Stochastic Approximations and Differential Inclusions
نویسندگان
چکیده
منابع مشابه
Stochastic Approximations and Differential Inclusions
The dynamical systems approach to stochastic approximation is generalized to the case where the mean differential equation is replaced by a differential inclusion. The limit set theorem of Benäım and Hirsch is extended to this situation. Internally chain transitive sets and attractors are studied in detail for set-valued dynamical systems. Applications to game theory are given, in particular to...
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We apply the theoretical results on “stochastic approximations and differential inclusions” developed in Benäım, Hofbauer and Sorin (2005) to several adaptive processes used in game theory including: classical and generalized approachability, no-regret potential procedures (Hart and Mas-Colell), smooth fictitious play (Fudenberg and Levine).
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We consider stochastic approximation processes with constant step size whose associated deterministic system is an upper semicontinous differential inclusion. We prove that over any finite time span, the sample paths of the stochastic process are closely approximated by a solution of the differential inclusion with high probability. We then analyze infinite horizon behavior, showing that if the...
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ژورنال
عنوان ژورنال: SIAM Journal on Control and Optimization
سال: 2005
ISSN: 0363-0129,1095-7138
DOI: 10.1137/s0363012904439301