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Consensus Monte Carlo (CMC) is a method for parallelizing MCMC for posterior inference over large datasets. It works by factorizing the posterior distribution into sub-posteriors each of which depend on only a subset of datapoints, sampling from each of these sub-posteriors in parallel, and then transforming samples from the sub-posteriors using an aggregation function to samples from the real posterior. Existing works use very naive methods of aggregation which result in high bias, or are computationally very expensive, which make it difficult to use Consensus Monte Carlo in practice. This paper proposes a more principled way of combining samples by optimizing over aggregation functions using variational inference. Clarity: The paper is well written and easy to follow.