Generative Adversarial Regression (GAR): Learning Conditional Risk Scenarios

We propose Generative Adversarial Regression (GAR), a framework for learning conditional risk scenarios through generators aligned with downstream risk objectives. GAR builds on a regression characterization of conditional risk for elicitable functionals, including quantiles, expectiles, and jointly elicitable pairs. We extend this principle from point prediction to generative modeling by training generators whose policy-induced risk matches that of real data under the same context. To ensure robustness across all policies, GAR adopts a minimax formulation in which an adversarial policy identifies worst-case discrepancies in risk evaluation while the generator adapts to eliminate them. This structure preserves alignment with the risk functional across a broad class of policies rather than a fixed, pre-specified set. We illustrate GAR through a tail-risk instantiation based on jointly elicitable $(\mathrm{VaR}, \mathrm{ES})$ objectives. Experiments on S\&P 500 data show that GAR produces scenarios that better preserve downstream risk than unconditional, econometric, and direct predictive baselines while remaining stable under adversarially selected policies.

Multi-Objective Optimization of Water Resource Allocation for Groundwater Recharge and Surface Runoff Management in Watershed Systems

Land degradation and air pollution are primarily caused by the salinization of soil and desertification that occurs from the drying of salinity lakes and the release of dust into the atmosphere because of their dried bottom. The complete drying up of a lake has caused a community environmental catastrophe. In this study, we presented an optimization problem to determine the total surface runoff to maintain the level of salinity lake (Urmia Lake). The proposed process has two key stages: identifying the influential factors in determining the lake water level using sensitivity analysis approaches based upon historical data and optimizing the effective variable to stabilize the lake water level under changing design variables. Based upon the Sobol'-Jansen and Morris techniques, the groundwater level and total surface runoff flow are highly effective with nonlinear and interacting impacts of the lake water level. As a result of the sensitivity analysis, we found that it may be possible to effectively manage lake levels by adjusting total surface runoff. We used genetic algorithms, non-linear optimization, and pattern search techniques to solve the optimization problem. Furthermore, the lake level constraint is established based on a pattern as a constant number every month. In order to maintain a consistent pattern of lake levels, it is necessary to increase surface runoff by approximately 8.7 times during filling season. It is necessary to increase this quantity by 33.5 times during the draining season. In the future, the results may serve as a guide for the rehabilitation of the lake.