For infinite-horizon control with unknown context-conditional noise, the Bayesian Bellman value function converges uniformly, and the scaled optimal value is asymptotically normal only if an unproved √N-equivalence assumption holds.
Arifo˘ glu and S.¨Ozekici
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Stochastic Optimal Control with Side Information and Bayesian Learning
For infinite-horizon control with unknown context-conditional noise, the Bayesian Bellman value function converges uniformly, and the scaled optimal value is asymptotically normal only if an unproved √N-equivalence assumption holds.