For C² potentials with known minimizer at zero and I≤∇²V≤2I, exact value-and-gradient oracle sampling to total-variation error at most 1/10 uses at most Cε d^ε queries for every ε>0, while every algorithm needs at least c log d queries eventually.
For C² potentials with known minimizer at zero and I≤∇²V≤2I, exact value-and-gradient oracle sampling to total-variation error at most 1/10 uses at most Cε d^ε queries for every ε>0, while every algorithm needs at least c log d queries eventually.
For C² potentials with known minimizer at zero and I≤∇²V≤2I, exact value-and-gradient oracle sampling to total-variation error at most 1/10 uses at most Cε d^ε queries for every ε>0, while every algorithm needs at least c log d queries eventually.
If correct, determines the infimal polynomial dimension exponent of this oracle query problem to be zero.
Can well-conditioned log-concave distributions be sampled with subpolynomial first-order queries?
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OpenAI reports a zero dimension exponent for well-conditioned log-concave sampling queries
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