Better portfolio optimization by linking predictions to investment decisions
Decision-Focused Learning for Mean-Variance Portfolio Optimization via KKT-Based Reformulation
Machine Learning
Summary
Portfolio optimization is about choosing investments to get the best balance of risk and reward. Usually, people predict returns first and then decide the portfolio, but that doesn’t always lead to the best outcome. The authors create a method that trains prediction models by directly focusing on how good the final investment decisions are, not just prediction accuracy. They do this by using a mathematical technique called KKT conditions to keep important investment rules intact. Tests with real financial data show this method leads to better investment results.
What this means in practice
- •For financial portfolio managers: Improve asset allocation by integrating prediction training with decision quality in portfolio optimization for better investment results.
- •For quantitative trading teams: Generate trading strategies that respect investment constraints while optimizing for actual financial outcomes using KKT-based learning.
Authors
Kensei Nosaka, Shunnosuke Ikeda, Yuichi Takano
Abstract
Mean-variance portfolio optimization (MVO) is a central framework in data-driven asset management. A widely adopted approach is a two-stage framework that first predicts expected returns and then solves the optimization problem based on these predictions, with the predictive models trained by minimizing prediction errors. However, this objective of prediction is not aligned with the quality of the downstream portfolio decision. Decision-focused learning (DFL), which directly minimizes the downstream decision loss within the learning process, has thus emerged as a promising direction. However, existing DFL approaches to MVO rely on surrogate losses or constraint relaxations for tractability, creating a structural mismatch between predictive model training and the constrained MVO solved at evaluation. We propose a single-level optimization formulation that incorporates the Karush-Kuhn-Tucker (KKT) optimality conditions of the lower-level MVO into the upper-level learning problem. This formulation explicitly preserves the budget and short-sale constraints while remaining tractable for standard nonlinear optimization solvers. Rolling-window experiments on real-world ETF (Exchange Traded Funds) data across two asset universes with different correlation structures show that our method achieved the best performance on multiple investment metrics and also demonstrated performance improvement due to the proposed regularization.