instruction:
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.
question:
This paper investigates stochastic and adversarial combinatorial multi-armed bandit problems. In the stochastic setting, we first derive problem-specific regret lower bounds, and analyze how these bounds scale with the dimension of the decision space. We then propose COMBUCB, algorithms that efficiently exploit the combinatorial structure of the problem, and derive finite-time upper bound on their regrets. These bounds improve over regret upper bounds of existing algorithms, and we show numerically thatCOMBUCB significantly outperforms any other algorithm. In the adversarial setting, we propose two simple algorithms, namely COMBEXP-1 and COMBEXP-2 for semi-bandit and bandit feedback, respectively. Their regrets have similar scaling as state-of-the-art algorithms, in spite of the simplicity of their implementation.
answer:
Stochastic and Adversarial Combinatorial Bandits


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Standard belief change assumes an underlying logic containing full classical propositional logic. However, there are good reasons for considering belief change in less expressive logics as well. In this paper we build on recent investigations by Delgrande on contraction for Horn logic. We show that the standard basic form of contraction, partial meet, is too strong in the Horn case. This result stands in contrast to Delgrande’s conjecture that orderly maxichoice is the appropriate form of contraction for Horn logic. We then define a more appropriate notion of basic contraction for the Horn case, influenced by the convexity property holding for full propositional logic and which we refer to as infra contraction. The main contribution of this work is a result which shows that the construction method for Horn contraction for belief sets based on our infra remainder sets corresponds exactly to Hansson’s classical kernel contraction for belief sets, when restricted to Horn logic. This result is obtained via a detour through contraction for belief bases. We prove that kernel contraction for belief bases produces precisely the same results as the belief base version of infra contraction. The use of belief bases to obtain this result provides evidence for the conjecture that Horn belief change is best viewed as a ‘hybrid’ version of belief set change and belief base change. One of the consequences of the link with base contraction is the provision of a representation result for Horn contraction for belief sets in which a version of the Core-retainment postulate features.
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On the Link between Partial Meet, Kernel, and Infra Contraction and its Application to Horn Logic


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Classification and clustering have been studied separately in machine learning and computer vision. Inspired by the recent success of deep learning models in solving various vision problems (e.g., object recognition, semantic segmentation) and the fact that humans serve as the gold standard in assessing clustering algorithms, here, we advocate for a unified treatment of the two problems and suggest that hierarchical frameworks that progressively build complex patterns on top of the simpler ones (e.g., convolutional neural networks) offer a promising solution. We do not dwell much on the learning mechanisms in these frameworks as they are still a matter of debate, with respect to biological constraints. Instead, we emphasize on the compositionality of the real world structures and objects. In particular, we show that CNNs, trained end to end using back propagation with noisy labels, are able to cluster data points belonging to several overlapping shapes, and do so much better than the state of the art algorithms. The main takeaway lesson from our study is that mechanisms of human vision, particularly the hierarchal organization of the visual ventral stream should be taken into account in clustering algorithms (e.g., for learning representations in an unsupervised manner or with minimum supervision) to reach human level clustering performance. This, by no means, suggests that other methods do not hold merits. For example, methods relying on pairwise affinities (e.g., spectral clustering) have been very successful in many cases but still fail in some cases (e.g., overlapping clusters).
answer:

A new look at clustering through the lens of deep convolutional neural networks