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.
We will not state the exact method here but refer to the publications by Li (2016) and Mirzaei (2015), whose analysis we are using here
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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.