Approximate policy iteration: A survey and some new methods

We consider the classical policy iteration method of dynamic programming (DP), where approximations and simulation are used to deal with the curse of dimensionality. We survey a number of issues: convergence and rate of convergence of approximate policy evaluation methods, singularity and susceptibility to simulation noise of policy evaluation, exploration issues, constrained and enhanced policy iteration, policy oscillation and chattering, and optimistic and distributed policy iteration. Our discussion of policy evaluation is couched in general terms and aims to unify the available methods in the light of recent research developments and to compare the two main policy evaluation approaches: projected equations and temporal differences (TD), and aggregation. In the context of these approaches, we survey two different types of simulation-based algorithms: matrix inversion methods, such as least-squares temporal difference (LSTD), and iterative methods, such as least-squares policy evaluation (LSPE) and TD (λ), and their scaled variants. We discuss a recent method, based on regression and regularization, which rectifies the unreliability of LSTD for nearly singular projected Bellman equations. An iterative version of this method belongs to the LSPE class of methods and provides the connecting link between LSTD and LSPE. Our discussion of policy improvement focuses on the role of policy oscillation and its effect on performance guarantees. We illustrate that policy evaluation when done by the projected equation/TD approach may lead to policy oscillation, but when done by aggregation it does not. This implies better error bounds and more regular performance for aggregation, at the expense of some loss of generality in cost function representation capability. Hard aggregation provides the connecting link between projected equation/TD-based and aggregation-based policy evaluation, and is characterized by favorable error bounds.National Science Foundation (U.S.) (No.ECCS-0801549)Los Alamos National Laboratory. Information Science and Technology InstituteUnited States. Air Force (No.FA9550-10-1-0412

Solving Markov Decision Processes via Simulation

This chapter presents an overview of simulation-based techniques useful for solving Markov decision processes (MDPs). MDPs model problems of sequential decision-making under uncertainty, in which decisions made in each state collectively affect the trajectory of the states visited by the system over a time horizon of interest. Traditionally, MDPs have been solved via dynamic programming (DP), which requires the transition probability model that is difficult to derive in many realistic settings. The use of simulation for solving MDPs allows us to bypass the transition probability model and solve large-scale MDPs considered intractable to solve by traditional DP. The simulation-based methodology for solving MDPs, which like DP is also rooted in the Bellman equations, goes by names such as reinforcement learning, neuro-DP, and approximate or adaptive DP.We begin with a description of algorithms for infinite-horizon discounted reward MDPs, followed by the same for infinite-horizon average reward MDPs. Then we present a discussion on finite-horizon MDPs. For each problem considered, we present a step-by-step description of a selected group of algorithms. In making this selection, we have attempted to blend the old and the classical with more recent developments. Finally, after touching upon extensions and convergence theory, we conclude with a brief summary of some applications and directions for future research