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Parallel tempering (PT), also known as replica exchange, is the go-toworkhorse for simulations of multi-modal distributions. The key to the successof PT is to adopt efficient swap schemes. The popular deterministic even-odd(DEO) scheme exploits the non-reversibility property and has successfullyreduced the communication cost from $O(P^2)$ to $O(P)$ given sufficiently many$P$ chains. However, such an innovation largely disappears in big data due tothe limited chains and few bias-corrected swaps. To handle this issue, wegeneralize the DEO scheme to promote non-reversibility and propose a fewsolutions to tackle the underlying bias caused by the geometric stopping time.Notably, in big data scenarios, we obtain an appealing communication cost$O(P\log P)$ based on the optimal window size. In addition, we also adoptstochastic gradient descent (SGD) with large and constant learning rates asexploration kernels. Such a user-friendly nature enables us to conductapproximation tasks for complex posteriors without much tuning costs.

Non-reversible Parallel Tempering for Deep Posterior Approximation