We consider the single facility ordered median location problem with uncertainty in the parameters (weights) defining the objective function. We study two cases. In the first case the uncertain weights belong to a region with a finite number of extreme points, and in the second case they must also satisfy some order constraints and belong to some box, (convex case). To deal with the uncertainty...

We consider a price-setting newsvendor problem with partial information. The newsvendor does not know the price-dependent probability distribution of demand, but is able to estimate lower and upper limits of the market size and consumer willingness-to-pay. The objective is to minimize the maximum loss in expected profit, or minimax regret. We derive closed-form expressions for optimal quantity ...

We propose the kl-UCB algorithm for regret minimization in stochastic bandit models with exponential families of distributions. We prove that it is simultaneously asymptotically optimal (in the sense of Lai and Robbins’ lower bound) and minimax optimal. This is the first algorithm proved to enjoy these two properties at the same time. This work thus merges two different lines of research with s...

Kernel online convex optimization (KOCO) is a framework combining the expressiveness of nonparametric kernel models with the regret guarantees of online learning. First-order KOCO methods such as functional gradient descent require onlyO(t) time and space per iteration, and, when the only information on the losses is their convexity, achieve a minimax optimal O( √ T ) regret. Nonetheless, many ...

|This paper studies minimax aspects of nonparametric classi cation. We rst study minimax estimation of the conditional probability of a class label, given the feature variable. This function, say f; is assumed to be in a general nonparametric class. We show the minimax rate of convergence under square L2 loss is determined by the massiveness of the class as measured by metric entropy. The secon...

Prediction of individual sequences is investigated for cases in which the decision maker observes a delayed version of the sequence or is forced to issue his her predictions a number of steps in advance with incomplete information For nite action and observation spaces it is shown that the prediction strategy that minimizes the worst case regret with respect to the Bayes envelope is obtained th...