REGRESS LATER MONTE-CARLO

FOR OPTIMAL CONTROL OF MARKOV PROCESSES
CHI: Alessandro Balata, University of Leeds
QUANDO: Martedì 10 Aprile, ore 16.00
DOVE: Aula Seminari, Dipartimento di Matematica
ABSTRACT: We develop two Regression Monte Carlo algorithms (value

and performance iteration) to solve general problems of optimal stochas-
tic control of discrete-time Markov processes. We formulate our method

within an innovative framework that allow us to prove the speed of conver-
gence of our numerical schemes. We rely on the Regress Later approach un-
like other attempts which employ the Regress Now technique. We exploit

error bounds obtained in our proofs, along with numerical experiments,

to investigate differences between the value and performance iteration ap-
proaches. Both introduced in 2001, their characteristics have gone largely

unnoticed in the literature; we show however that their differences are
paramount in practical solution of stochastic control problems. Finally,
we provide some guidelines for the tuning of our algorithms. During the
seminar I will also provide a general introduction to the numerical solution
of stochastic control problems with a focus on least-squares approximation
of conditional expectations.