  We focus on data-driven, risk-averse optimization problems where
decision-makers exhibit constant absolute risk aversion (CARA), represented by
an exponential utility function. We consider payoff functions expressible as
conic optimization problems, highlighting their expansive use in prescriptive
analytics. Aiming to mitigate the overfitting issues inherent in empirical
distribution-based optimization, we employ a robust satisficing strategy, which
combines a target parameter with a Wasserstein distance metric, to define
acceptable solutions, robustly. This target parameter could be determined via
cross validation to mitigate overfitting and improve out-of-sample performance.
Nevertheless, integrating an exponential utility function into a robust
satisficing framework introduces substantial computational challenges.
Traditional convex approximations, despite being safe and tractable, do not
guarantee feasibility when applied to some appropriate target levels. We
overcome this inconsistency by delineating specific conditions, namely, a
scenario with complete and bounded recourse, polyhedral uncertainty support and
polyhedral metric norm, under which a safe, tractable, and consistent
approximation of the data-driven robust satisficing problem can be guaranteed
for any reasonably specified target. To ensure compliance with the complete and
bounded recourse conditions, we subsequently introduce the notion of augmented
exponential utility by restricting the domain of the utility function. We
validate our theoretical results with computational experiments in two
applications: data-driven portfolio optimization and an optimal location
problem. The numerical results underscore the efficacy of incorporating
robustness into optimization models, significantly enhancing solution quality
as compared to traditional empirical optimization approaches.
