Convergence Rates for Non-Log-Concave Sampling and Log-Partition Estimation

Understand

Sampling from Gibbs distributions and computing their log-partition function are fundamental tasks in statistics, machine learning, and statistical physics.

• While efficient algorithms are known for log-concave densities, the worst-case non-log-concave setting necessarily suffers from the curse of dimensionality.
• For many numerical problems, the curse of dimensionality can be alleviated when the target function is smooth, allowing the exponent in the rate to improve linearly with the number of available derivatives.
• Recently, it has been shown that similarly fast convergence rates can be achieved by efficient optimization algorithms.