Policy Iteration is well suited to optimize PageRank
Romain Hollanders, Jean-Charles Delvenne, Rapha\"el Jungers

TL;DR
This paper demonstrates that policy iteration is efficient for a class of Markov Decision Processes related to PageRank optimization, supported by theoretical analysis and numerical evidence, suggesting polynomial complexity in these cases.
Contribution
The paper identifies a class of MDPs based on PageRank optimization where policy iteration is conjectured to be polynomial-time, supported by proofs and numerical experiments.
Findings
Policy iteration is efficient for PageRank-based MDPs.
Adding constraints links PageRank optimization to path length optimization.
Numerical evidence supports polynomial complexity conjecture.
Abstract
The question of knowing whether the policy Iteration algorithm (PI) for solving Markov Decision Processes (MDPs) has exponential or (strongly) polynomial complexity has attracted much attention in the last 50 years. Recently, Fearnley proposed an example on which PI needs an exponential number of iterations to converge. Though, it has been observed that Fearnley's example leaves open the possibility that PI behaves well in many particular cases, such as in problems that involve a fixed discount factor, or that are restricted to deterministic actions. In this paper, we analyze a large class of MDPs and we argue that PI is efficient in that case. The problems in this class are obtained when optimizing the PageRank of a particular node in the Markov chain. They are motivated by several practical applications. We show that adding natural constraints to this PageRank Optimization problem…
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Taxonomy
TopicsWeb Data Mining and Analysis · Complex Network Analysis Techniques · Distributed and Parallel Computing Systems
