Abstract: Open set detection (OSD) aims at identifying data samples of an unknown class ($i.e.$, open set) from those of known classes ($i.e.$, closed set) based on a model trained from closed set samples. However, a closed set may involve a highly imbalanced class distribution. Accurately differentiating open set samples and those from a minority class in the closed set poses a fundamental challenge as the model may be equally uncertain when recognizing samples from the minority class. In this paper, we propose Adaptive Robust Evidential Optimization (AREO) that offers a principled way to quantify sample uncertainty through evidential learning while optimally balancing the model training over all classes in the closed set through adaptive distributively robust optimization (DRO). To avoid the model to primarily focus on the most difficult samples by following the standard DRO, adaptive DRO training is performed, which is governed by a novel multi-scheduler learning mechanism to ensure an optimal model training behavior that gives sufficient attention to the difficult samples and the minority class while capable of learning common patterns from the majority classes. Our experimental results on multiple real-world datasets demonstrate that the proposed model outputs uncertainty scores that can clearly separate samples from closed and open sets, respectively, and the detection results outperform the competitive baselines.