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

arXiv: https://arxiv.org/abs/2503.13544 · HTML: https://mlsanity.com/paper/2503.13544/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 30 references that are in the map.
- First posted on arXiv 16 Mar 2025.

## Builds on (most cited first, 10 of 10)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Sophia: A Scalable Stochastic Second-order Optimizer for Language Model Pre-training](https://mlsanity.com/paper/2305.14342/) (2023)
- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [Model-based Deep Reinforcement Learning for Dynamic Portfolio Optimization](https://mlsanity.com/paper/1901.08740/) (2019)
- [A Globally Optimal Portfolio for m-Sparse Sharpe Ratio Maximization](https://mlsanity.com/paper/2410.21100/) (2024)
- [Deep Deterministic Portfolio Optimization](https://mlsanity.com/paper/2003.06497/) (2020)
- [Deep Reinforcement Learning and Mean-Variance Strategies for Responsible Portfolio Optimization](https://mlsanity.com/paper/2403.16667/) (2024)
- [DF2: Distribution-Free Decision-Focused Learning](https://mlsanity.com/paper/2308.05889/) (2023)

## Built on by (most cited first, 1 of 1)

- [Generating Input Distributions for Explaining Portfolio Optimization Pipelines](https://mlsanity.com/paper/2606.25808/) (2026)

## Abstract (arXiv)

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.