## Abstract

Stein Variational Gradient Descent (SVGD) is an algorithm for sampling from a target density which is known up to a multiplicative constant. Although SVGD is a popular algorithm in practice, its theoretical study is limited to a few recent works. We study the convergence of SVGD in the population limit, (i.e., with an infinite number of particles) to sample from a non-logconcave target distribution satisfying Talagrand's inequality T1. We first establish the convergence of the algorithm. Then, we establish a dimension-dependent complexity bound in terms of the Kernelized Stein Discrepancy (KSD). Unlike existing works, we do not assume that the KSD is bounded along the trajectory of the algorithm. Our approach relies on interpreting SVGD as a gradient descent over a space of probability measures.

Original language | English (US) |
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Pages | 19139-19152 |

Number of pages | 14 |

State | Published - 2022 |

Event | 39th International Conference on Machine Learning, ICML 2022 - Baltimore, United States Duration: Jul 17 2022 → Jul 23 2022 |

### Conference

Conference | 39th International Conference on Machine Learning, ICML 2022 |
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Country/Territory | United States |

City | Baltimore |

Period | 07/17/22 → 07/23/22 |

### Bibliographical note

Publisher Copyright:Copyright © 2022 by the author(s)

## ASJC Scopus subject areas

- Artificial Intelligence
- Software
- Control and Systems Engineering
- Statistics and Probability