Dynamic social learning under graph constraints

Konstantin Avrachenkov; Vivek S. Borkar; Sharayu Moharir; Suhail M. Shah

doi:10.1109/tcns.2021.3114377

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arXiv · 2007.03983

Dynamic social learning under graph constraints

Konstantin Avrachenkov·Vivek S. Borkar·Sharayu Moharir·Suhail M. Shah

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Abstract

We introduce a model of graph-constrained dynamic choice with reinforcement modeled by positively $\alpha$-homogeneous rewards. We show that its empirical process, which can be written as a stochastic approximation recursion with Markov noise, has the same probability law as a certain vertex reinforced random walk. We use this equivalence to show that for $\alpha > 0$, the asymptotic outcome concentrates around the optimum in a certain limiting sense when `annealed' by letting $\alpha\uparrow\infty$ slowly.

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Konstantin Avrachenkov, Vivek S. Borkar, Sharayu Moharir, Suhail M. Shah. 2020-07-08. Dynamic social learning under graph constraints. https://doi.org/10.1109/tcns.2021.3114377

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