Speaker : Professor Hidehiro Kaise (Nagoya University)
Title : Idempotent expansions for continuous-time stochastic control
Time : 2011-03-14 (Mon) 14:10 - 15:10
Place : Seminar Room 722, Institute of Mathematics (NTU Campus)
Abstract: It is now well-known that many classes of deterministic control problems may be solved by max-plus or min-plus (more generally idempotent) numerical methods. By these methods, we can have max-plus or min-plus expansions for solutions of dynamic programming PDEs in deterministic control problems which lead to curse-of-dimensionality-free numerical methods. In this talk, we present idempotent numerical methods for dynamic programming PDEs in stochastic control. By generalizing min-plus distributive property, we obtain a new algorithm to compute the time-discretized value functions, which we call idempotent distributed dynamic programming principle (IDDPP). In an example, we illustrate that the value functions can be expanded by quadratic functions via IDPPP. Complexity reductions of the value functions will be discussed. The material of this talk is based on collaboration with W.M. McEneaney (UC San Diego).