Swarm-based gradient descent meets simulated annealing
<|reference_start|>Swarm-based gradient descent meets simulated annealing: We introduce a novel method for non-convex optimization, called Swarm-based Simulated Annealing (SSA), which is at the interface between the swarm-based gradient-descent (SBGD) [J. Lu et. al., ArXiv:2211.17157; E.Tadmor and A. Zenginoglu, Acta Applicandae Math., 190, 2024] and Simulated Annealing (SA) [V. Cerny, J. optimization theory and appl., 45:41-51, 1985; S.Kirkpatrick et. al., Science, 220(4598):671-680, 1983; S. Geman and C.-R. Hwang, SIAM J. Control and Optimization, 24(5):1031-1043, 1986]. Similar to SBGD, we introduce a swarm of agents, each identified with a position, ${\mathbf x}$ and mass $m$, to explore the ambient space. Similar to SA, the agents proceed in the gradient descent direction, and are subject to Brownian motion. The annealing rate, however, is dictated by a decreasing function of their mass. As a consequence, instead of the SA protocol for time-decreasing temperature, we let the swarm decide how to `cool down' agents, depending on their accumulated mass over time. The dynamics of masses is coupled with the dynamics of positions: agents at higher ground transfer (part of) their mass to those at lower ground. Consequently, resulting SSA optimizer is dynamically divided between heavier, cooler agents viewed as `leaders' and lighter, warmer agents viewed as `explorers'. Mean-field convergence analysis and benchmark optimizations demonstrate the effectiveness of the swarm-based method as a multi-dimensional global optimizer.<|reference_end|>
@article{ding2024swarm-based,
    title={Swarm-based gradient descent meets simulated annealing},
    author={Zhiyan Ding, Martin Guerra, Qin Li, Eitan Tadmor},
    journal={arXiv preprint arXiv:2404.18015},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.18015},
    primaryClass={math.OC cs.NA math.NA}
}