Machine learning and data mining techniques are increasingly being applied to electronic health record (EHR) data to discover underlying patterns and make predictions for clinical use. For instance, these data may be evaluated to predict clinical deterioration events such as cardiopulmonary arrest or escalation of care to the intensive care unit (ICU). In clinical practice, early warning systems with multiple time horizons could indicate different levels of urgency, allowing clinicians to make decisions regarding triage, testing, and interventions for patients at risk of poor outcomes. These different horizon alerts are related and have intrinsic dependencies, which elicit multi-task learning. In this paper, we investigate approaches to properly train deep multi-task models for predicting clinical deterioration events via generating multi-horizon alerts for hospitalized patients outside the ICU, with particular application to oncology patients. Prior knowledge is used as a regularization to exploit the positive effects from the task relatedness. Simultaneously, we propose task-specific loss balancing to reduce the negative effects when optimizing the joint loss function of deep multi-task models. In addition, we demonstrate the effectiveness of the feature-generating techniques from prediction outcome interpretation. To evaluate the model performance of predicting multi-horizon deterioration alerts in a real world scenario, we apply our approaches to the EHR data from 20,700 hospitalizations of adult oncology patients. These patients' baseline high-risk status provides a unique opportunity: the application of an accurate model to an enriched population could produce improved positive predictive value and reduce false positive alerts. With our dataset, the model applying all proposed learning techniques achieves the best performance compared with common models previously developed for clinical deterioration warning.