Human society had a long history of suffering from cognitive biases leading to social prejudices and mass injustice. The prevalent existence of cognitive biases in large volumes of historical data can pose a threat of being manifested as unethical and seemingly inhuman predictions as outputs of AI systems trained on such data. To alleviate this problem, we propose a bias-aware multi-objective learning framework that given a set of identity attributes (e.g. gender, ethnicity etc.) and a subset of sensitive categories of the possible classes of prediction outputs, learns to reduce the frequency of predicting certain combinations of them, e.g. predicting stereotypes such as `most blacks use abusive language', or `fear is a virtue of women'. Our experiments conducted on an emotion prediction task with balanced class priors shows that a set of baseline bias-agnostic models exhibit cognitive biases with respect to gender, such as women are prone to be afraid whereas men are more prone to be angry. In contrast, our proposed bias-aware multi-objective learning methodology is shown to reduce such biases in the predictied emotions.