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• W2952908320 abstract "This paper analyzes the problem of Gaussian process (GP) bandits with deterministic observations. The analysis uses a branch and bound algorithm that is related to the UCB algorithm of (Srinivas et al, 2010). For GPs with Gaussian observation noise, with variance strictly greater than zero, Srinivas et al proved that the regret vanishes at the approximate rate of $O(1/sqrt{t})$, where t is the number of observations. To complement their result, we attack the deterministic case and attain a much faster exponential convergence rate. Under some regularity assumptions, we show that the regret decreases asymptotically according to $O(e^{-frac{tau t}{(ln t)^{d/4}}})$ with high probability. Here, d is the dimension of the search space and tau is a constant that depends on the behaviour of the objective function near its global maximum." @default.
• W2952908320 created "2019-06-27" @default.
• W2952908320 creator A5066732643 @default.
• W2952908320 creator A5082304130 @default.
• W2952908320 creator A5090351022 @default.
• W2952908320 date "2012-06-27" @default.
• W2952908320 modified "2023-09-27" @default.
• W2952908320 title "Exponential Regret Bounds for Gaussian Process Bandits with Deterministic Observations" @default.
• W2952908320 cites W1545211435 @default.
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• W2952908320 hasPublicationYear "2012" @default.
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