Uniform Race: Parameter-Free Approximate Rejection Sampling

We study approximate sampling: given $N$ independent samples from a proposal distribution $μ$, the goal is to select one whose distribution is close to a target $π$ specified only up to a normalizing constant. Block and Polyanskiy (2023) provide finite budget error bounds for approximate rejection sampling (RS) as a function of the acceptance threshold $M$. The threshold $M$ giving the smallest bound, however, depends on properties of $(π,μ)$ that are typically unavailable from the observed sample. This raises a natural question: Can one attain the best RS guarantee without taking $M$ as input? We answer affirmatively by proposing a parameter-free sampling algorithm called uniform race (U...

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