An asset subset-constrained minimax optimization framework for online portfolio selection

Effective online portfolio selection necessitates seamless integration of three key properties: diversity, sparsity, and risk control. However, existing algorithms often prioritize one property at the expense of the others due to inherent conflicts. To address this issue, we propose an asset subset-constrained minimax (ASCM) optimization framework, which generates optimal portfolios from diverse investment strategies represented as asset subsets. ASCM consists of: (i) a minimax optimization model that focuses on risk control by considering a set of loss functions constrained by different asset subsets; (ii) the construction of asset subsets via price-feature clipping, which effectively reduces redundant assets in the portfolio; (iii) a state-based estimation of price trends that guides all ASCM loss functions, facilitating the generation of sparse solutions. We solve the ASCM minimax model using an efficient iterative updating formula derived from the projected subgradient method. Furthermore, we achieve near O(1) time complexity through a novel initialization scheme. Experimental results demonstrate that ASCM outperforms eight representative algorithms, including the best constant rebalanced portfolio in hindsight (BCRP) on five out of the six real-world financial datasets. Notably, ASCM achieves a 67-fold improvement over BCRP in cumulative wealth on the TSE dataset.