Paper: arXiv 2503.13544

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.

Complexity vs Empirical Score

  • Math Complexity: 3.0/10
  • Empirical Rigor: 9.0/10
  • Quadrant: Street Traders — practical and empirical, lighter on theory

Why this score: The paper is mathematically straightforward, using standard supervised learning frameworks and ensemble methods without advanced derivations, but demonstrates high empirical rigor through comprehensive backtests, diverse datasets, and an open-source GitHub repository.

Research Flowchart

  flowchart TD
  A["Research Goal: Robust Portfolio Optimization via Supervised Learning"] --> B["Methodology: Decision by Supervised Learning DSL Deep Ensemble"]
  B --> C{"Input: Historical Market Data"}
  C --> D["Compute Target Portfolios<br>Maximizing Sharpe/Sortino Ratio"]
  D --> E["Train Ensemble Models<br>Cross-Entropy Loss on Weights"]
  E --> F["Ensemble Aggregation<br>Reduce Variance & Improve Stability"]
  F --> G["Backtest on Diverse Universes"]
  G --> H["Key Findings: Superior Risk-Adjusted Returns<br>Stability Increases with Ensemble Size"]

Cited References (35)

  1. Advances in Financial Machine Learning (2018)
  2. Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities (2024) — link
  3. Anatomy of Machines for Markowitz: Decision-Focused Learning for Mean-Variance Portfolio Optimization (2024) — link
  4. DF2: Distribution-Free Decision-Focused Learning (2023) — link
  5. End-to-End Risk Budgeting Portfolio Optimization with Neural Networks (2021) — link
  6. Mean-variance optimization for asset allocation (2021)
  7. A Globally Optimal Portfolio for m-Sparse Sharpe Ratio Maximization (2024) — link
  8. Decision-Focused Learning without Decision-Making: Learning Locally Optimized Decision Losses (2022) — link
and 27 more
  1. Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles (2017) — link
  2. Long Short-Term Memory (1997) — link
  3. Attention is All you Need (2017) — link
  4. Mamba: Linear-Time Sequence Modeling with Selective State Spaces (2024) — link
  5. Deep Learning for Portfolio Optimization (2020) — link
  6. Deep deterministic portfolio optimization (2020) — link
  7. Deep reinforcement learning for portfolio management of markets with a dynamic number of assets (2021) — link
  8. Market sentiment-aware deep reinforcement learning approach for stock portfolio allocation (2021) — link
  9. Model-based Deep Reinforcement Learning for Dynamic Portfolio Optimization (2019) — link
  10. Deep reinforcement learning for portfolio selection (2024) — link
  11. Deep reinforcement learning for stock portfolio optimization by connecting with modern portfolio theory (2023) — link
  12. Deep Reinforcement Learning and Mean-Variance Strategies for Responsible Portfolio Optimization (2024) — link
  13. Deep Reinforcement Learning for Optimal Portfolio Allocation: A Comparative Study with Mean-Variance Optimization — link
  14. Multi-task Predict-then-Optimize (2023)
  15. Ensembles of Classifiers: a Bias-Variance Perspective (2022) — link
  16. Sophia: A Scalable Stochastic Second-order Optimizer for Language Model Pre-training (2024) — link
  17. On Nonlinear Fractional Programming (1967) — link
  18. Mutual Fund Performance (1965) — link
  19. Performance Measurement in a Downside Risk Framework (1994) — link
  20. A Universal End-to-End Approach to Portfolio Optimization via Deep Learning (2021) — link
  21. Pattern Recognition and Machine Learning (Information Science and Statistics) (2006)
  22. An Overview of Machine Learning for Asset Management. (2023)
  23. An Overview of Machine Learning for Portfolio Optimization. (2024)
  24. The effects of errors in means, variances, and correlations on the mean-variance framework (2022)
  25. Sophia: A Scalable Stochastic Second-order Optimizer for Language Model Pre-training (2024) — link
  26. GuruAgents: Emulating Wise Investors with Prompt-Guided LLM Agents (2025) — link
  27. LLM-Enhanced Black-Litterman Portfolio Optimization (2025) — link

0 of 35 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.