Comparing discounted and average-cost Markov Decision Processes: a statistical significance perspective

Dylan Solms

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arXiv · 2112.00684

Comparing discounted and average-cost Markov Decision Processes: a statistical significance perspective

Dylan Solms

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Abstract

Optimal Markov Decision Process policies for problems with finite state and action space are identified through a partial ordering by comparing the value function across states. This is referred to as state-based optimality. This paper identifies when such optimality guarantees some form of system-based optimality as measured by a scalar. Four such system-based metrics are introduced. Uni-variate empirical distributions of these metrics are obtained through simulation as to assess whether theoretically optimal policies provide a statistically significant advantage. This has been conducted using a Student's t-test, Welch's $t$-test and a Mann-Whitney $U$-test. The proposed method is applied to a common problem in queuing theory: admission control.

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Dylan Solms. 2021-12-01. Comparing discounted and average-cost Markov Decision Processes: a statistical significance perspective. https://arxiv.org/abs/2112.00684

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