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|a Dekel, Ofer
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|a Massachusetts Institute of Technology. Operations Research Center
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|a Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
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|a Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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|a Flajolet, Arthur
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|a Haghtalab, Nika
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|a Jaillet, Patrick
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|a Online learning with a hint
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|c 2021-11-08T15:22:31Z.
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|z Get fulltext
|u https://hdl.handle.net/1721.1/137673.2
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|a © 2017 Neural information processing systems foundation. All rights reserved. We study a variant of online linear optimization where the player receives a hint about the loss function at the beginning of each round. The hint is given in the form of a vector that is weakly correlated with the loss vector on that round. We show that the player can benefit from such a hint if the set of feasible actions is sufficiently round. Specifically, if the set is strongly convex, the hint can be used to guarantee a regret of O(log(T)), and if the set is q-uniformly convex for q ∈ (2, 3), the hint can be used to guarantee a regret of o(√T). In contrast, we establish Ω(VT) lower bounds on regret when the set of feasible actions is a polyhedron.
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|a Office of Naval Research (Grant N00014-15-1-2083)
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