We obtain minimax lower bounds on the regret for the classical two-armed bandit problem. We provide a nite-sample minimax version of the well-known log n asymptotic lower bound of Lai and Robbins. Also, in contrast to the logn asymptotic results on the regret, we show that the minimax regret is achieved by mere random guessing under fairly mild conditions on the set of allowable con gurations o...

This paper addresses the e€ects of the anticipation of regret on decision making under uncertainty. Regret is a negative, cognitively based emotion that we experience when realizing or imagining that our present situation would have been better, had we decided di€erently. The experience of post-decisional regret is for a large part conditional on the knowledge of the outcomes of the rejected al...

Regret and relief are related to counterfactual thinking and rely on comparison processes between what has been and what might have been. In this article, we study the development of regret and relief from late childhood to adulthood (11.2-20.2 years), and we examine how these two emotions affect individuals' willingness to retrospectively reconsider their choice in a computerized monetary gamb...

We consider the following linearly combinatorial multiarmed bandits (MABs) problem. In a discrete time system, there are K unknown random variables (RVs), i.e., arms, each evolving as an i.i.d stochastic process over time. At each time slot, we select a set of N (N ≤ K) RVs, i.e., strategy, subject to an arbitrarily constraint. We then gain a reward that is a linear combination of observations ...

We consider the non-stochastic Multi-Armed Bandit problem in a setting where there is a fixed and known metric on the action space that determines a cost for switching between any pair of actions. The loss of the online learner has two components: the first is the usual loss of the selected actions, and the second is an additional loss due to switching between actions. Our main contribution giv...

Regret minimization is an effective technique for almost surely producing Nash equilibrium policies in coordination games in the strategic form. Decentralized POMDPs offer a realistic model for sequential coordination problems, but they yield doubly exponential sized games in the strategic form. Recently, counterfactual regret has offered a way to decompose total regret along a (extensive form)...

This paper investigates the complexity of the min-max and min-max regret versions of the min s-t cut and min cut problems. Even if the underlying problems are closely related and both polynomial, the complexity of their min-max and min-max regret versions, for a constant number of scenarios, is quite contrasted since they are respectively strongly NP hard and polynomial. However, for a non cons...

Apprehending the development of complex emotions is crucial to understand the development of decision-making. Regret and relief are complex counterfactual emotions, which can arise in private or in social contexts. The aims of the present study were (i) to uncover the development of regret and relief and (ii) to explore the development of a social form of regret and relief in a context of compe...

To examine the association between healthcare-related regrets and sleep difficulties among nurses and physicians, we surveyed 240 nurses and 220 physicians at the University Hospitals of Geneva. Regret intensity and regret coping were measured using validated scales. Sleep difficulties were measured using the Insomnia Severity Index (ISI), and an additional question assessed the frequency of sl...

We obtain minimax lower bounds on the regret for the classical two-armed bandit problem. We provide a finite-sample minimax version of the well-known log asymptotic lower bound of Lai and Robbins. The finite-time lower bound allows us to derive conditions for the amount of time necessary to make any significant gain over a random guessing strategy. These bounds depend on the class of possible d...