Risk-aware black-box portfolio construction using Bayesian optimization with adaptive weighted Lagrangian estimator

Abstract: Existing portfolio management approaches are often black-box models due to safety and commercial issues in the industry. However, their performance can vary considerably whenever market conditions or internal trading strategies change. Furthermore, evaluating these non-transparent systems is expensive, where certain budgets limit observations of the systems. Therefore, optimizing performance while controlling the potential risk of these financial systems has become a critical challenge. This work presents a novel Bayesian optimization framework to optimize black-box portfolio management models under limited observations. In conventional Bayesian optimization settings, the objective function is to maximize the expectation of performance metrics. However, simply maximizing performance expectations leads to erratic optimization trajectories, which exacerbate risk accumulation in portfolio management. Meanwhile, this can lead to misalignment between the target distribution and the actual distribution of the black-box model. To mitigate this problem, we propose an adaptive weight Lagrangian estimator considering dual objective, which incorporates maximizing model performance and minimizing variance of model observations. Extensive experiments demonstrate the superiority of our approach over five backtest settings with three black-box stock portfolio management models. Ablation studies further verify the effectiveness of the proposed estimator.