We consider the sequential Bayesian optimization problem with bandit feedback, adopting a formulation that allows for the reward function to vary with time. We model the reward function using a Gaussian process whose evolution obeys a simple Markov model. We introduce two natural extensions of the classical Gaussian pr…
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48 results for “GP-UCB”
GP-UCB performs suboptimally under certain conditions, as shown by a new regret lower bound.
problem The suboptimality of GP-UCB under polynomial effective optimism.
method Analysis of effective optimism level and new regret lower bound.
result GP-UCB is not minimax optimal under polynomial growth of effective optimism.
GP-UCB resolves sublinear regret for kernelized bandits.
problem Minimizing regret in kernelized bandit problems.
method Using a new regularization technique for kernel ridge estimators, improving GP-UCB's sublinear regret rate.
result GP-UCB achieves nearly optimal sublinear regret for the Matérn kernel.
This paper improves Bayesian optimization methods with tighter regret bounds and practical solutions.
problem Improving Bayesian optimization methods with tighter regret bounds and practical solutions.
method The paper analyzes and compares different acquisition functions (GP-UCB, TS, PIMS) to achieve tighter Bayesian cumulative regret bounds and address practical issues.
result PIMS achieves the tighter BCR bound and avoids hyperparameter tuning, unlike GP-UCB and TS.
This paper improves GP-UCB by using a shifted exponential distribution for confidence parameters.
problem Theoretical confidence parameter in GP-UCB increases with iterations, leading to large values.
method Introduced IRGP-UCB, a randomized variant of GP-UCB using a shifted exponential distribution for confidence parameters.
result IRGP-UCB achieves sub-linear regret without increasing the confidence parameter.
ET-GP-UCB optimizes time-varying functions without knowing change rates.
problem Sequentially optimizing a time-varying objective function with unknown change rates.
method Event-triggered Bayesian optimization with adaptive resets based on probabilistic uniform error bounds.
result ET-GP-UCB outperforms other GP-UCB algorithms in synthetic and real-world data.
A new method optimizes robustness measures under input uncertainty using randomized Gaussian process upper confidence bound.
problem Optimizing robustness measures under input uncertainty.
method Randomized robustness measure GP-UCB (RRGP-UCB) that samples β from a chi-squared-based distribution.
result RRGP-UCB provides tight bounds on expected regret.
First private Bayesian optimization algorithm with provable performance.
problem Privacy-preserving Bayesian optimization in outsourced settings.
method Random projection-based transformation to preserve privacy and distances.
result Regret bound similar to non-private GP-UCB established for PO-GP-UCB.
We consider the problem of optimising functions in the reproducing kernel Hilbert space (RKHS) of a Matérn kernel with smoothness parameter over the domain under noisy bandit feedback. Our contribution, the -GP-UCB algorithm, is the first practical approach with guaranteed sublinear regret for all $ν>1…
In this paper, we analyze a generic algorithm scheme for sequential global optimization using Gaussian processes. The upper bounds we derive on the cumulative regret for this generic algorithm improve by an exponential factor the previously known bounds for algorithms like GP-UCB. We also introduce the novel Gaussian P…
Paper improves regret bounds for Gaussian process upper confidence bound in Bayesian optimization.
problem Minimizing regret in Gaussian process bandit optimization.
method Gaussian process upper confidence bound (GP-UCB) algorithm with refined analysis.
result Achieves cumulative regret under squared exponential kernel.
We consider a novel setting of zeroth order non-convex optimization, where in addition to querying the function value at a given point, we can also duel two points and get the point with the larger function value. We refer to this setting as optimization with dueling-choice bandits since both direct queries and duels a…
Bayesian Optimisation with Unknown Hyperparameters: Regret Bounds Logarithmically Closer to Optimalstat.ML
New algorithm reduces regret bounds for Bayesian optimization with unknown hyperparameters.
problem Optimizing black-box functions with unknown hyperparameters, especially length scale.
method Length Scale Balancing (LB) - aggregating multiple surrogate models with varying length scales.
result LB achieves a regret bound only logaritically away from the oracle algorithm.
In this paper, we consider the problem of stochastic optimization under a bandit feedback model. We generalize the GP-UCB algorithm [Srinivas and al., 2012] to arbitrary kernels and search spaces. To do so, we use a notion of localized chaining to control the supremum of a Gaussian process, and provide a novel optimiza…
Improved Bayesian optimisation method using randomised Gaussian process UCB.
problem Improving performance in Bayesian optimisation.
method Developed a modified Gaussian process upper confidence bound (GP-UCB) acquisition function.
result The method achieves better performance than GP-UCB in various problems.
BONSAI optimizes parameters while respecting a default configuration, reducing unnecessary changes.
problem Standard BO pushes weakly relevant parameters to the boundary, making it hard to distinguish between important and spurious changes.
method BONSAI is a default-aware BO policy that prunes low-impact deviations from a default configuration while controlling acquisition value loss.
result BONSAI matches the GP-UCB regret rate while recovering the minimal- solution, reducing the number of non-default parameters in recommended configurations.
Recently, there has been rising interest in Bayesian optimization -- the optimization of an unknown function with assumptions usually expressed by a Gaussian Process (GP) prior. We study an optimization strategy that directly uses an estimate of the argmax of the function. This strategy offers both practical and theore…
Proposes PE-GP-UCB for time-varying Bayesian optimisation.
problem Time-varying Gaussian process bandits with unknown prior.
method PE-GP-UCB algorithm, relying on consistency of function values with priors.
result Regret bound provided for the proposed algorithm.
