Enza Messina

Many real-life systems are usually controlled through policies replicating experts’ knowledge, typically favouring “safety” at the expense of optimality. Indeed, these control policies are usually aimed at avoiding a system’s disruptions or deviations from a target behaviour, leading to suboptimal performances. This paper proposes a statistical learning approach to exploit the historical safe experience—collected through the application of a safe control policy based on experts’ knowledge— to “safely explore” new and more efficient policies. The basic idea is that performances can be improved by facing a reasonable and quantifiable risk in terms of safety. The proposed approach relies on Gaussian Process regression to obtain a probabilistic model of both a system’s dynamics and performances, depending on the historical safe experience. The new policy consists of solving a constrained optimization problem, with two Gaussian Processes modelling, respectively, the safety constraints and the performance metric (i.e., objective function). As a probabilistic model, Gaussian Process regression provides an estimate of the target variable and the associated uncertainty; this property is crucial for dealing with uncertainty while new policies are safely explored. Another important benefit is that the proposed approach does not require any implementation of an expensive digital twin of the original system. Results on two real-life systems are presented, empirically proving the ability of the approach to improve performances with respect to the initial safe policy without significantly affecting safety.

Stochastic Programming is a powerful framework that addresses decision-making under uncertainties, which is a frequent occurrence in real-world problems. To effectively solve Stochastic Programming problems, scenario generation is one of the common practices that organizes realizations of stochastic processes with finite discrete distributions, which enables the use of mathematical programming models of the original problem. The quality of solutions is significantly influenced by the scenarios employed, necessitating a delicate balance between incorporating informative scenarios and preventing overfitting. Distributions-based scenario generation methodologies have been extensively studied over time, while a relatively recent concept of problem-driven scenario generation has emerged, aiming to incorporate the underlying problem’s structure during the scenario generation process. This survey explores recent literature on problem-driven scenario generation algorithms and methodologies. The investigation aims to identify circumstances under which this approach is effective and efficient. The work provides a comprehensive categorization of existing literature, supplemented by illustrative examples. Additionally, the survey examines potential applications and discusses avenues for its integration with machine learning technologies. By shedding light on the effectiveness of problem-driven scenario generation and its potential for synergistic integration with machine learning, this survey contributes to enhanced decision-making strategies in the context of uncertainties.