Timezone: »

 
Poster
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) @ None #None
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)

More from the Same Authors