Stochastic Approximations and Differential Inclusions

By M. Benaim, Josef Hofbauer, Sylvain Sorin. 2005

393 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance

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Citations in the corpus

The Unusual Effectiveness of Averaging in GAN Training (2018, background): “Robustness of time-average convergence to Nash equilibria to network zero-sum games: The time average of all no-regret dynamics converges to equilibria even in network extension of zero-sum games (for arbitrary network interactions) Daskalakis and Papadimitriou [2009], Cai and Daskalakis [2011], Cai”
BEST RESPONSE DYNAMICS FOR CONTINUOUS ZERO{SUM GAMES (2005, background): “Thus we extend the basic result on numerical approximation (convergence to a global attractor) to the more general multivalued setting of a difierential inclusion (section 5). More reflned results involving chain recurrent components are established in [ 3 ].”
Convergence of a Multi-Agent Projected Stochastic Gradient Algorithm for Non-Convex Optimization (2011, methodology): “To formalize this, we shall rely on the notion of perturbed differential inclusions of [7].”
Two-Timescale Networks for Nonlinear Value Function Approximation (2019, background): “In order to analyze the limiting behaviour of the GTD2 algorithm under the relaxed singularity setting, henceforth one has to view the stochastic recursion (30) as a stochastic recursion inclusion (Benaïm et al., 2005) and apply the recent results from (Ramaswamy and Bhatnagar, 2016) which analyzes ”
Distributed off-Policy Actor-Critic Reinforcement Learning with Policy Consensus (2019, background): “terior. This assumption is satisﬁed when the objective function Jβ(θ) is smooth,accordingto Sard’s theorem.It is a common assumption in the stochastic approximation and optimization literature, e.g., [23,25]. Theorem IV.12. Given Assumptions III.1 and from IV.1 to IV.11, θi(t) converges to the set Λ”
Local stability under evolutionary game dynamics (2010, background): “It is possible, though, to provide a precise account of evolutionary processes based on multivalued protocols; see Benaïm et al. (2005) and Gorodeisky (2008, 2009).”
Dynamic fictitious play, dynamic gradient play, and distributed convergence to Nash equilibria (2005, methodology): “These are the dynamics obtained by viewing discrete-time FP as stochastic approximation iterations and applying associated ordinary differential equation (ODE) analysis methods [5], [7], [32].”
Risk-Constrained Reinforcement Learning with Percentile Risk Criteria (2015, methodology): “Therefore, by the Lyapunov theory for asymptotically stable differential inclusions (see Theorem 3.10 and Corollary 3.11 in Benaim et al. (2006), where the Lyapunov function Lθ,λ(ν) satisfies Hypothesis 3.1 and the property in (53) is equivalent to Hypothesis 3.9 in the reference), the above…”