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Recent developments in artificial intelligence and automation support a new drug design paradigm: autonomous drug design. Under this paradigm, generative models can provide suggestions on thousands of molecules with specific properties, and automated laboratories can potentially make, test and analyze molecules with minimal human supervision. However, since still only a limited number of molecules can be synthesized and tested, an obvious challenge is how to efficiently select among provided suggestions in a closed-loop system. We formulate this task as a stochastic multi-armed bandit problem with multiple plays, volatile arms and similarity information. To solve this task, we adapt previous work on multi-armed bandits to this setting, and compare our solution with random sampling, greedy selection and decaying-epsilon-greedy selection strategies. According to our simulation results, our approach has the potential to perform better exploration and exploitation of the chemical space for autonomous drug design.