Stochastic approximation with discontinuous dynamics, differential inclusions, and applications

This work develops new results for stochastic approximation algorithms. The emphases are on treating algorithms and limits with discontinuities. main ingredients include the use of differential inclusions, set-valued analysis, nonsmooth inclusions. Under broad conditions, it is shown that a suitably scaled sequence iterates has inclusion limit. In addition, first time centered converges weakly to then used treat several application examples including Markov decision processes, Lasso algorithms, Pegasos support vector machine classification, learning. Some numerical demonstrations also provided.