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We aim to efficiently allocate a fixed simulation budget to identify the top-mc designs for each context among a finite number of contexts. The performance of each design under a context is measured by an identifiable statistical characteristic, possibly with the existence of nuisance parameters. Under a Bayesian framework, we extend the top-two Thompson sampling method designed for selecting the best design in a single context to the contextual top-mc selection problems, leading to an efficient sampling policy that simultaneously allocates simulation samples to both contexts and designs. To demonstrate the asymptotic optimality of the proposed sampling policy, we characterize the exponential convergence rate of the posterior distribution for a wide range of identifiable sampling distribution families. The proposed sampling policy is proved to be consistent, and asymptotically satisfies a necessary condition for optimality. In particular, when selecting contextual best designs (i.e., mc = 1), the proposed sampling policy is proved to be asymptotically optimal. Numerical experiments demonstrate the good finite sample performance of the proposed sampling policy.

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.

We consider the popular tree-based search strategy within the framework of reinforcement learning, the Monte Carlo Tree Search (MCTS), in the context of finite-horizon Markov decision process. We propose a dynamic sampling tree policy that efficiently allocates limited computational budget to maximize the probability of correct selection of the best action at the root node of the tree. Experimental results on Tic-Tac-Toe and Gomoku show that the proposed tree policy is more efficient than other competing methods.

We consider selecting the top-$m$ alternatives from a finite number of alternatives via Monte Carlo simulation. Under a Bayesian framework, we formulate the sampling decision as a stochastic dynamic programming problem, and develop a sequential sampling policy that maximizes a value function approximation one-step look ahead. To show the asymptotic optimality of the proposed procedure, the asymptotically optimal sampling ratios which optimize large deviations rate of the probability of false selection for selecting top-$m$ alternatives has been rigorously defined. The proposed sampling policy is not only proved to be consistent but also achieves the asymptotically optimal sampling ratios. Numerical experiments demonstrate superiority of the proposed allocation procedure over existing ones.

The note studies the problem of selecting a good enough subset out of a finite number of alternatives under a fixed simulation budget. Our work aims to maximize the posterior probability of correctly selecting a good subset. We formulate the dynamic sampling decision as a stochastic control problem in a Bayesian setting. In an approximate dynamic programming paradigm, we propose a sequential sampling policy based on value function approximation. We analyze the asymptotic property of the proposed sampling policy. Numerical experiments demonstrate the efficiency of the proposed procedure.