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Innovations in batteries take years to formulate and commercialize, requiring extensive experimentation during the design and optimization phases. We approached the design and selection of a battery electrolyte through a black-box optimization algorithm directly integrated into a robotic test-stand. We report here the discovery of a novel battery electrolyte by this experiment completely guided by the machine-learning software without human intervention. Motivated by the recent trend toward super-concentrated aqueous electrolytes for high-performance batteries, we utilize Dragonfly - a Bayesian machine-learning software package - to search mixtures of commonly used lithium and sodium salts for super-concentrated aqueous electrolytes with wide electrochemical stability windows. Dragonfly autonomously managed the robotic test-stand, recommending electrolyte designs to test and receiving experimental feedback in real time. In 40 hours of continuous experimentation over a four-dimensional design space with millions of potential candidates, Dragonfly discovered a novel, mixed-anion aqueous sodium electrolyte with a wider electrochemical stability window than state-of-the-art sodium electrolyte. A human-guided design process may have missed this optimal electrolyte. This result demonstrates the possibility of integrating robotics with machine-learning to rapidly and autonomously discover novel battery materials.