Optimal rates for non-log-concave sampling and log-partition estimation are sometimes equal to or faster than optimization rates, but polynomial-time algorithms fall short of near-optimal performance.
Let ˜Pf be the distribution of REJECTION SAMPLING ( ˜f , g,1), which only uses one evaluation of ˜f and therefore only one evaluation of f
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Convergence Rates for Non-Log-Concave Sampling and Log-Partition Estimation
Optimal rates for non-log-concave sampling and log-partition estimation are sometimes equal to or faster than optimization rates, but polynomial-time algorithms fall short of near-optimal performance.