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We consider the multiarm bandit problems in the timevarying dynamic systemfor rich structural features. For the nonlinear dynamic model, we propose theapproximate inference for the posterior distributions based on LaplaceApproximation. For the context bandit problems, Thompson Sampling is adoptedbased on the underlying posterior distributions of the parameters. Morespecifically, we introduce the discount decays on the previous samples impactand analyze the different decay rates with the underlying sample dynamics.Consequently, the exploration and exploitation is adaptively tradeoff accordingto the dynamics in the system.

Thompson Sampling in Dynamic Systems for Contextual Bandit Problems