Presentation on YouTube

In this talk, I introduce a model of graph-constrained dynamic choice with reinforcement modeled by positively \(\alpha\)-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 \(\alpha > 0\), the asymptotic outcome concentrates around the optimum in a certain limiting sense when 'annealed' by letting \( \alpha \uparrow \infty \) slowly. (Joint work with Konstantin Avrachenkov, Sharayu Moharir and Suhail Mohmad Shah.)