Effective Online Portfolio Selection for the Long-Short Market Using Mirror Gradient Descent

Online portfolio selection has been actively studied to maximise overall returns by selecting the optimal portfolio weights using online algorithms. However, most work has focused on long-only portfolios, and developing efficient algorithms with loose portfolio constraints remains a challenge. In this letter, the classical online portfolio selection problem is reformulated to allow long/short and margin. For this problem, conventional gradient-based online algorithms face the challenges of high regret and computational complexity due to non-optimal gradients and high-dimensional projections. To tackle this, we propose a novel online algorithm that introduces mirror descent to achieve dimension-free regret in a non-Euclidean space. Specifically, a Bregman divergence is introduced to replace the
$\ell _{2}$
norm as a valid proximal setup for the problem to achieve uniform gradients and reduce projection computations. Furthermore, a smoothing technique is developed to reduce the variance of the gradients. The evaluation shows that our algorithm achieves low regret bound and computational complexity, which guarantees a 30% advantage over other strategies in Chinese futures market.