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.
Using that exp(−x) ≤ Om,d(x−m/d) for x > 0, we obtain exp(−n/∥pf ∥∞) ≤ ∥pf ∥m/d ∞ n−m/d Theorem 23 ≤ Om,d max{1, ∥f ∥C1 }mn−m/d
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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.