Adaptive MCMC cannot converge faster than a subgeometric rate dictated by the target tails and worst-case drift, and matching upper bounds hold when adaptation fades quickly.
An adaptive Metropolis algorithm
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Upper and lower bounds on the subgeometric convergence of adaptive Markov chain Monte Carlo
Adaptive MCMC cannot converge faster than a subgeometric rate dictated by the target tails and worst-case drift, and matching upper bounds hold when adaptation fades quickly.