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 bene\ufb01t from such a hint if the set of feasible actions is su\ufb03ciently round. Speci\ufb01cally, 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 \u2208 (2,3), the hint can be used to guarantee a regret of o(\\sqrt{T}). In contrast, we establish \u2126(\\sqrt{T}) lower bounds on regret when the set of feasible actions is a polyhedron.<\/p>\n","protected":false},"excerpt":{"rendered":"
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. 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