394. Long-time convergence of a consensus-based optimization method
Invited abstract in session WC-8: Advances in non-convex optimization, stream Optimization for machine learning.
Wednesday, 14:00-16:00Room: B100/7007
Authors (first author is the speaker)
| 1. | Victor Priser
|
| Télécom Paris | |
| 2. | Pascal Bianchi
|
| Telecom ParisTech | |
| 3. | Radu-Alexandru Dragomir
|
| Telecom Paris |
Abstract
This paper studies a global optimization, derivative-free algorithm for a non-convex function f. In particular, the proposed algorithm is a variant of the Consensus-Based Optimization (CBO) algorithm. CBO is a particle-based algorithm that consists of two terms: a drift term attracting particles toward a consensus, modeling the local best results of the particles, and a noise term allowing particles to explore the domain. Unlike other existing approaches that focus on a finite time window, we are interested in the long-time convergence of the algorithm. The study of this algorithm is first conducted in the mean-field limit framework with an infinite number of particles, where we show the long-time convergence of the law of the particles to the Dirac measure centered at the minimizer. In the second step, we demonstrate the long-time convergence, for a finite number of particles, of the law of the particles to a set of measures which are concentrated around the minimizer of f . The strength of our result is that we control the distance of the law of the particles to the Dirac measure centered at the minimizer at any time during the algorithm, whereas other studies lose control of this distance at some time, as their analyses are conducted within a finite time window.
Keywords
- Global optimization
- Derivative-free optimization
Status: accepted
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