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We consider a linear stochastic bandit problem where the dimension $K$ of the unknown parameter $\theta$ is larger than the sampling budget $n$.
Restless bandits: Activity allocation in a changing world
P. Whittle · 1988
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Nonlinear programming
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Atomic decomposition by basis pursuit
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Restless bandits, partial conservation laws and indexability
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Online convex optimization in the bandit setting: gradient descent without a gradient
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The dantzig selector: statistical estimation when p is much larger than n
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S. Filippi, O. Cappé, A. Garivier, and C. Szepesvári · 2010
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On upper-confidence bound policies for non-stationary bandit problems
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Improved algorithms for linear stochastic bandits
Y. Abbasi-yadkori, D. Pal, and C. Szepesvari · 2011
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Minimax policies for combinatorial prediction games
J.Y. Audibert, S. Bubeck, and G. Lugosi · 2011
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Online-to-confidence-set conversions and application to sparse stochastic bandits
Y. Abbasi-yadkori, D. Pal, and C. Szepesvari · 2012
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