Generating Informative Scenarios via Active Learning

Scenario generation is a crucial task in Stochastic Programming (SP). It involves a trade-off between keeping the scenario set small while making it representative for the target problem. While most state-of-the-art methods focus on matching the uncertainty of the stochastic process using distribution-driven approaches, problem-driven methodologies have been proposed in recent years to exploit the structure of the target problem during the scenario generation process. In order to represent uncertainties in a more concise way, we propose a novel approach based on Active Learning that sequentially generates a set of scenarios by including a new promising scenario at each iteration. Searching for the most promising scenario is a black-box global optimization problem, efficiently solved via Bayesian Optimization. Preliminary experimental results are presented on a classical newsvendor problem, providing empirical evidence that the proposed method can both identify the smallest and most informative scenario set for the problem. Our method can also efficiently and effectively handle multi-modal and fat-tailed distributions, analogously to the most recent problem-driven methods.