There is significant interest in improving the performance of batteries to increase electrification of transportation and aviation. Recently, performance improvements have been in large part due to changes in the composition of the cathode material family, LiNixMnyCo(1-x-y)O2 (e.g., 111-622-811). Despite the importance of these materials and tremendous progress with density functional theory (DFT) calculations in understanding basic design principles, it is computationally prohibitively expensive to make this problem tractable. Specifically, predicting the open circuit voltage for any cathode material in this family requires evaluation of stability in a quaternary phase space. In this work, we develop machine-learning potentials using fingerprinting based on atom-centered symmetry functions, used with a neural network model, trained on DFT calculations with a prediction accuracy of 3.7 meV/atom and 0.13 eV/Å for energy and force, respectively. We perform hyperparameter optimization of the fingerprinting parameters using Bayesian optimization through the Dragonfly package. Using this ML calculator, we first test its performance in predicting thermodynamic properties within the Debye-Grüneisen model and find good agreement for most thermodynamic properties, including the Gibbs free energy and entropy. Then, we use this to calculate the Li-vacancy ordering as a function of Li composition to simulate the process of discharging/charging of the cathode using grand canonical Monte Carlo simulations. The predicted voltage profiles are in good agreement with the experimental ones and provide an approach to rapidly perform design optimization in this phase space. This study serves as a proof-point of machine-learned DFT surrogates to enable battery materials optimization.