This paper investigates a deep learning (DL) method for on-off keying (OOK) based visible light communication (VLC) systems where a lighting emitting diode transmits binary optical pulses to a receiver. Universal dimming abilities are considered such that the VLC transceiver meets arbitrary dimming requirement of external users. This poses a combinatorial formulation optimizing binary codewords under multiple dimming constraints. To tackle this, DL techniques are employed to design an OOK encoder-decoder pair over noisy optical channels. For universal dimming support, the training of the DL-based VLC transceiver turns out to be a constrained training problem with multiple dimming constraints. This paper employs a dual formulation to develop a constrained training strategy. Numerical results show the effectiveness of the proposed transceiver design.