Consensus based optimization: Difference between revisions

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=== Sampling ===
 
Consensus-based optimization can be transformed into a sampling method<ref>{{Citation |last1=Carrillo |first1=J. A. |title=Consensus Based Sampling |date=2021-11-04 |url=https://arxiv.org/abs/2106.02519 |access-date=2024-08-17 |arxiv=2106.02519 |last2=Hoffmann |first2=F. |last3=Stuart |first3=A. M. |last4=Vaes |first4=U.}}</ref> by modifying the noise term and choosing appropriate hyperparameters. Namely, one considers the following SDE
 
<math>dx^i_t = -(x^i_t-c_\alpha(x_t))\,dt + \sqrt{2 \tilde{\lambda}^{-1}\, C_\alpha(x_t)}\,dB^i_t,</math>