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.
From: Benny Avelin [view email]
[v1]
Wed, 18 Jun 2025 13:12:17 UTC (911 KB)
[v2]
Thu, 5 Feb 2026 08:51:33 UTC (916 KB)
[v3]
Wed, 1 Apr 2026 07:26:01 UTC (727 KB)
[v4]
Fri, 14 Aug 2026 12:03:38 UTC (744 KB)
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