The multi-objective multi-armed bandit (MOMAB) problem is a sequential decision process with stochastic rewards. Each arm generates a vector of rewards instead of a single scalar reward. Moreover, these multiple rewards might be conflicting. The MOMAB-problem has a set of Pareto optimal arms and an agent’s goal is not only to find that set but also to play evenly or fairly the arms in that set....

Consider the problem of learning a parametric distribution from observations. A frequentist approach to learning considers parameters to be fixed, and uses the data learn those parameters as accurately as possible. For example, consider the problem of learning Bernoulli distribution’s parameter ( a random variable is distributed as Bernoulli(μ) is 1 with probability μ and 0 with probability 1 −...

Kurt Z. Long, Jose Ignacio Santos, Jorge L. Rosado, Catalina Lopez-Saucedo, Rocio Thompson-Bonilla, Maricela Abonce, Herbert L. DuPont, Ellen Hertzmark, and Teresa Estrada-Garcia Department of Nutrition and Department of Epidemiology, Harvard School of Public Health, Boston, Massachusetts, and University of Texas Medical School and School of Public Health, Houston; Hospital Infantil de Mexico F...

Although the word “dog” and an unambiguous barking sound may point to the same concept DOG, verbal labels and nonverbal cues appear to activate conceptual information in systematically different ways (Lupyan & Thompson-Schill, 2012). Here we investigate these differences in more detail. We replicate the finding that labels activate a more prototypical representation than do sounds, and find tha...

Thompson sampling has impressive empirical performance for many multi-armed bandit problems. But current algorithms for Thompson sampling only work for the case of conjugate priors since these algorithms require to infer the posterior, which is often computationally intractable when the prior is not conjugate. In this paper, we propose a novel algorithm for Thompson sampling which only requires...

Thompson C, Thompson S, Smith R. Prevalence of seasonal affective disorder in primary care; a comparison of the seasonal health questionnaire and the seasonal pattern assessment questionnaire. J Affect Disord 2004;78:219–26. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

An example was given in the textbook All of Statistics (Wasserman, 2004, pages 186-188) for arguing that, in the problems with a great many parameters Bayesian inferences are weak, because they rely heavily on the likelihood function that captures information of only a tiny fraction of the total parameters. Alternatively he suggested non-Bayesian Horwitz-Thompson estimator, which cannot be obta...

Much of the recent literature on bandit learning focuses on algorithms that aim to converge on an optimal action. One shortcoming is that this orientation does not account for time sensitivity, which can play a crucial role when learning an optimal action requires much more information than near-optimal ones. Indeed, popular approaches such as upper-confidence-bound methods and Thompson samplin...