Graph-constrained dynamic choice

Vivek Borkar – Département de génie électrique, Indian Institute of Technology Bombay, Inde

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In this talk, I introduce a model of graph-constrained dynamic choice with reinforcement modeled by positively α

-homogeneous rewards. 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. Thus the limiting differential equation that it tracks coincides with the forward Kolmogorov equation for the latter, which in turn is a scaled version of a special instance of replicator dynamics with potential. This equivalence is exploited to show that for α>0, the asymptotic outcome concentrates around the optimum in a certain limiting sense when 'annealed' by letting α↑∞ slowly. (Joint work with Konstantin Avrachenkov, Sharayu Moharir and Suhail Mohmad Shah.)