Title: Heterogeneous Loss Function with Aggressive Rejection for Contaminated data in anomaly detection. Abstract: A training clean dataset, which consists of only normal data, is crucial for detecting anomalous data. However, a clean dataset is challenging to produce in practice. Here, heterogeneous loss function with aggressive rejection is proposed, which strengthens robustness against contamination. Aggressive rejection constrains training on the intersection of normal and abnormal distributions to handle the potential anomalies. Heterogeneous loss function utilizes an adaptive mini-batch stochastic choice of an order of asymptotic polynomial of GA loss, which dynamically optimizes the gradient for the intersection further. Through the proposed method, mean square error based models can outperform various robust loss functions and generate comparable performance with robust models for contaminated data on three image datasets.