Uncertainties in stochastic programming models: The minimax approach

50 years ago, stochastic programming was introduced to deal with uncertain values of coefficients which were observed in applications of mathematical programming. These uncertainties were modeled as random and the assumption of complete knowledge of the probability distribution of random parameters became a standard. Hence, there is a new type of uncertainty concerning the probability distribution. Using a hypothetical, ad hoc distribution may lead to bad, costly decisions. Besides of a subsequent output analysis it pays to include the existing, possibly limited information into the model, cf. the minimax approach which will be the main item of this presentation. It applies to cases when the probability distribution is only known to belong to a specified class of probability distributions and one wishes to hedge against the least favorable distribution. The minimax approach has been developed for special types of stochastic programs and special choices of the class of probability distributions and there are recent results aiming at algorithmic solution of minimax problems and on stability properties of minimax solutions

A Survey of Monte Carlo Tree Search Methods

Monte Carlo tree search (MCTS) is a recently proposed search method that combines the precision of tree search with the generality of random sampling. It has received considerable interest due to its spectacular success in the difficult problem of computer Go, but has also proved beneficial in a range of other domains. This paper is a survey of the literature to date, intended to provide a snapshot of the state of the art after the first five years of MCTS research. We outline the core algorithm's derivation, impart some structure on the many variations and enhancements that have been proposed, and summarize the results from the key game and nongame domains to which MCTS methods have been applied. A number of open research questions indicate that the field is ripe for future work

Efficient pointwise estimation based on discrete data in ergodic nonparametric diffusions

A truncated sequential procedure is constructed for estimating the drift coefficient at a given state point based on discrete data of ergodic diffusion process. A nonasymptotic upper bound is obtained for a pointwise absolute error risk. The optimal convergence rate and a sharp constant in the bounds are found for the asymptotic pointwise minimax risk. As a consequence, the efficiency is obtained of the proposed sequential procedure.Comment: Published at http://dx.doi.org/10.3150/14-BEJ655 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm