorithm with memory that minimizes dynamic regret, i.e., that minimizes the suboptimality against any sequence of time-varying decisions. We are motivated by artificial intelligence applications where autonomous agents need to adapt to time-varying environments in real-time, accounting for how past decisions affect the present. Examples of such applications are: online control of dynamical systems; statistical arbitrage; and time series prediction. The algorithm builds on the Online Frank-Wolfe (OFW) and Hedge algorithms. We demonstrate how our algorithm can be applied to the online control of linear time-varying systems in the presence of unpredictable process noise. To this end, we develop a controller with memory and bounded dynamic regret against any optimal time-varying linear feedback control policy. We validate our algorithm in simulated scenarios of online control of linear time-invariant systems.Comment: The version corrects proofs and updates presentatio

Ensembling and Dynamic Asset Selection for Risk-Controlled Statistical Arbitrage

In recent years, machine learning algorithms have been successfully employed to leverage the potential of identifying hidden patterns of financial market behavior and, consequently, have become a land of opportunities for financial applications such as algorithmic trading. In this paper, we propose a statistical arbitrage trading strategy with two key elements: an ensemble of regression algorithms for asset return prediction, followed by a dynamic asset selection. More specifically, we construct an extremely heterogeneous ensemble ensuring model diversity by using state-of-the-art machine learning algorithms, data diversity by using a feature selection process, and method diversity by using individual models for each asset, as well models that learn cross-sectional across multiple assets. Then, their predictive results are fed into a quality assurance mechanism that prunes assets with poor forecasting performance in the previous periods. We evaluate the approach on historical data of component stocks of the SP500 index. By performing an in-depth risk-return analysis, we show that this setup outperforms highly competitive trading strategies considered as baselines. Experimentally, we show that the dynamic asset selection enhances overall trading performance both in terms of return and risk. Moreover, the proposed approach proved to yield superior results during both financial turmoil and massive market growth periods, and it showed to have general application for any risk-balanced trading strategy aiming to exploit different asset classes