  The solution of multistage stochastic linear problems (MSLP) represents a
challenge for many application areas. Long-term hydrothermal dispatch planning
(LHDP) materializes this challenge in a real-world problem that affects
electricity markets, economies, and natural resources worldwide. No closed-form
solutions are available for MSLP and the definition of non-anticipative
policies with high-quality out-of-sample performance is crucial. Linear
decision rules (LDR) provide an interesting simulation-based framework for
finding high-quality policies for MSLP through two-stage stochastic models. In
practical applications, however, the number of parameters to be estimated when
using an LDR may be close to or higher than the number of scenarios of the
sample average approximation problem, thereby generating an in-sample overfit
and poor performances in out-of-sample simulations. In this paper, we propose a
novel regularized LDR to solve MSLP based on the AdaLASSO (adaptive least
absolute shrinkage and selection operator). The goal is to use the parsimony
principle, as largely studied in high-dimensional linear regression models, to
obtain better out-of-sample performance for LDR applied to MSLP. Computational
experiments show that the overfit threat is non-negligible when using classical
non-regularized LDR to solve the LHDP, one of the most studied MSLP with
relevant applications. Our analysis highlights the following benefits of the
proposed framework in comparison to the non-regularized benchmark: 1)
significant reductions in the number of non-zero coefficients (model
parsimony), 2) substantial cost reductions in out-of-sample evaluations, and 3)
improved spot-price profiles.
