Current hearing aids mostly provide sound amplification fittings based on individual hearing thresholds or perceived loudness, even though it is known that sensorineural hearing damage is functionally complex, and requires different treatment strategies. To meet this demand, we propose an optimisation framework for the design of individualised hearingaid signal processing based on simulated (hearing-impaired) auditory-nerve responses. The framework is fully differentiable, thus the backpropagation algorithm can be used to train DNN-based hearing-aid models that optimally process sound to restore hearing in impaired cochleae. The auditory models within the framework can be tuned to the precise hearing-loss profile of a listener to yield trully individualised restoration strategies. Our simulations show that the trained hearing-aid models were able to enhance the auditory-nerve responses of hearing-impaired cochleae, and this provides a promising outlook for embedding our framework within future hearing aids and augmented-hearing applications.