5,397 research outputs found
Distributed Exploration in Multi-Armed Bandits
We study exploration in Multi-Armed Bandits in a setting where players
collaborate in order to identify an -optimal arm. Our motivation
comes from recent employment of bandit algorithms in computationally intensive,
large-scale applications. Our results demonstrate a non-trivial tradeoff
between the number of arm pulls required by each of the players, and the amount
of communication between them. In particular, our main result shows that by
allowing the players to communicate only once, they are able to learn
times faster than a single player. That is, distributing learning to
players gives rise to a factor parallel speed-up. We complement
this result with a lower bound showing this is in general the best possible. On
the other extreme, we present an algorithm that achieves the ideal factor
speed-up in learning performance, with communication only logarithmic in
An Oracle Inequality for Quasi-Bayesian Non-Negative Matrix Factorization
The aim of this paper is to provide some theoretical understanding of
quasi-Bayesian aggregation methods non-negative matrix factorization. We derive
an oracle inequality for an aggregated estimator. This result holds for a very
general class of prior distributions and shows how the prior affects the rate
of convergence.Comment: This is the corrected version of the published paper P. Alquier, B.
Guedj, An Oracle Inequality for Quasi-Bayesian Non-negative Matrix
Factorization, Mathematical Methods of Statistics, 2017, vol. 26, no. 1, pp.
55-67. Since then Arnak Dalalyan (ENSAE) found a mistake in the proofs. We
fixed the mistake at the price of a slightly different logarithmic term in
the boun
A PAC-Bayesian Analysis of Graph Clustering and Pairwise Clustering
We formulate weighted graph clustering as a prediction problem: given a
subset of edge weights we analyze the ability of graph clustering to predict
the remaining edge weights. This formulation enables practical and theoretical
comparison of different approaches to graph clustering as well as comparison of
graph clustering with other possible ways to model the graph. We adapt the
PAC-Bayesian analysis of co-clustering (Seldin and Tishby, 2008; Seldin, 2009)
to derive a PAC-Bayesian generalization bound for graph clustering. The bound
shows that graph clustering should optimize a trade-off between empirical data
fit and the mutual information that clusters preserve on the graph nodes. A
similar trade-off derived from information-theoretic considerations was already
shown to produce state-of-the-art results in practice (Slonim et al., 2005;
Yom-Tov and Slonim, 2009). This paper supports the empirical evidence by
providing a better theoretical foundation, suggesting formal generalization
guarantees, and offering a more accurate way to deal with finite sample issues.
We derive a bound minimization algorithm and show that it provides good results
in real-life problems and that the derived PAC-Bayesian bound is reasonably
tight
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