Matches in SemOpenAlex for { <https://semopenalex.org/work/W4300649864> ?p ?o ?g. }
Showing items 1 to 61 of
61
with 100 items per page.
- W4300649864 abstract "We show that one can approximate the least fixed point solution for a multivariate system of monotone probabilistic max(min) polynomial equations, referred to as maxPPSs (and minPPSs, respectively), in time polynomial in both the encoding size of the system of equations and in log(1/epsilon), where epsilon > 0 is the desired additive error bound of the solution. (The model of computation is the standard Turing machine model.) We establish this result using a generalization of Newton's method which applies to maxPPSs and minPPSs, even though the underlying functions are only piecewise-differentiable. This generalizes our recent work which provided a P-time algorithm for purely probabilistic PPSs. These equations form the Bellman optimality equations for several important classes of infinite-state Markov Decision Processes (MDPs). Thus, as a corollary, we obtain the first polynomial time algorithms for computing to within arbitrary desired precision the optimal value vector for several classes of infinite-state MDPs which arise as extensions of classic, and heavily studied, purely stochastic processes. These include both the problem of maximizing and mininizing the termination (extinction) probability of multi-type branching MDPs, stochastic context-free MDPs, and 1-exit Recursive MDPs. Furthermore, we also show that we can compute in P-time an epsilon-optimal policy for both maximizing and minimizing branching, context-free, and 1-exit-Recursive MDPs, for any given desired epsilon > 0. This is despite the fact that actually computing optimal strategies is Sqrt-Sum-hard and PosSLP-hard in this setting. We also derive, as an easy consequence of these results, an FNP upper bound on the complexity of computing the value (within arbitrary desired precision) of branching simple stochastic games (BSSGs)." @default.
- W4300649864 created "2022-10-03" @default.
- W4300649864 creator A5003946901 @default.
- W4300649864 creator A5025014162 @default.
- W4300649864 creator A5043084405 @default.
- W4300649864 date "2012-02-21" @default.
- W4300649864 modified "2023-10-14" @default.
- W4300649864 title "Polynomial Time Algorithms for Branching Markov Decision Processes and Probabilistic Min(Max) Polynomial Bellman Equations" @default.
- W4300649864 doi "https://doi.org/10.48550/arxiv.1202.4798" @default.
- W4300649864 hasPublicationYear "2012" @default.
- W4300649864 type Work @default.
- W4300649864 citedByCount "0" @default.
- W4300649864 crossrefType "posted-content" @default.
- W4300649864 hasAuthorship W4300649864A5003946901 @default.
- W4300649864 hasAuthorship W4300649864A5025014162 @default.
- W4300649864 hasAuthorship W4300649864A5043084405 @default.
- W4300649864 hasBestOaLocation W43006498641 @default.
- W4300649864 hasConcept C105795698 @default.
- W4300649864 hasConcept C106189395 @default.
- W4300649864 hasConcept C118615104 @default.
- W4300649864 hasConcept C126255220 @default.
- W4300649864 hasConcept C134306372 @default.
- W4300649864 hasConcept C159886148 @default.
- W4300649864 hasConcept C164660894 @default.
- W4300649864 hasConcept C28826006 @default.
- W4300649864 hasConcept C33923547 @default.
- W4300649864 hasConcept C37404715 @default.
- W4300649864 hasConcept C49937458 @default.
- W4300649864 hasConcept C90119067 @default.
- W4300649864 hasConceptScore W4300649864C105795698 @default.
- W4300649864 hasConceptScore W4300649864C106189395 @default.
- W4300649864 hasConceptScore W4300649864C118615104 @default.
- W4300649864 hasConceptScore W4300649864C126255220 @default.
- W4300649864 hasConceptScore W4300649864C134306372 @default.
- W4300649864 hasConceptScore W4300649864C159886148 @default.
- W4300649864 hasConceptScore W4300649864C164660894 @default.
- W4300649864 hasConceptScore W4300649864C28826006 @default.
- W4300649864 hasConceptScore W4300649864C33923547 @default.
- W4300649864 hasConceptScore W4300649864C37404715 @default.
- W4300649864 hasConceptScore W4300649864C49937458 @default.
- W4300649864 hasConceptScore W4300649864C90119067 @default.
- W4300649864 hasLocation W43006498641 @default.
- W4300649864 hasLocation W43006498642 @default.
- W4300649864 hasLocation W43006498643 @default.
- W4300649864 hasLocation W43006498644 @default.
- W4300649864 hasLocation W43006498645 @default.
- W4300649864 hasOpenAccess W4300649864 @default.
- W4300649864 hasPrimaryLocation W43006498641 @default.
- W4300649864 hasRelatedWork W2002454365 @default.
- W4300649864 hasRelatedWork W2041621488 @default.
- W4300649864 hasRelatedWork W2047890136 @default.
- W4300649864 hasRelatedWork W2072084563 @default.
- W4300649864 hasRelatedWork W2076762960 @default.
- W4300649864 hasRelatedWork W2156021013 @default.
- W4300649864 hasRelatedWork W2156992384 @default.
- W4300649864 hasRelatedWork W2328176891 @default.
- W4300649864 hasRelatedWork W4232993046 @default.
- W4300649864 hasRelatedWork W4322718218 @default.
- W4300649864 isParatext "false" @default.
- W4300649864 isRetracted "false" @default.
- W4300649864 workType "article" @default.