# Deep Empirical Risk Minimization in finance: looking into the future

arXiv: https://arxiv.org/abs/2011.09349 · HTML: https://mlsanity.com/paper/2011.09349/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Nov 2020.

## Built on by (most cited first, 6 of 6)

- [Data-Driven Merton's Strategies via Policy Randomization](https://mlsanity.com/paper/2312.11797/) (2023)
- [Distributionally robust risk evaluation with a causality constraint and structural information](https://mlsanity.com/paper/2203.10571/) (2022)
- [Adversarial Reinforcement Learning: A Duality-Based Approach To Solving Optimal Control Problems](https://mlsanity.com/paper/2506.00801/) (2025)
- [A hierarchical resource-efficient deep policy gradient method for continuous-time optimal control problems](https://mlsanity.com/paper/2502.14141/) (2025)
- [Mean-Field Generalisation Bounds for Learning Controls in Stochastic Environments](https://mlsanity.com/paper/2508.16001/) (2025)
- [NeuralChaos: Optimal Adapted Approximation of Square Integrable Predictable Processes](https://mlsanity.com/paper/2607.14361/) (2026)

## Abstract (arXiv)

Many modern computational approaches to classical problems in quantitative finance are formulated as empirical loss minimization (ERM), allowing direct applications of classical results from statistical machine learning. These methods, designed to directly construct the optimal feedback representation of hedging or investment decisions, are analyzed in this framework demonstrating their effectiveness as well as their susceptibility to generalization error. Use of classical techniques shows that over-training renders trained investment decisions to become anticipative, and proves overlearning for large hypothesis spaces. On the other hand, non-asymptotic estimates based on Rademacher complexity show the convergence for sufficiently large training sets. These results emphasize the importance of synthetic data generation and the appropriate calibration of complex models to market data. A numerically studied stylized example illustrates these possibilities, including the importance of problem dimension in the degree of overlearning, and the effectiveness of this approach.