Fast Approximate Dynamic Programming for Infinite-Horizon Markov Decision ProcessesDownload PDF

Published: 09 Nov 2021, Last Modified: 05 May 2023NeurIPS 2021 PosterReaders: Everyone
Keywords: Stochastic optimal control, value iteration, input-affine systems, Fenchel duality, computational complexity.
Abstract: In this study, we consider the infinite-horizon, discounted cost, optimal control of stochastic nonlinear systems with separable cost and constraints in the state and input variables. Using the linear-time Legendre transform, we propose a novel numerical scheme for implementation of the corresponding value iteration (VI) algorithm in the conjugate domain. Detailed analyses of the convergence, time complexity, and error of the proposed algorithm are provided. In particular, with a discretization of size $X$ and $U$ for the state and input spaces, respectively, the proposed approach reduces the time complexity of each iteration in the VI algorithm from $O(XU)$ to $O(X+U)$, by replacing the minimization operation in the primal domain with a simple addition in the conjugate domain.
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