TASK DEFINITION: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
PROBLEM: This manuscript develops the theory of agglomerative clustering with Bregman divergences. Geometric smoothing techniques are developed to deal with degenerate clusters. To allow for cluster models based on exponential families with overcomplete representations, Bregman divergences are developed for nondifferentiable convex functions.

SOLUTION: Agglomerative Bregman Clustering

PROBLEM: Abstract: We often encounter situations in which an experimenter wants to find, by sequential experimentation, xmax = arg maxx f(x), where f(x) is a (possibly unknown) function of a well controllable variable x. Taking inspiration from physics and engineering, we have designed a new method to address this problem. In this paper, we first introduce the method in continuous time, and then present two algorithms for use in sequential experiments. Through a series of simulation studies, we show that the method is effective for finding maxima of unknown functions by experimentation, even when the maximum of the functions drifts or when the signal to noise ratio is low.

SOLUTION: Thompson sampling with the online bootstrap

PROBLEM: Standard algorithms for finding the short­ est path in a graph require that the cost of a path be additive in edge costs, and typically assume that costs are determinis­ tic. We consider the problem of uncertain edge costs, with potential probabilistic de­ pendencies among the costs. Although these dependencies violate the standard dynamic­ programming decomposition, we identify a weaker stochastic consistency condition that justifies a generalized dynamic-programming approach based on stochastic dominance. We present a revised path-planning algorithm and prove that it produces optimal paths under time-dependent uncertain costs. We test the algorithm by applying it to a model of stochastic bus networks, and present em­ pirical performance results comparing it to some alternatives. Finally, we consider ex­ tensions of these concepts to a more general class of problems of heuristic search under uncertainty.

SOLUTION:
Path Planning under Time-Dependent Uncertainty