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The n th-Order Bias Optimality for Multichain Markov Decision Processes

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2 Author(s)
Xi-Ren Cao ; Dept. of Electron. & Comput. Eng., Hong Kong Univ. of Sci. & Technol., Hong Kong ; Junyu Zhang

In this paper, we propose a new approach to the theory of finite multichain Markov decision processes (MDPs) with different performance optimization criteria. We first propose the concept of nth-order bias; then, using the average reward and bias difference formulas derived in this paper, we develop an optimization theory for finite MDPs that covers a complete spectrum from average optimality, bias optimality, to all high-order bias optimality, in a unified way. The approach is simple, direct, natural, and intuitive; it depends neither on Laurent series expansion nor on discounted MDPs. We also propose one-phase policy iteration algorithms for bias and high-order bias optimal policies, which are more efficient than the two-phase algorithms in the literature. Furthermore, we derive high-order bias optimality equations. This research is a part of our effort in developing sensitivity-based learning and optimization theory.

Published in:

IEEE Transactions on Automatic Control  (Volume:53 ,  Issue: 2 )