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Using Randomization to Break the Curse of Dimensionality

By John Rust


Abstract: This paper introduces random versions of successive approximations and multigrid algorithms for computing approximate solutions to a class of finite and infinite horizon Markovian decision problems (MDPs). We prove that these algorithms succeed in breaking the “curse of dimensionality ” for a subclass of MDPs known as discrete decision processes (DDPs).

Topics: dynamic programming, curse of dimensionality, Bellman operator, random Bellman operator, computational complexity, maximal inequalities, empirical processes 1
Year: 1997
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