Regret Bounds for Gaussian Process Bandit Problems

By Steffen Grünewälder, Jean-Yves Audibert, Manfred Opper, John Shawe-Taylor. 2010

101 citations recorded by the source corpus.

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Citations in the corpus

Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization (2016, background): “Gaussian processes have also been studied in the bandit setting using confidence bound acquisition functions (GP-UCB), with associated sublinear regret bounds (Srinivas et al., 2010; Grünewälder et al., 2010).”
Taking the Human Out of the Loop: A Review of Bayesian Optimization (2016, background): “See Section 4 of [64] for another introduction.”
Regret Analysis of Stochastic and Nonstochastic Multi-armed Bandit Problems (2012, neutral): “[2010] and Grünewälder et al. [2010], where it is assumed that the payoff functions are drawn from Gaussian processes.”
Entropy Search for Information-Efficient Global Optimization (2011, background): “But it is useful to pause at this point to contrast this deﬁnition with other concepts of optimization.”
Information-Theoretic Regret Bounds for Gaussian Process Optimization in the Bandit Setting (2009, background): “Gr¨unew¨alder et al. (2010) consider the pure exploration problem for GPs, where the goal is to ﬁnd the optimal decision over T rounds, rather than maximize cumulative reward (with no exploration/exploitation dilemma).”
Optimization as Estimation with Gaussian Processes in Bandit Settings (2015, background): “Other theoretical studies focus on simple regret [4, 11] or finite budgets [11].”
Convergence Rates of Efficient Global Optimization Algorithms (2011, background): “Vazquez and Bect (2010) and Grunewalder et al. (2010) consider a more Bayesian formulation of the problem, where the unknown function f is distributed according to the prior π , but this approach can prove restrictive: as we saw in Section 3.3, placing too much faith in the prior may exclude…”
Adaptive Submodularity: Theory and Applications in Active Learning and Stochastic Optimization (2010, background): “However, while recently performance guarantees where obtained in the no-regret setting (Grünewälder et al., 2010; Srinivas et al., 2010), we are not aware of any approximation guarantees for Bayesian Global Optimization.”
Contextual Gaussian Process Bandit Optimization (2011, background): “An alternative rule (in the context free setting) is the Expected Improvement algorithm [20], for which no bounds on the cumulative regret are known.”
On Kernelized Multi-armed Bandits (2017, background): “Other relevant work focuses on best arm identification problem in the Bayesian setup considering pure exploration (Grünewälder et al., 2010).”
Gaussian Process Optimization with Mutual Information (2013, background): “, 2011; Chen & Krause, 2013) or Bayesian optimization (Mockus, 1989; Grunewalder et al., 2010; Srinivas et al., 2012; de Freitas et al., 2012).”
Robust Gaussian Process-Based Global Optimization Using a Fully Bayesian Expected Improvement Criterion (2011, background): “Itiswell-known [6–12] that an optimal Bayesian optimization strategy, i.e. a strategy X ⋆N such that E 0 ( ε ( X ⋆N , ξ )) = r B , can be formally obtained by dynamic programming.”