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We propose a Deep Reinforcement Learning (Deep RL) algorithm for solving the online 3D bin packing problem for an arbitrary number of bins and any bin size. The focus is on producing decisions that can be physically implemented by a robotic loading arm, a laboratory prototype used for testing the concept. The problem considered in this paper is novel in two ways. First, unlike the traditional 3D bin packing problem, we assume that the entire set of objects to be packed is not known a priori. Instead, a fixed number of upcoming objects is visible to the loading system, and they must be loaded in the order of arrival. Second, the goal is not to move objects from one point to another via a feasible path, but to find a location and orientation for each object that maximises the overall packing efficiency of the bin(s). Finally, the learnt model is designed to work with problem instances of arbitrary size without retraining. Simulation results show that the RL-based method outperforms state-of-the-art online bin packing heuristics in terms of empirical competitive ratio and volume efficiency.