On choosing the number of look-ahead stages in the rolling-horizon procedure for multistage stochastic programming

Abstract Multistage stochastic programming (MSP) is a class of models for sequential decision-making under uncertainty. MSP problems are known for their computational difficulties, and one common approach to find an approximate decision policy is to resort to the rolling-horizon procedure (RHP). The RHP is a method that involves solving an MSP problem at each roll of its procedure, which is referred to as a look-ahead model. The look-ahead model is typically defined with a smaller number of stages than the original MSP, making them computationally less demanding to solve. However, the reduction in the number of stages may compromise the quality of the resulting decision policy. This leads to an important question of how many stages to use for each look-ahead model in the RHP. In this paper, we propose two alternative approaches to address this question. First, we propose a surrogate model to the original MSP as an infinite-horizon MSP problem with a certain discount factor, from which we derive a bound which can be used to prescribe an appropriate number of stages. Alternatively, we propose a supervised learning approach that learns how to choose an appropriate number of stages for each look-ahead model based on the state of the system in each roll of the RHP, using data collected from offline experiments. Our numerical experiments demonstrate the effectiveness of the proposed approaches on these problems.