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We propose an adaptive procedure for improving the response outcomes of complex combinatorial experiments. New experiment batches are chosen by minimizing the co-information composite likelihood (COIL) objective function, which is derived by coupling importance sampling and composite likelihood principles. We show convergence of the best experiment within each batch to the globally optimal experiment in finite time, and carry out simulations to assess the convergence behavior as the design space size increases. The procedure is tested as a new enzyme engineering protocol in an experiment with a design space size of order 10 7 .

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