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.

Input: Consider Input: Common statistical practice has shown that the full power of Bayesian methods is not realized until hierarchical priors are used, as these allow for greater "robustness" and the ability to "share statistical strength." Yet it is an ongoing challenge to provide a learning-theoretically sound formalism of such notions that: offers practical guidance concerning when and how best to utilize hierarchical models; provides insights into what makes for a good hierarchical prior; and, when the form of the prior has been chosen, can guide the choice of hyperparameter settings. We present a set of analytical tools for understanding hierarchical priors in both the online and batch learning settings. We provide regret bounds under log-loss, which show how certain hierarchical models compare, in retrospect, to the best single model in the model class. We also show how to convert a Bayesian log-loss regret bound into a Bayesian risk bound for any bounded loss, a result which may be of independent interest. Risk and regret bounds for Student's t and hierarchical Gaussian priors allow us to formalize the concepts of "robustness" and "sharing statistical strength." Priors for feature selection are investigated as well. Our results suggest that the learning-theoretic benefits of using hierarchical priors can often come at little cost on practical problems.

Output: Risk and Regret of Hierarchical Bayesian Learners

Input: Consider Input: We explore deep reinforcement learning methods for multi-agent domains. We begin by analyzing the difficulty of traditional algorithms in the multi-agent case: Q-learning is challenged by an inherent non-stationarity of the environment, while policy gradient suffers from a variance that increases as the number of agents grows. We then present an adaptation of actor-critic methods that considers action policies of other agents and is able to successfully learn policies that require complex multiagent coordination. Additionally, we introduce a training regimen utilizing an ensemble of policies for each agent that leads to more robust multi-agent policies. We show the strength of our approach compared to existing methods in cooperative as well as competitive scenarios, where agent populations are able to discover various physical and informational coordination strategies.

Output: Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environments

Input: Consider Input: Information fusion is an advanced research area which can assist decision makers in enhancing their decisions. This paper aims at designing a new multi-layer framework that can support the process of performing decisions from the obtained beliefs using information fusion. Since it is not an easy task to cross the gap between computed beliefs of certain hypothesis and decisions, the proposed framework consists of the following layers in order to provide a suitable architecture (ordered bottom up): 1. A layer for combination of basic belief assignments using an information fusion approach. Such approach exploits Dezert-Smarandache Theory, DSmT, and proportional conflict redistribution to provide more realistic final beliefs. 2. A layer for computation of pignistic probability of the underlying propositions from the corresponding final beliefs. 3. A layer for performing probabilistic reasoning using a Bayesian network that can obtain the probable reason of a proposition from its pignistic probability. 4. Ranking the system decisions is ultimately used to support decision making. A case study has been accomplished at various operational conditions in order to prove the concept, in addition it pointed out that: 1. The use of DSmT for information fusion yields not only more realistic beliefs but also reliable pignistic probabilities for the underlying propositions. 2. Exploiting the pignistic probability for the integration of the information fusion with the Bayesian network provides probabilistic inference and enable decision making on the basis of both belief based probabilities for the underlying propositions and Bayesian based probabilities for the corresponding reasons. Vol. 8, No. 28, July 2013, 1237-1250
Output: Design of a Framework to Facilitate Decisions Using Information Fusion