Bayesian inference without the access of likelihood, or likelihood-free inference, has been a key research topic in simulations, to yield a more realistic generation result. Recent likelihood-free inference updates an approximate posterior sequentially with the dataset of the cumulative simulation input-output pairs over inference rounds. Therefore, the dataset is gathered through the iterative simulations with sampled inputs from a proposal distribution by MCMC, which becomes the key of inference quality in this sequential framework. This paper introduces a new proposal modeling, named as Implicit Surrogate Proposal (ISP), to generate a cumulated dataset with further sample efficiency. ISP constructs the cumulative dataset in the most diverse way by drawing i.i.d samples via a feed-forward fashion, so the posterior inference does not suffer from the disadvantages of MCMC caused by its non-i.i.d nature, such as auto-correlation and slow mixing. We analyze the convergence property of ISP in both theoretical and empirical aspects to guarantee that ISP provides an asymptotically exact sampler. We demonstrate that ISP outperforms the baseline inference algorithms on simulations with multi-modal posteriors.
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