Segmentation of multiple surfaces in optical coherence tomography (OCT) images is a challenging problem, further complicated by the frequent presence of weak boundaries, varying layer thicknesses, and mutual influence between adjacent surfaces. The traditional graph-based optimal surface segmentation method has proven its effectiveness with its ability to capture various surface priors in a uniform graph model. However, its efficacy heavily relies on handcrafted features that are used to define the surface cost for the "goodness" of a surface. Recently, deep learning (DL) is emerging as a powerful tool for medical image segmentation thanks to its superior feature learning capability. Unfortunately, due to the scarcity of training data in medical imaging, it is nontrivial for DL networks to implicitly learn the global structure of the target surfaces, including surface interactions. This study proposes to parameterize the surface cost functions in the graph model and leverage DL to learn those parameters. The multiple optimal surfaces are then simultaneously detected by minimizing the total surface cost while explicitly enforcing the mutual surface interaction constraints. The optimization problem is solved by the primal-dual interior-point method (IPM), which can be implemented by a layer of neural networks, enabling efficient end-to-end training of the whole network. Experiments on spectral-domain optical coherence tomography (SD-OCT) retinal layer segmentation demonstrated promising segmentation results with sub-pixel accuracy. (C) 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement