This research tests the general proposition that people are motivated to reduce future regret under escalation situations. This is supported by the findings that (a) escalation of commitment is stronger when the possibility of future regret about withdrawal is high than when this possibility is low (Studies 1a and 1b) and (b) escalation of commitment increases as the net anticipated regret abou...

Given a multi-armed bandit problem it may be desirable to achieve a smallerthan-usual worst-case regret for some special actions. I show that the price for such unbalanced worst-case regret guarantees is rather high. Specifically, if an algorithm enjoys a worst-case regret of B with respect to some action, then there must exist another action for which the worst-case regret is at least Ω(nK/B),...

We discuss a multiple-play multi-armed bandit (MAB) problem in which several arms are selected at each round. Recently, Thompson sampling (TS), a randomized algorithm with a Bayesian spirit, has attracted much attention for its empirically excellent performance, and it is revealed to have an optimal regret bound in the standard single-play MAB problem. In this paper, we propose the multiple-pla...

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...