Rates of Convergence for Variable Resolution Schemes in Optimal Control

This paper presents a general method to derive tight rates of 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 or linear approximators (Bertsekas & Tsitsiklis, 1996; Tsitsiklis & Van Roy, 1996; Gordon, 1999), multigrids (Chow & Tsitsiklis, 1991), random or low-discrepancy grids (Rust, 1996). These results provide bounds on the error on the value function in terms of the representation power of the class of approximators considered, thus for uniform grids, in terms of the space discretization resolution (or the number of grid-points). Consequently, they do not explicitly consider the bene t of using non-uniform resolutions. However, empirical results (Munos & Moore, 1999b) have shown the importance of using variable resolution discretizations, especially for problems ...

• Type: Conference
• Year: 2000
• Where: ICML
• Authors: Andrew W. Moore, Rémi Munos
• Keywords: ICML 2000, Local Interpolation Error, Machine Learning, Value Function, Variable Resolution Grids