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2023

Improved Bound for Mixing Time of Parallel Tempering

Lee, Holden, Shen, Zeyu

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Understand

In the field of sampling algorithms, MCMC (Markov Chain Monte Carlo) methods are widely used when direct sampling is not possible.

However, multimodality of target distributions often leads to slow convergence and mixing.
One common solution is parallel tempering.
Though highly effective in practice, theoretical guarantees on its performance are limited.

Improved Bound for Mixing Time of Parallel Tempering · Around

Built on

Geometric bounds for eigenvalues of Markov chains
Persi Diaconis and Daniel Stroock · 1991
Earlier work this paper cites.
Geometric l2 and l1 convergence are equivalent for reversible Markov chains
Gareth Roberts and Richard Tweedie · 2000
Earlier work this paper cites.
On the swapping algorithm
Neal Madras and Zhongrong Zheng · 2003
Earlier work this paper cites.

Similar

General state space Markov chains and MCMC algorithms
Gareth O. Roberts and Jeffrey S. Rosenthal · 2004
Cited alongside, same era.
Sufficient conditions for torpid mixing of parallel and simulated tempering
Dawn Woodard, Scott Schmidler, and Mark Huber · 2009
Cited alongside, same era.

Then

Conditions for rapid mixing of parallel and simulated tempering on multimodal distributions
Dawn B. Woodard, Scott C. Schmidler, and Mark Huber · 2009
Later among the works it cites.
Beyond log-concavity: Provable guarantees for sampling multi-modal distributions using simulated tempering langevin monte carlo, 2017
Rong Ge, Holden Lee, and Andrej Risteski · 2017
Later among the works it cites.

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