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On the Complexity of Value Iteration [article]

Nikhil Balaji, Stefan Kiefer, Petr Novotný, Guillermo A. Pérez,, Mahsa Shirmohammadi
2019 arXiv   pre-print
At the same time, value iteration provides a policy for the MDP that is optimal on a given finite horizon n. In this paper, we settle the computational complexity of value iteration.  ...  We show that, given a horizon n in binary and an MDP, computing an optimal policy is EXP-complete, thus resolving an open problem that goes back to the seminal 1987 paper on the complexity of MDPs by Papadimitriou  ...  In this paper, we provide a fresh look on one of the most familiar algorithms for MDPs: value iteration (VI).  ... 
arXiv:1807.04920v3 fatcat:jckqz6aju5a73oyqg5fbx3rhbe

On the Complexity of Value Iteration

Nikhil Balaji, Stefan Kiefer, Petr Novotný, Guillermo A. Pérez, Mahsa Shirmohammadi, Michael Wagner
2019 International Colloquium on Automata, Languages and Programming  
At the same time, value iteration provides a policy for the MDP that is optimal on a given finite horizon n. In this paper, we settle the computational complexity of value iteration.  ...  We show that, given a horizon n in binary and an MDP, computing an optimal policy is EXPTIME-complete, thus resolving an open problem that goes back to the seminal 1987 paper on the complexity of MDPs  ...  I C A L P 2 0 1 9 102: 6 96 On the Complexity of Value Iteration 2 P 2 )I C A L P 2 0 1 9 102: 8 298 (s, a)(s ) • p =n−1 (s ) , (On the Complexity of Value Iterationwhere p 0 (t) = 1 and p 0 (s) = 0  ... 
doi:10.4230/lipics.icalp.2019.102 dblp:conf/icalp/BalajiK0PS19 fatcat:zvi2hkgderge3hyxhtk4nano6e

Value Iteration Using Universal Graphs and the Complexity of Mean Payoff Games

Nathanaël Fijalkow, Paweł Gawrychowski, Pierre Ohlmann, Daniel Kráľ, Javier Esparza
2020 International Symposium on Mathematical Foundations of Computer Science  
The contribution of this paper is to prove tight bounds on the complexity of algorithms for mean payoff games using universal graphs.  ...  We show that they yield a family of value iteration algorithms for solving mean payoff games which includes the value iteration algorithm due to Brim, Chaloupka, Doyen, Gentilini, and Raskin.  ...  value iteration algorithms.  ... 
doi:10.4230/lipics.mfcs.2020.34 dblp:conf/mfcs/FijalkowGO20 fatcat:gw46lenlefanpfe4whisivwyau

Improving Approximate Value Iteration with Complex Returns by Bounding

Robert Wright, Xingye Qiao, Steven Loscalzo, Lei Yu
2015 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
We propose a bounding method which uses a negatively biased but relatively low variance estimator generated from a complex return to provide a lower bound on the observed value of a traditional one-step  ...  Approximate value iteration (AVI) is a widely used technique in reinforcement learning.  ...  Qiao's contribution was partially supported by a Collaboration Grant from the Simons Foundation (# 246649).  ... 
doi:10.1609/aaai.v29i1.9568 fatcat:fqwczp3f2zht7npbiwqno7wmtu

Turbo Decoding Complexity Reduction by Symbol Selection and Partial Iterations

Jinhong Wu, Branimir R. Vojcic, Zhengdao Wang
2007 IEEE GLOBECOM 2007-2007 IEEE Global Telecommunications Conference  
Based on an analysis on the recursive computation of the iterative maximum a posteriori (MAP) algorithm for turbo decoding, this paper considers a modified MAP scheme with reduced block lengths for symbols  ...  By omitting computations for symbols with reliable detection results, this approach significantly reduces complexity but well maintains the performance by complete iterations.  ...  COMPLEXITY BY PARTIAL ITERATIONS As the recursive computation of (9) -(11) is identical to complete iterations except with reduced number of symbols and different initial values for trellis decoding, the  ... 
doi:10.1109/glocom.2007.743 dblp:conf/globecom/WuVW07 fatcat:kl6addamynhcnbx437543fr5fu

Algorithm to Compute Cubes of 1st &quotN" Natural Numbers using Single Multiplication per Iteration

Rajat Tandon, Rajika Tandon
2014 International Journal of Computer Applications  
overall computational complexity per iteration is of the order of O  ...  So, keeping the number of iterations same in both, in the traditional approach, the overall computational complexity per iteration is expressed in the order of O(n 2 ) while in the current approach the  ...  METHODOLOGY As the number of iterations involved in both the cases is same, the comparison is based on the operation computational complexity per iteration.  ... 
doi:10.5120/17761-8872 fatcat:a3o6iz5op5gonaxkjtracdncxa

A Comparison of Two Equivalent Real Formulations for Complex-Valued Linear Systems Part 2: Results

Abnita Munankarmy, Michael Heroux
2003 American journal of undergraduate research  
Many iterative linear solver packages focus on real-valued systems and do not deal well with complex-valued systems, even though preconditioned iterative methods typically apply to both real and complex-valued  ...  Instead, commonly available packages such as PETSc and Aztec tend to focus on the real-valued systems, while complex-valued systems are seen as a late addition.  ...  Eigenvalues of the original complex matrix in problem M3D2, with imaginary components graphed on the vertical axis and real parts of the eigenvalues graphed on the horizontal axis.  ... 
doi:10.33697/ajur.2003.005 fatcat:zjmv7orwqjgvbe6xvvlddsaddm

Reduced complexity iterative decoding of low-density parity check codes based on belief propagation

