The regret bound of an optimization algorithms is one of the basic criteria for evaluating the performance of the given algorithm. By inspecting the differences between the regret bounds of traditional algorithms and adaptive one, we provide a guide for choosing an optimizer with respect to the given data set and the loss function. For analysis, we assume that the loss function is convex and it...

We consider the online setting of optimizing an unknown function, sampled from a Gaussian Proccess, over a given bounded decision set so that that our cumulative regret is low. Our analysis of an upper confidence algorithm provides sublinear regret bounds for popular classes of kernels by exploiting a surprising connection to optimal experimental design– in particular, our rates do no explicitl...

Social media users who post bullying related tweets may later experience regret, potentially causing them to delete their posts. In this paper, we construct a corpus of bullying tweets and periodically check the existence of each tweet in order to infer if and when it becomes deleted. We then conduct exploratory analysis in order to isolate factors associated with deleted posts. Finally, we pro...

A model is considered where firms internalize the regret costs that consumers experience when they see an unexpected price change. Regret costs are assumed to be increasing in the size of price changes and this can explain why the size of price increases is less sensitive to inflation than in models with fixed costs of changing prices. The latter predict unrealistically large responses of price...

Background: Pancreatic adenocarcinoma is uniformly fatal without operative intervention. Resection can prolong survival in some patients; however, it is associated with significant morbidity and mortality. Regret theory serves as a novel framework linking both rationality and intuition to determine the optimal course for physicians facing difficult decisions related to treatment. Methods: We us...

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We explore the construction of nonsubjective prior distributions in Bayesian statistics via a posterior predictive relative entropy regret criterion. We carry out a minimax analysis based on a derived asymptotic predictive loss function and show that this approach to prior construction has a number of attractive features. The approach here differs from previous work that uses either prior or po...

Multi-Criteria Decision Analysis (MCDA) is well-equipped to deal with conflicting objectives when evaluating strategic options. Scenario Planning provides a framework for confronting uncertainty which MCDA lacks. Integration of these methods offers various advantages, yet its effective application in evaluating strategic options would benefit from scenarios that reflect a larger number of wide-...

We consider a new class of online classification problems motivated by Internet recommendation and forecasting applications in which the learner receives advice sequentially over time from experts who may be adversarial or genuine. We show that, for this set of problems, the use of a market trading metaphor is useful in constructing a learning algorithm. We illustrate this by considering the co...