We consider the framework of stochastic multi-armed bandit problems and study the possibilities and limitations of forecasters that perform an on-line exploration of the arms. These forecasters are assessed in terms of their simple regret, a regret notion that captures the fact that exploration is only constrained by the number of available rounds (not necessarily known in advance), in contrast...

The area under the ROC curve (AUC) is a widely used performance measure in machine learning, and has been widely studied in recent years particularly in the context of bipartite ranking. A dominant theoretical and algorithmic framework for AUC optimization/bipartite ranking has been to reduce the problem to pairwise classification; in particular, it is well known that the AUC regret can be form...

Regret is a decision-related emotion that arises when a chosen outcome is, or is believed to be, worse than a non-chosen alternative (Connolly & Zeelenberg, 2002). The experience and anticipation of regret has been linked to important real-life decisions such as health behaviors (medical screening, condom use) and financial decisions (Zeelenberg, 1999). The behavioral consequences of regret inc...

Both guilt and regret typically result from counterfactual evaluations of personal choices that caused a negative outcome and are thought to regulate human decisions by people's motivation to avoid these emotions. Despite these similarities, studies asking people to describe typical situations of guilt and regret identified the social dimension as a fundamental distinguishing factor, showing th...

We study a strategic facility location problem under uncertainty. The uncertainty associated with future events is modeled by defining alternative future scenarios with probabilities. We present a new model which minimizes the expected regret with respect to an endogenously selected subset of worst-case scenarios whose collective probability of occurrence is exactly 1-α. We demonstrate the effe...

We present several online algorithms with dimension-free regret bounds for general nonconvex quadratic losses by viewing them as functions in Reproducing Hilbert Kernel Spaces. In our work we adapt the Online Gradient Descent, Follow the Regularized Leader and the Conditional Gradient method meta algorithms for RKHS spaces and provide regret bounds in this setting. By analyzing them as algorith...

The iterated regret minimization solution exhibits the good qualitative behavior as that observed in experiments in many games that have proved problematic for Nash Equilibrium(NE). It is worthy exploring epistemic characterizations unearthing players’rationality for an algorithm of Iterated Eliminations Regret-dominated Strategy (IERS) related to the solution. In this paper, based on the dynam...

We design differentially private algorithms for the problem of online linear optimization in the full information and bandit settings with optimal Õ( √ T )1 regret bounds. In the full-information setting, our results demonstrate that ε-differential privacy may be ensured for free – in particular, the regret bounds scale as O( √ T ) + Õ ( 1 ε ) . For bandit linear optimization, and as a special ...

Prior research on regret has assumed a consideration set of only two-alternatives. The authors have relaxed that assumption and have developed hypotheses to examine the influence of the unawareness set and order effects in the measurement of consumer regret in a post-purchase evaluation. The results demonstrated that the brands consumers were previously unaware of, do indeed influence consumer ...

Various papers have analyzed the noisy optimization of convex functions. This analysis has been made according to several criteria used to evaluate the performance of algorithms: uniform rate, simple regret and cumulative regret. We propose an iterative optimization framework, a particular instance of which, using Hessian approximations, provably (i) reaches the same rate as Kiefer-Wolfowitz al...