Simulation Based Algorithms for Markov Decision Processes and Multi-Action Restless Bandits

We consider multi-dimensional Markov decision processes and formulate a long term discounted reward optimization problem. Two simulation based algorithmsMonte Carlo rollout policy and parallel rollout policy are studied, and various properties for these policies are discussed. We next consider a restless multi-armed bandit (RMAB) with multi-dimensional state space and multi-actions bandit model. A standard RMAB consists of two actions for each arms whereas in multi-actions RMAB, there are more that two actions for each arms. A popular approach for RMAB is Whittle index based heuristic policy. Indexability is an important requirement to use index based policy. Based on this, an RMAB is classified into indexable or non-indexable bandits. Our interest is in the study of Monte-Carlo rollout policy for both indexable and non-indexable restless bandits. We first analyze a standard indexable RMAB (two-action model) and discuss an index based policy approach. We present approximate index computation algorithm using Monte-Carlo rollout policy. This algorithm's convergence is shown using two-timescale stochastic approximation scheme. Later, we analyze multi-actions indexable RMAB, and discuss the index based policy approach. We also study non-indexable RMAB for both standard and multi-actions bandits using Monte-Carlo rollout policy.