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Directed evolution is a versatile technique in protein engineering that mimics the process of natural selection by iteratively alternating between mutagenesis and screening in order to search for sequences that optimize a given property of interest, such as catalytic activity and binding affinity to a specified target. However, the space of possible proteins is too large to search exhaustively in the laboratory, and functional proteins are scarce in the vast sequence space. Machine learning (ML) approaches can accelerate directed evolution by learning to map protein sequences to functions without building a detailed model of the underlying physics, chemistry and biological pathways. Despite the great potentials held by these ML methods, they encounter severe challenges in identifying the most suitable sequences for a targeted function. These failures can be attributed to the common practice of adopting a high-dimensional feature representation for protein sequences and inefficient search methods. To address these issues, we propose an efficient, experimental design-oriented closed-loop optimization framework for protein directed evolution, termed ODBO, which employs a combination of novel low-dimensional protein encoding strategy and Bayesian optimization enhanced with search space prescreening via outlier detection. We further design an initial sample selection strategy to minimize the number of experimental samples for training ML models. We conduct and report four protein directed evolution experiments that substantiate the capability of the proposed framework for finding of the variants with properties of interest. We expect the ODBO framework to greatly reduce the experimental cost and time cost of directed evolution, and can be further generalized as a powerful tool for adaptive experimental design in a broader context.