Chee-Seng Chow and John Tsitsiklis. An optimal one-way multigrid algorithm for discretetime stochastic control. IEEE Transactions on Automatic Control, 36(8):898--914, 1991. Home/Search Document Not in Database Summary Related Articles Check |
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Rates of Convergence for Variable Resolution Schemes in.. - Munos, Moore (2000) (4 citations) (Correct)
....convergence for numerical approximations in optimal control when we consider variable resolution grids. We study the continuous space, discrete time, and discrete controls case. Previous work described methods to obtain rates of convergence using general approximators (Bertsekas, 1987) multi grid (Chow Tsitsiklis, 1991) or Random grids (Rust, 1996) These results provide bounds on the error of approximation of the value function as a function of the space discretization resolution (or the number of grid points) which is assumed to be uniform. Consequently, they do not consider the benefit of using non uniform ....
....the error of approximation: N u (x) jT N u V N (x) Gamma TuV (x)j and: N (x) jV N (x) Gamma V (x)j This paper proposes a general method to estimate bounds on the error of approximation of the value function for variable resolution (VR) grids. Previous work (Bertsekas, 1987) (Chow Tsitsiklis, 1991), and (Rust, 1996) have considered bounds for uniform resolution grids, that could be used for VR grids only in a worst case analysis in which we consider the lowest resolution of the grid. Section 1 provides bounds on the approximation error N in terms of the interpolation error e N . As ....
Chow, C., & Tsitsiklis, J. (1991). An optimal one-way multigrid algorithm for discrete-time stochastic control.
A Survey of Computational Complexity Results in Systems and.. - Blondel, Tsitsiklis (2000) (32 citations) (Correct)
....desired precision. General continuous state problems can be solved approximately, by discretizing them, as long as the problem data (transition probabilities and cost per stage) are su#ciently smooth functions of the state [Whitt, 1978a] Whitt, 1978b] References [Chow and Tsitsiklis, 1989] and [Chow and Tsitsiklis, 1991] establish that O 1 # 2n m arithmetic operations are necessary and su#cient for uniformly approximating the function J # within #, for the case where the state and control spaces are the sets [0, 1] n and [0, 1] m , respectively, under a Lipschitz continuity assumption on the problem ....
Chow, C.-S. and J. N. Tsitsiklis (1991). An optimal one-way multigrid algorithm for discrete-time stochastic control, IEEE Transactions on Automatic Control, 36, 898-914.
A Multigrid Form of Value Iteration Applied to a Markov.. - Heckendorn, Anderson (1998) (2 citations) (Correct)
....by applying it to the mountain car problem. We look at some of the fundamental differences between these kinds of problems and those traditionally treated with multigrid methods. We demonstrate that significant performance improvements can be achieved by using these techniques. 1 INTRODUCTION Chow and Tsitsiklis (1991) define a multigrid version of the value iteration, or successive approximation, algorithm for discounted, infinite horizon Markov Decision Problems (MDP) The multigrid version is performed by discretizing the continuous state and action spaces of an MDP at different granularities. First, the ....
Chow, C.-S. and Tsitsiklis, J. N. (1991) An optimal one-way multigrid algorithm for discrete time stochastic control, IEEE Transactions on Automatic Control, August 1991, vol. 36, no. 8, pp. 898--914.
Planning In Hybrid Structured Stochastic - Domains Comenius University (Correct)
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Chee-Seng Chow and John Tsitsiklis. An optimal one-way multigrid algorithm for discretetime stochastic control. IEEE Transactions on Automatic Control, 36(8):898--914, 1991.
Linear Program Approximations for Factored Continuous-State .. - Hauskrecht, Kveton (2003) (Correct)
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C.S. Chow and J.N. Tsitsiklis. An optimal one-way multigrid algorithm for discretetime stochastic control. IEEE Transactions on Automatic Control, 36:898--914, 1991.
Solving Factored MDPs with Exponential-Family Transition Models - Kveton, Hauskrecht (2006) (Correct)
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Chow, C.-S., and Tsitsiklis, J. 1991. An optimal oneway multigrid algorithm for discrete-time stochastic control. IEEE Transactions on Automatic Control 36(8):898-- 914.
Heuristic Refinements of Approximate Linear Programming for .. - Kveton, Hauskrecht (2004) (Correct)
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Chow, C., and Tsitsiklis, J. 1991. An optimal one-way multigrid algorithm for discrete-time stochastic control. IEEE Transactions on Automatic Control 36:898--914.
Linear Program Approximations for Factored Continuous-State .. - Hauskrecht, Kveton (2003) (Correct)
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C.S. Chow and J.N. Tsitsiklis. An optimal one-way multigrid algorithm for discretetime stochastic control. IEEE Transactions on Automatic Control, 36:898--914, 1991.
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