Randomized Simplicial Approximate Stochastic Dynamic Programming for Mid-term Reservoir Optimization - Zephyr, Luckny; Lamond, Bernard F. (International Conference on Control, Decision and Information Technologies (Online), 2022)
Midterm reservoir management problems are often cast as stochastic dynamic programs, due to their sequential nature. Because of the well known dimensionality issue of dynamic programming, several approximate dynamic programming (ADP) techniques have been proposed to tackled these problems. In this work, we investigate a new ADP scheme based on a hydrid simplicial and Monte Carlo sampling strategy. Our starting point is the works [1]-[3], which proposed a simplicial decomposition scheme guided by the curvature of the value function, as estimated by local differences between lower and upper bounds. In contrast to these approaches, which store an exhaustive list of "active" simplices at each iteration, our proposals choose grid points in small random samples of simplices. Our proposal is tested on the approximation of randomly generated concave functions and mid-term reservoir management problems.