On the Effectiveness of Classical Regression Methods for Optimal Switching Problems

TL;DR

This paper demonstrates that simple classical regression methods, especially k-NN, can effectively solve high-dimensional optimal switching problems with minimal tuning, outperforming more complex models.

Contribution

The study shows classical regression methods, including k-NN, are robust and scalable solutions for optimal switching problems, challenging the reliance on complex neural networks.

Findings

k-NN regression performs consistently well across benchmarks

Classical regression methods outperform tested neural networks

PCA enables k-NN to scale to high-dimensional problems

Abstract

Simple regression methods provide robust, near-optimal solutions for optimal switching problems, including high-dimensional ones (up to 50). While the theory requires solving intractable PDE systems, the Longstaff-Schwartz algorithm with classical regression methods achieves excellent switching decisions without extensive hyperparameter tuning. Testing linear models (OLS, Ridge, LASSO), tree-based methods (random forests, gradient boosting), $k$-nearest neighbors, and feedforward neural networks on four benchmark problems, we find that several simple methods maintain stable performance across diverse problem characteristics, outperforming the neural networks we tested against. In our comparison, $k$-NN regression performs consistently well, and with minimal hyperparameter tuning. We establish concentration bounds for this regressor and show that PCA enables $k$-NN to scale to high dimensions.