Adopting a robust attitude: risk-constrained decisions and knowledge acquisition
Résumé
Good decisions, in design or operation stages, positively impact system performances and can prevent it form suffering undesired scenarios and their consequences, in a uncertain environment. Using Robust Optimization (RO), a so-called chance-constraint, here denoted as risk-constraint as it embeds the preferences of the decision maker with respect to risk tolerance, can be enforced to ensure that the obtained solution of the decision problem is acceptable in this regard. Yet, this solution will only be as good as the knowledge of the uncertain environment that is used in the decision-making process. In this paper, we study the possibility for the decision-maker to refine its knowledge of the system in its operating environment, through information collection. The concept of Value of Information (VoI) is used to quantify potential improvements in decisions outcomes that may be achieved through a modification of the state of knowledge and a reduction in uncertainty. In particular, using decisions that are conditioned on an environment with reduced uncertainty, it is often possible to lower the level of risk for a given total operating cost (or Value-at-Risk) or vice versa. Hence, in a wide sense, knowledge acquisition may represent a step towards adopting a more robust attitude, with respect to risk, when making decisions.
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