Performance guarantees for online learning algorithms typically take the form of regret bounds, which express that the cumulative loss overhead compared to the best expert in hindsight is small. In the common case of large but structured expert sets we typically wish to keep the regret especially small compared to simple experts, at the cost of modest additional overhead compared to more comple...

T paper introduces a method to measure regret theory, a popular theory of decision under uncertainty. Regret theory allows for violations of transitivity, and it may seem paradoxical to quantitatively measure an intransitive theory. We adopt the trade-off method and show that it is robust to violations of transitivity. Our method makes no assumptions about the shape of the functions reflecting ...

We consider the problem of online linear regression on arbitrary deterministic sequences when the ambient dimension d can be much larger than the number of time rounds T . We introduce the notion of sparsity regret bound, which is a deterministic online counterpart of recent risk bounds derived in the stochastic setting under a sparsity scenario. We prove such regret bounds for an online-learni...

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...

In (online) learning theory the concepts of sparsity, variance and curvature are well-understood and are routinely used to obtain refined regret and generalization bounds. In this paper we further our understanding of these concepts in the more challenging limited feedback scenario. We consider the adversarial multi-armed bandit and linear bandit settings and solve several open problems pertain...

We consider the problem of online linear regression on individual sequences. The goal in this paper is for the forecaster to output sequential predictions which are, after T time rounds, almost as good as the ones output by the best linear predictor in a given l-ball in R. We consider both the cases where the dimension d is small and large relative to the time horizon T . We first present regre...

VIKOR is one of the multiple criteria decision making (MCDM) models to determine the preference ranking from a set of alternatives in the presence of conflicting criteria. The justification of VIKOR is to use the concept of the compromise programming to determine the preference ranking by the results of the individual and group regrets. However, VIKOR has a critical problem in deriving the pref...

Regret is more than just an individual cognitive and emotional phenomenon, it can, should, be seen as social cultural well. Because of this, regret can tell us a lot, both about someone’s biography, the society culture that shape it. In this brief reflection, aim to look at phenomenon worthy sociological focus. We focus on three main ways in which understood object: part something culturally sh...