Aggregating exponential gradient expert advice for online portfolio selection

In recent years, online portfolio selection, one of the fundamental problems in computational finance, has attracted increasing interest from online learning. Although existing online portfolio strategies have been shown to achieve good performance, appropriate values of their parameters need to be set in advance. However, the optimal values can only be known in hindsight. To overcome this limitation, this paper proposes a new online portfolio strategy by aggregating exponential gradient (EG(η)) expert advice using the weak aggregating algorithm (WAA). First, we consider a pool of EG(η) strategies with different learning rates as experts, and compute the portfolio on the next period by aggregating all the expert advice using the WAA according to their previous performance. Second, we theoretically prove that the proposed strategy is universal, i.e. its average logarithmic growth rate is asymptotically the same as that of the best constant rebalanced portfolio (BCRP) in hindsight. Finally, we conduct extensive experiments to examine the performance of the proposed strategy on actual stock market. Numerical results show that the proposed strategy overcomes the drawbacks of existing online strategies and achieves significant performance.