This paper introduces a conceptual framework for the robust optimization under uncertainty in the directed energy deposition (DED) of M4 High-Speed Steel. The goal is to identify optimal process parameters for robust manufacturing of printed parts with a stationary melt pool depth and low consumed energy under uncertainty within the multiple layers of a bulk sample. To increase the computational efficiency, a deep learning-based surrogate model is built using the training data generated by a validated high-fidelity DED two-dimensional FE model. The robustness of the optimized result is verified using the Monte-Carlo method and compared with experiments and two other deterministic approaches. Furthermore, we conduct a global sensitivity analysis, which indicates that among six uncertain input variables, the thermal conductivity and the convection have the most significant impact on the melt pool depth variation. This study shows the promising possibilities of the presented framework in optimizing the DED process.