Sampling regime
Stochastic and finite-sum oracles
Compare theorems by mathematical guarantee, rate, and source — not by raw crawler rows.
Theorem and frontier cases
best upper · Normalized SampleWiki statement
High-accuracy stochastic-gradient sampler
Primary theorem audit pending — this is not presented as a verbatim paper theorem
Guarantee / accuracy
\[\lVert\mu_N-\pi\rVert_{\rm TV}\le\varepsilon\]
Complexity / rate
\[\widetilde O((\kappa\sqrt d+\sigma_\psi^2/\alpha)\operatorname{polylog}(1/\varepsilon))\]
best lower · Normalized SampleWiki statement
Bounded-variance stochastic-gradient lower bound
Primary theorem audit pending — this is not presented as a verbatim paper theorem
Guarantee / accuracy
\[\varepsilon\]
Complexity / rate
\[\Omega(\sigma^2/(\alpha\varepsilon))\]
upper · Normalized SampleWiki statement
Variance-reduced high-accuracy sampler
Primary theorem audit pending — this is not presented as a verbatim paper theorem
Complexity / rate
\[\widetilde O((m+\kappa\sqrt{dm})\operatorname{polylog}(1/\varepsilon))\]
upper · Normalized SampleWiki statement
Finite-sum RM-ULMC
Primary theorem audit pending — this is not presented as a verbatim paper theorem
Complexity / rate
\[\widetilde O(m+\kappa^2+\kappa^{4/3}d^{1/3}m^{2/3}/\varepsilon^{2/3})\]
lower · Normalized SampleWiki statement
Finite-sum zeroth-order lower bound
Primary theorem audit pending — this is not presented as a verbatim paper theorem
Complexity / rate
\[\widetilde\Theta(L^2/\alpha)\]