In real world scenarios, out-of-distribution (OOD) datasets may have a large distributional shift from training datasets. This phenomena generally occurs when a trained classifier is deployed on varying dynamic environments, which causes a significant drop in performance. To tackle this issue, we are proposing an end-to-end deep multi-task network in this work. Observing a strong relationship between rotation prediction (self-supervised) accuracy and semantic classification accuracy on OOD tasks, we introduce an additional auxiliary classification head in our multi-task network along with semantic classification and rotation prediction head. To observe the influence of this addition classifier in improving the rotation prediction head, our proposed learning method is framed into bi-level optimisation problem where the upper-level is trained to update the parameters for semantic classification and rotation prediction head. In the lower-level optimisation, only the auxiliary classification head is updated through semantic classification head by fixing the parameters of the semantic classification head. The proposed method has been validated through three unseen OOD datasets where it exhibits a clear improvement in semantic classification accuracy than other two baseline methods. Our code is available on GitHub https://github.com/harshita-555/OSSL