Miroslav Pǐstěk Approximate Dynamic Programming based on High Dimensional Model Representation 2310 October 2011

In this article, an efficient algorithm for an optimal decision strategy approximation is introduced. The proposed approximation of the Bellman equation is based on HDMR technique. This non-parametric function approximation is used not only to reduce memory demands necessary to store Bellman function, but also to allow its fast approximate minimization. On that account, a clear connection between HDMR minimization and discrete optimization is newly established. In each time step of the backward evaluation of the Bellman function, we relax the parameterized discrete minimization subproblem to obtain parameterized trust region problem. We observe that the involved matrix is the same for all parameters owning to the structure of HDMR approximation. We find eigenvalue decomposition of this matrix to solve all trust region problems effectively. The achieved estimates of minima are immediately stored in HDMR approximation to avoid a full-domain representation of Bellman function. We assume that the newly developed approximate minimzation of HDMR can be beneficial also in other applications.