Decision by Supervised Learning with Deep Ensembles: A Practical Framework for Robust Portfolio Optimization

TL;DR

Decision by Supervised Learning (DSL) tackles robust portfolio optimization by reframing asset allocation as a supervised learning task that directly predicts optimal weights. By employing cross-entropy loss and aggregating multiple independently trained models (Deep Ensembles), DSL achieves reduced allocation variance and improved out-of-sample stability. Empirical backtesting across diverse market universes and architectures shows DSL often surpasses traditional strategies and leading ML baselines (PFL and E2E), with larger ensembles delivering higher median returns and tighter risk-adjusted performance. The framework offers a practical, scalable approach to systematic portfolio construction, with potential extensions to long-short portfolios and adaptive objective functions.

Abstract

We propose Decision by Supervised Learning (DSL), a practical framework for robust portfolio optimization. DSL reframes portfolio construction as a supervised learning problem: models are trained to predict optimal portfolio weights, using cross-entropy loss and portfolios constructed by maximizing the Sharpe or Sortino ratio. To further enhance stability and reliability, DSL employs Deep Ensemble methods, substantially reducing variance in portfolio allocations. Through comprehensive backtesting across diverse market universes and neural architectures, shows superior performance compared to both traditional strategies and leading machine learning-based methods, including Prediction-Focused Learning and End-to-End Learning. We show that increasing the ensemble size leads to higher median returns and more stable risk-adjusted performance. The code is available at https://github.com/DSLwDE/DSLwDE.

Figures (2)

• Figure 1: Comparing cumulative return trajectory with classical portfolio strategies.
• Figure 2: Impact of Ensemble Size on Performance