Cooling schedules for optimal annealing
Mathematics of Operations Research
Stochastic Approximations and Differential Inclusions
SIAM Journal on Control and Optimization
Stochastic Approximations and Differential Inclusions, Part II: Applications
Mathematics of Operations Research
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This paper studies a class of non-Markovian and nonhomogeneous stochastic processes on a finite state space. Relying on a recent paper by Benaïm, Hofbauer, and Sorin [SIAM J. Control Optim., 44 (2005), pp. 328-348] it is shown that, under certain assumptions, the asymptotic behavior of occupation measures can be described in terms of a certain set-valued deterministic dynamical system. This provides a unified approach to simulated annealing type processes and permits the study of new models of vertex reinforced random walks and new models of learning in games such as Markovian fictitious play.