On the Effectiveness of Classical Regression Methods for Optimal Switching Problems

Abstract: Simple regression methods provide robust, near-optimal solutions for optimal switching problems in dimensions ranging from 1 to 50. While the theory requires solving intractable PDE systems, the Longstaff-Schwartz algorithm with classical approaches like $k$-NN achieves excellent switching decisions without extensive hyperparameter tuning. Testing eight regression approaches on four benchmark problems, we find that simple methods maintain stable performance across diverse problem characteristics, even after extensive neural network optimization. The contaminated training targets inherent to backward induction-where each target contains both approximation bias and Monte Carlo noise-actually favor these robust approaches over more complex alternatives such as neural networks. Further, we establish concentration bounds for $k$-NN regression under jump-diffusion dynamics and show that PCA enables $k$-NN to scale to high dimensions. For practitioners: simple, minimally-tuned regression methods offer reliable performance for computationally demanding switching problems.