Multi-level stochastic approximation algorithms

Abstract

This paper studies multi-level stochastic approximation algorithms. Our aim is to extend the scope of the multi-level Monte Carlo method recently introduced by Giles [Oper. Res. 56 (2008) 607–617] to the framework of stochastic optimization by means of stochastic approximation algorithm. We first introduce and study a two-level method, also referred as statistical Romberg stochastic approximation algorithm. Then its extension to a multi-level method is proposed. We prove a central limit theorem for both methods and give optimal parameters. Numerical results confirm the theoretical analysis and show a significant reduction in the initial computational cost.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 23 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.