M.P.C. Fossorier, M. Mihaljevic, H. Imai
1999 IEEE Transactions on Communications  
In this paper, two simplified versions of the belief propagation algorithm for fast iterative decoding of low-density parity check codes on the additive white Gaussian noise channel are proposed.  ...  Both versions are implemented with real additions only, which greatly simplifies the decoding complexity of belief propagation in which products of probabilities have to be computed.  ...  MacKay for providing the generator matrices of the LDPC codes used in this paper by allowing access to his website, as well as the reviewers for improving the presentation of the paper.  ... 
doi:10.1109/26.768759 fatcat:gdv36essnfbbrllbl7lqipay7y

Fractals Generated via Numerical Iteration Method

Wadia Faid Hassan Al-shameri, Mohamed El El Sayed
2022 Fractal and Fractional  
In this research article, a modified algorithm for the generation of a fractal pattern resulting from the iteration of an algebraic function using the numerical iteration method is presented.  ...  This fractal pattern shows the dynamical behavior of the numerical iterations. A nonstandard convergence test of the displayable fractal pattern was applied.  ...  Conflicts of Interest: The authors declare that they have no conflicts of interest.  ... 
doi:10.3390/fractalfract6040196 fatcat:trfvbtspybesdmnokkp5qqdugq

Convergence and Analysis of K-iteration Scheme in Complex Valued Banach Space

Khushboo Basra
2021 Revista GEINTEC  
Also, the assumption of the initial value (close of far from fixed point) has negligible impact on the step achieving a fixed point.  ...  In this paper, the convergence of a three-step iterative process i.e., K-iteration scheme is established in complex valued Banach spaces under the setting of generalized F-contractions.  ...  Also, lim ⟶∞ = 0, then for any sequence of positive numbers, Then is referred to as a complex valued metric on and ( , ) is referred to as a complex valued metric space.  ... 
doi:10.47059/revistageintec.v11i3.2051 fatcat:7qmalaee65belaaote27dbxuiq

Performance Anatomization of Computer Algorithms Based on Iterative and Recursive Methodologies

2020 International journal of recent technology and engineering  
This research provides a detailed study of how algorithms being written using different approaches work and then compares them on the basis of various parameters such as time complexity and space complexity  ...  This research paper presents the different methodologies of writing algorithms of data structure and also provides their performance analysis with respect to time complexity and space complexity.  ...  In the while loop, the value of "i" is incremented by one and the value of "S" gets incremented by "i" value.  ... 
doi:10.35940/ijrte.e4584.018520 fatcat:tn6l6ygz65ertpbdhimqdxv6fu

Low-complexity iteration control for MIMO-BICM systems

C. Gimmler, T. Lehnigk-Emden, N. Wehn
2010 21st Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications  
Energy consumption, latency and throughput of a hardware implementation strongly depend on the number of iterations.  ...  To the best of our knowledge, we present the first analysis of iteration control in MIMO bit interleaved coded modulation systems.  ...  As a comparison, the complexity for one iteration of the convolutional decoder normalized on one information bit is given.  ... 
doi:10.1109/pimrc.2010.5671725 dblp:conf/pimrc/GimmlerLW10 fatcat:fcnofnovondczfhlgqlshmlxru

Turbo greedy multiuser detection

A.A. AlRustamani, A.D. Damnjanovic, B.R. Vojcic
2001 IEEE Journal on Selected Areas in Communications  
However, the main drawback of the scheme is its exponential complexity in the number of users, which is due to the complexity of the maximum a posteriori probability (MAP) multiuser detector.  ...  In this paper, we demonstrate that, for both the additive white Gaussian noise and the frequency-nonselective Rayleigh fading, the substantial reduction in complexity of the iterative scheme proposed by  ...  . denotes complex conjugate and is the expected value of the -th user. is the value of the th user's th coded bit, is the symbol duration, is a complex zero-mean Gaussian random process and is the coded  ... 
doi:10.1109/49.942524 fatcat:llv45v2g7zferefkrqll3cwfbu

Low Complexity LSD Scheme for Joint Iterative MIMO Detection
반복 MIMO 검출을 위한 저 복잡도 LSD 기법

Saleem Ahmed, Sooyoung Kim
2013 The Journal of Korean Institute of Communications and Information Sciences  
We evaluate the performance of the proposed scheme with a joint soft-input-soft-ouput iterative MIMO detection in combination with turbo codes.  ...  We propose a simple and efficient radius update method for complexity reduction of list version sphere decoding and its application to iterative soft MIMO detection.  ...  At the start, the value for    is considered in its own single dimension. The value is chosen from the point in the sphere on the size of   .  ... 
doi:10.7840/kics.2013.38c.11.1051 fatcat:inkqobjnz5fb7bmnmc5uvwh5im

Low-Complexity DCD-Based Sparse Recovery Algorithms

Yuriy V. Zakharov, Vitor H. Nascimento, Rodrigo C. De Lamare, Fernando Goncalves De Almeida Neto
2017 IEEE Access  
In this paper, we propose computationally efficient techniques based on dichotomous coordinate descent (DCD) iterations for recovery of sparse complex-valued signals.  ...  The algorithm complexity is reduced when DCD iterations with a warm start are used for the LS optimization, and, as most of the DCD operations are additions and bit-shifts, it is especially suited to real  ...  The term 11C i is the complexity of C i tests at steps 5 and 6 in Table II ; each computation involves analysis of one direction on the complex plane for one element, which can be done with 11 real-valued  ... 
doi:10.1109/access.2017.2715882 fatcat:tduqdbkpxbdrnhrv5kiqyskxxi
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