Tractable Instances of Bilinear Maximization: Implementing LinUCB on Ellipsoids
NeutralArtificial Intelligence
The publication titled 'Tractable Instances of Bilinear Maximization: Implementing LinUCB on Ellipsoids' introduces two novel algorithms that efficiently solve the maximization of a bilinear function over a convex set and an ellipsoid. This problem is crucial in the context of linear bandits, where learners must optimize their strategies at each time step. The study highlights that for certain convex sets, such as ℓ_p balls with p>2, no efficient algorithms exist unless P=NP, indicating the complexity of the problem. However, the new algorithms provide a breakthrough by enabling efficient solutions when the convex set is a centered ellipsoid. This advancement is particularly important as it represents the first known method to implement optimistic algorithms for linear bandits in high dimensions, which could have significant implications for the development of more effective machine learning strategies.
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