In this paper, it is shown, for the first time, that centralized performance is achievable in decentralized learning without sharing the local datasets. Specifically, when clients adopt an empirical risk minimization with relative-entropy regularization (ERM-RER) learning framework and a forward-backward communication between clients is established, it suffices to share the locally obtained Gibbs measures to achieve the same performance as that of a centralized ERM-RER with access to all the datasets. The core idea is that the Gibbs measure produced by client~$k$ is used, as reference measure, by client~$k+1$. This effectively establishes a principled way to encode prior information through a reference measure. In particular, achieving centralized performance in the decentralized setting requires a specific scaling of the regularization factors with the local sample sizes. Overall, this result opens the door to novel decentralized learning paradigms that shift the collaboration strategy from sharing data to sharing the local inductive bias via the reference measures over the set of models.

You can now buy a humanoid robot housekeeper for less than the price of a second-hand car. But before splashing out, there's something you need to know Science fiction is strewn with humanoid robots, from bad-tempered Bender in to cunning Ava in . And it has long seemed like that's the natural home for such robots - on the screen and in books. The idea of a walking, talking, functioning robot with two arms and two legs has appeared to be a distant dream. Last year, machines ran, boxed and even played football at China's World Humanoid Robot Games, albeit sometimes falling over in the process . Meanwhile, companies have been readying their own range of humanoids that promise to do something a bit more useful: help around the house .

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Unlike AC, DAC can dynamically adjust the algorithm's configuration during

Often in machine learning, data are collected as a combination of multiple conditions, e.g., the voice recordings of multiple persons, each labeled with an ID.

Neural Information Processing Systems http://nips.cc/

Relevant to this paper are examinations of the computational power of neural networks after training, i.e., the training process is not taken into account but instead the computational power of an optimally trained network is studied. Starting already in the nineties, the expressive power of feed-forward neural networks (FNNs) has been related to Boolean threshold circuits, see, e.g., [Maass et al., 1991, Siegelmann and Sontag, 1995,

The authors contributed equally to this work.