Non linear programming for stochastic dynamic programming

Olivier Teytaud (1) , Sylvain Gelly (1)

1 TANC - Algorithmic number theory for cryptology

Many stochastic dynamic programming tasks in continuous action-spaces are tackled through discretization. We here avoid discretization; then, approximate dynamic programming (ADP) involves (i) many learning tasks, performed here by Support Vector Machines, for Bellman-function-regression (ii) many non-linearoptimization tasks for action-selection, for which we compare many algorithms. We include discretizations of the domain as particular non-linear-programming-tools in our experiments, so that by the way we compare optimization approaches and discretization methods. We conclude that robustness is strongly required in the non-linear-optimizations in ADP, and experimental results show that (i) discretization is sometimes inefficient, but some specific discretization is very efficient for "bang-bang" problems (ii) simple evolutionary tools outperform quasi-random in a stable manner (iii) gradient-based techniques are much less stable (iv) for most high-dimensional "less unsmooth" problems Covariance-Matrix-Adaptation is first ranked.

Mots clés: Control; Dynamic programming; Non Linear Programming

Domaines: Optimisation et contrôle [math.OC]

Olivier Teytaud, Sylvain Gelly. Non linear programming for stochastic dynamic programming. Icinco 2007, 2007, Angers, France. ⟨inria-00173202⟩