Algorithms for stable marriage and related matching problems typically assume that full preference information is available. While the Gale-Shapley algorithm can be viewed as a means of eliciting preferences incrementally, it does not prescribe a general means for matching with incomplete information, nor is it designed to minimize elicitation. We propose the use of maximum regret to measure th...

We consider a setting where an decision maker’s uncertainty is represented by a set of probability measures, rather than a single measure. Measure-by-measure updating of such a set of measures upon acquiring new information is well-known to suffer from problems. To deal with these problems, we propose using weighted sets of probabilities: a representation where each measure is associated with a...

We adapt the competitive location model based on maximal covering to include the knowledge that a competitor will enter the market later with a single new facility. The objective is to locate facilities under a budget constraint in order to maximise the remaining market share after the competitor’s later entry. We develop mixed zero-one programming formulations for each of the following three s...

In many situations, a set of hard constraints encodes the feasible configurations of some system or product over which users have preferences. We consider the problem of computing a best feasible solution when the user’s utilities are partially known. Assuming bounds on utilities, efficient mixed integer linear programs are devised to compute the solution with minimax regret while exploiting ge...

We consider a generalization of stochastic bandit problems where the set of arms, X , is allowed to be a generic topological space. We constraint the mean-payoff function with a dissimilarity function over X in a way that is more general than Lipschitz. We construct an arm selection policy whose regret improves upon previous result for a large class of problems. In particular, our results imply...

We study the regret of an online learner playing a multi-round game in a Banach space B against an adversary that plays a convex function at each round. We characterize the minimax regret when the adversary plays linear functions in terms of the Rademacher type of the dual of B. The cases when the adversary plays bounded and uniformly convex functions respectively are also considered. Our resul...

We address the problem of robust decision making for stochastic network design. Our work is motivated by spatial conservation planning where the goal is to take management decisions within a fixed budget to maximize the expected spread of a population of species over a network of land parcels. Most previous work for this problem assumes that accurate estimates of different network parameters (e...

Contextual bandits are widely used in Internet services from news recommendation to advertising, and to Web search. Generalized linear models (logistical regression in particular) have demonstrated stronger performance than linear models in many applications where rewards are binary. However, most theoretical analyses on contextual bandits so far are on linear bandits. In this work, we propose ...

Consider a decision maker who faces a number of possible models of the world. Every model generates objective probabilities, but no probabilities of models are given. This is the classic setting of statistical decision theory; recent and less standard applications include decision making with model uncertainty, e.g. due to concerns for misspecification, treatment choice with partial identificat...

We aim to design strategies for sequential decision making that adjust to the difficulty of the learning problem. We study this question both in the setting of prediction with expert advice, and for more general combinatorial decision tasks. We are not satisfied with just guaranteeing minimax regret rates, but we want our algorithms to perform significantly better on easy data. Two popular ways...