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The ability to accelerate the design of biological sequences can have a substantial impact on the progress of the medical field. The problem can be framed as a global optimization problem where the objective is an expensive black-box function such that we can query large batches restricted with a limitation of a low number of rounds. Bayesian Optimization is a principled method for tackling this problem. However, the astronomically large state space of biological sequences renders brute-force iterating over all possible sequences infeasible. In this paper, we propose MetaRLBO where we train an autoregressive generative model via Meta-Reinforcement Learning to propose promising sequences for selection via Bayesian Optimization. We pose this problem as that of finding an optimal policy over a distribution of MDPs induced by sampling subsets of the data acquired in the previous rounds. Our in-silico experiments show that meta-learning over such ensembles provides robustness against reward misspecification and achieves competitive results compared to existing strong baselines.