Title :
Application of the Mirror Descent Method to minimize average losses coming by a poisson flow
Author :
Nazin, Alexander ; Anulova, Svetlana ; Tremba, Andrey
Author_Institution :
Ya.Z. Tsypkin Lab. of Adaptive & Robust Syst., V.A. Trapeznikov Inst. of Control Sci., Moscow, Russia
Abstract :
We treat a convex problem to minimize average loss function for a stochastic system operating in continuous time. The losses on time horizon T arise at the jump times of a Poisson process with intensity being an unknown random process. The oracle gives randomly noised gradients of the loss function; the noises are additive, unbiased, with the bounded dual norm in average square sense. The goal consists in minimizing the average integral loss over a given convex compact set in the N-dimension space. We propose a mirror descent algorithm and prove an explicit upper bound for the average integral loss regret. The bound is of type “square root of T” with an explicit coefficient. Finally, we describe an example of optimization for a server processing a stream of incoming requests, and we discuss simulation results.
Keywords :
continuous time systems; convex programming; random processes; stochastic processes; stochastic systems; N-dimension space; Poisson flow; Poisson process; additive noise; average integral loss function minimization; average integral loss regret; average square sense; bounded dual norm; continuous time system; convex compact set; convex optimization; convex problem; explicit coefficient; explicit upper bound; mirror descent method; random noised gradients; stochastic system; time horizon T; unbiased noise; unknown random process; Convex functions; Integral equations; Mirrors; Optimization; Random variables; Servers; Upper bound;
Conference_Titel :
Control Conference (ECC), 2014 European
Conference_Location :
Strasbourg
Print_ISBN :
978-3-9524269-1-3
DOI :
10.1109/ECC.2014.6862486