  We consider the multiarm bandit problems in the timevarying dynamic system
for rich structural features. For the nonlinear dynamic model, we propose the
approximate inference for the posterior distributions based on Laplace
Approximation. For the context bandit problems, Thompson Sampling is adopted
based on the underlying posterior distributions of the parameters. More
specifically, we introduce the discount decays on the previous samples impact
and analyze the different decay rates with the underlying sample dynamics.
Consequently, the exploration and exploitation is adaptively tradeoff according
to the dynamics in the system.
