On the Effectiveness of Classical Regression Methods for Optimal Switching Problems

2025/06/18 by Martin Andersson, Andersson, Martin, Benny Avelin +3
Computer Science · Engineering · #Advanced Research in Systems and Signal Processing #Control Systems and Identification #FOS: Mathematics #Neural Networks and Applications #Optimization and Control (math.OC) #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2506.15436

openalex publication_date 2025/06/18 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

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.

Citations

• A deep solver for BSDEs with jumps
• A neural network approach to high-dimensional optimal switching problems with jumps in energy markets
• Neural Optimal Stopping Boundary
• Deep Reinforcement Learning for Optimal Stopping with Application in Financial Engineering
• Systems of fully nonlinear parabolic obstacle problems with Neumann boundary conditions
• Optimal Stopping via Randomized Neural Networks
• Density estimates for jump diffusion processes
• Solving optimal stopping problems with Deep Q-Learning
• Do We Really Need Deep Learning Models for Time Series Forecasting?
• Management strategies for run-of-river hydropower plants -an optimal\n switching approach
• A Finite Horizon Optimal Switching Problem with Memory and Application\n to Controlled SDDEs
• Deep backward schemes for high-dimensional nonlinear PDEs
• Deep Learning for Ranking Response Surfaces with Applications to Optimal\n Stopping Problems
• On the Finite Horizon Optimal Switching Problem with Random Lag
• A probabilistic verification theorem for the finite horizon two-player zero-sum optimal switching game in continuous time
• Simulation Methods for Stochastic Storage Problems: A Statistical\n Learning Perspective
• A Limited-Feedback Approximation Scheme for Optimal Switching Problems with Execution Delays
• A Brownian optimal switching problem under incomplete information
• Julia: A Fresh Approach to Numerical Computing
• Julia: A Fresh Approach to Numerical Computing
• Optimal Switching in Finite Horizon under State Constraints
• Optimal Switching Problems under Partial Information
• Systems of variational inequalities for non-local operators related to optimal switching problems: Existence and uniqueness
• The Finite Horizon Optimal Multi-Modes Switching Problem: the Viscosity Solution Approach
• A Finite Horizon Optimal Multiple Switching Problem
• Greedy function approximation: A gradient boosting machine.
• Ridge Regression: Biased Estimation for Nonorthogonal Problems
• Nearest neighbor pattern classification

Related

• Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems
• Is RL fine-tuning harder than regression? A PDE learning approach for diffusion models
• Learning in PINNs: Phase transition, total diffusion, and generalization
• Physics-Informed Neural Networks: Minimizing Residual Loss with Wide Networks and Effective Activations
• Stability in Training PINNs for Stiff PDEs: Why Initial Conditions Matter