Abstract
This work develops new results for stochastic approximation algorithms. The emphases are on treating algorithms and limits with discontinuities. The main ingredients include the use of differential inclusions, set-valued analysis, nonsmooth analysis, and stochastic differential inclusions. Under broad conditions, it is shown that a suitably scaled sequence of the iterates has a differential inclusion limit. In addition, it is shown for the first time that a centered and scaled sequence of the iterates converges weakly to a stochastic differential inclusion limit. The results are then used to treat several application examples including Markov decision processes, Lasso algorithms, Pegasos algorithms, support vector machine classification, and learning. Some numerical demonstrations are also provided.
Funding Statement
This research was supported in part by the National Science Foundation Grant DMS-2204240.
Citation
Nhu Nguyen. George Yin. "Stochastic approximation with discontinuous dynamics, differential inclusions, and applications." Ann. Appl. Probab. 33 (1) 780 - 823, February 2023. https://doi.org/10.1214/22-AAP1829
Information