This paper provides an axiomatic model of decision making under uncertainty in which the decision maker is driven by anticipated ex-post regrets. Our model allows both regret aversion and likelihood judgement over states to coexist. Also, we characterize two special cases, minimax regret with multiple priors that generalizes Savage’s minimax regret, and a smooth model of regret aversion.

For convex games, connections between playing by no-regret algorithms and playing equilibrium strategies have previously been made for Φregret, a generalization of external regret [5]. In particular, Gordon et al. present a no-Φ-regret algorithm for several different classes of transformations Φ [4]. In this paper, we instantiate the algorithm for the class of linear transformations using a var...

INTRODUCTION Nearly all smokers in high-income Western countries report that they regret smoking (Fong, G. T., Hammond, D., Laux, F. L., Zanna, M. P., Cummings, M. K., Borland, R., & Ross, H. [2004]. The near-universal experience of regret among smokers in four countries: Findings from the International Tobacco Control Policy Evaluation Survey. Nicotine and Tobacco Research, 6, S341-S351. doi:1...

BACKGROUND Explicit consideration of anticipated regret is not part of the standard shared decision-making protocols. This pilot study aimed to compare decisions about a hypothetical surgery for breast cancer and examined whether regret is a consideration in treatment decisions. METHODS In this randomized experimental study, 184 healthy female volunteers were randomized to receive a standard ...

We consider a variant of the multiarmed bandit problem where jobs queue for service, and service rates of different servers may be unknown. We study algorithms that minimize queue-regret: the (expected) difference between the queue-lengths obtained by the algorithm, and those obtained by a “genie”-aided matching algorithm that knows exact service rates. A naive view of this problem would sugges...

This work deals with four classical prediction settings, namely full information, bandit, label efficient and bandit label efficient as well as four different notions of regret: pseudoregret, expected regret, high probability regret and tracking the best expert regret. We introduce a new forecaster, INF (Implicitly Normalized Forecaster) based on an arbitrary function ψ for which we propose a u...

We consider regret minimization in repeated games with non-convex loss functions. Minimizing the standard notion of regret is computationally intractable. Thus, we define a natural notion of regret which permits efficient optimization and generalizes offline guarantees for convergence to an approximate local optimum. We give gradient-based methods that achieve optimal regret, which in turn guar...

W model a dynamic purchase context in which a consumer is uncertain about the product’s valuation. The consumer has two purchase opportunities for the product: forward purchase in Period 1 or spot purchase in Period 2. Two forms of regret are considered: buyer’s regret over the money paid in excess of his valuation of the product when buying forward and hesitater’s regret for the lost opportuni...

When a good decision leads to a bad outcome, the experience of regret can bias subsequent choices: people are less likely to select the regret-producing alternative a second time, even when it is still objectively the best alternative (non-adaptive choice switching). The first study presented herein showed that nearly half of participants experiencing regret rejected a previous alternative they...

BACKGROUND Decision-making relies on both analytical and emotional thinking. Cognitive reasoning styles (e.g. maximizing and satisficing tendencies) heavily influence analytical processes, while affective processes are often dependent on regret. The relationship between regret and cognitive reasoning styles has not been well studied in physicians, and is the focus of this paper. METHODS A reg...