  We consider a simulation optimization problem for a context-dependent
decision-making, which aims to determine the top-m designs for all contexts.
Under a Bayesian framework, we formulate the optimal dynamic sampling decision
as a stochastic dynamic programming problem, and develop a sequential sampling
policy to efficiently learn the performance of each design under each context.
The asymptotically optimal sampling ratios are derived to attain the optimal
large deviations rate of the worst-case of probability of false selection. The
proposed sampling policy is proved to be consistent and its asymptotic sampling
ratios are asymptotically optimal. Numerical experiments demonstrate that the
proposed method improves the efficiency for selection of top-m
context-dependent designs.
