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Double-Loop Unadjusted Langevin Algorithm
Paul Rolland · Armin Eftekhari · Ali Kavis · Volkan Cevher

Thu Jul 16 12:00 PM -- 12:45 PM & Fri Jul 17 12:00 AM -- 12:45 AM (PDT) @
A well-known first-order method for sampling from log-concave probability distributions is the Unadjusted Langevin Algorithm (ULA). This work proposes a new annealing step-size schedule for ULA, which allows to prove new convergence guarantees for sampling from a smooth log-concave distribution, which are not covered by existing state-of-the-art convergence guarantees. To establish this result, we derive a new theoretical bound that relates the Wasserstein distance to total variation distance between any two log-concave distributions that complements the reach of Talagrand $T_2$ inequality. Moreover, applying this new step size schedule to an existing constrained sampling algorithm, we show state-of-the-art convergence rates for sampling from a constrained log-concave distribution, as well as improved dimension dependence.

Author Information

Paul Rolland (Ecole Polytechnique Fédérale de Lausanne)
Armin Eftekhari (Umea University)
Ali Kavis (EPFL)
Volkan Cevher (EPFL)

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