We tackle the problem of online reward maximisation over a large finite set of actions described by their contexts. We focus on the case when the number of actions is too big to sample all of them even once. However we assume that we have access to the similarities between actions' contexts and that the expected reward…
In many scientific and engineering applications, we are tasked with the maximisation of an expensive to evaluate black box function . Traditional settings for this problem assume just the availability of this single function. However, in many cases, cheap approximations to may be obtainable. For example, the exp…
Safe Gaussian Process Bandit Optimization with sub-linear regret bounds.
problem Sequential decision-making under uncertainty and safety constraints.
method Developed SGP-UCB, a safe variant of GP-UCB with modifications to respect safety constraints.
result First sub-linear regret bounds for safe Gaussian Process Bandit Optimization.
In this paper, we consider the challenge of maximizing an unknown function f for which evaluations are noisy and are acquired with high cost. An iterative procedure uses the previous measures to actively select the next estimation of f which is predicted to be the most useful. We focus on the case where the function ca…
This paper analyzes regret bounds for Gaussian process Thompson sampling.
problem Analyzing the performance of Gaussian process Thompson sampling (GP-TS) in Bayesian optimization.
method The paper derives several regret bounds for GP-TS, including a lower bound, upper bounds on the second moment of cumulative regret, expected lenient regret, and improved cumulative regret.
result The paper provides improved regret upper bounds for GP-TS, showing that it suffers from a polynomial dependence on with probability .
New algorithms for optimizing functions with noisy feedback, even when the model is misspecified.
problem Optimizing a black-box function with noisy bandit feedback, especially when the model is misspecified.
method Developed two algorithms based on Gaussian process methods: EC-GP-UCB and Phased GP Uncertainty Sampling.
result Achieved optimal dependence on misspecification error without prior knowledge, and effective in stochastic contextual settings.
Ada-BKB: Scalable Gaussian Process Optimization on Continuous Domains by Adaptive Discretizationcs.LG
Ada-BKB optimizes black-box functions on continuous domains with adaptive discretization.
problem Optimizing functions with continuous domains using Gaussian process optimization.
method Adaptive discretization of the function domain to avoid non-convex optimization costs.
result Ada-BKB algorithm runs in , significantly faster than existing methods.
Post-ADC inference corrects bias in statistical inference after active data collection.
problem Bias in inference after active data collection.
method Post-ADC inference framework that corrects bias from both ADC process and data-driven target construction.
result Valid inference for data collected by SMBO methods like GP-UCB and TPE.
No-regret optimization for time-varying functions using uncertainty injection.
problem Optimizing time-varying functions with no-regret in bandit feedback.
method W-SparQ-GP-UCB, incorporating uncertainty injection and additional queries.
result Achieves no-regret with a vanishing number of additional queries per iteration.
Unified proof for various bandit algorithms with logarithmic regret.
problem Achieving logarithmic regret in stochastic bandit algorithms.
method Minimal high-probability concentration condition and two deterministic lemmas.
result Unified proofs for classical and contemporary bandit algorithms.
Safe Bayesian Optimization algorithms are improved to ensure safety in real-world applications.
problem Ensuring safety in Bayesian Optimization algorithms for real-world applications.
method Investigated and improved three safety-related issues of SafeOpt-type algorithms: frequentist uncertainty bounds, RKHS norm assumptions, and discrete search spaces.
result Introduced Real-{eta}-SafeOpt, Lipschitz-only Safe Bayesian Optimization (LoSBO), and Lipschitz-only GP-UCB (LoS-GP-UCB) algorithms that retain safety guarantees and superior performance.
Bayesian optimization usually assumes that a Bayesian prior is given. However, the strong theoretical guarantees in Bayesian optimization are often regrettably compromised in practice because of unknown parameters in the prior. In this paper, we adopt a variant of empirical Bayes and show that, by estimating the Gaussi…
New algorithm optimizes Hölder smooth functions in RKHS with tighter regret bounds.
problem Optimizing Hölder smooth functions in RKHS with bounded norm.
method Proposes a new algorithm ( exttt{LP-GP-UCB}) using Local Polynomial (LP) estimators and multi-scale UCB.
result Derives high probability bounds on simple and cumulative regret, matching optimal performance for SE kernel and uniformly tighter bounds for Matérn kernels.
New algorithm robust to outliers in Bayesian Optimization.
problem Vulnerability of Bayesian Optimization to extreme outliers.
method Introduces a new adversary with a frequency-bounded corruption budget and derives RCGP-UCB algorithm.
result Achieves sublinear regret in the presence of up to and corruptions with possibly infinite magnitude.
Research aims to improve confidence intervals for RKHS elements in online learning.
problem Improper confidence intervals lead to suboptimal regret bounds in kernel-based bandit and reinforcement learning.
method Formalizes the open problem of online confidence intervals in RKHS and reviews existing results.
result Identifies the online nature of observation points as the main challenge for tight confidence intervals.
Can one parallelize complex exploration exploitation tradeoffs? As an example, consider the problem of optimal high-throughput experimental design, where we wish to sequentially design batches of experiments in order to simultaneously learn a surrogate function mapping stimulus to response and identify the maximum of t…
Improves Bayesian optimization using Gaussian process Thompson sampling.
problem Global optimization of Gaussian process posterior samples.
method Carefully selects starting points for gradient-based multi-start optimizers, identifies all local optima via univariate global rootfinding, and optimizes the posterior sample.
result Dramatic improvements in overall performance of Bayesian optimization.
Improved BO algorithms reduce prediction error under Gaussian noise.
problem Reducing prediction error in Bayesian optimization with Gaussian noise.
method Established new prediction error bounds for Gaussian process under frequentist setting.
result Proved improved convergence rates of cumulative regret for GP-UCB and GP-TS.
Study lenient regret and good-action identification in Gaussian process bandits.
problem Optimizing function values above a certain threshold in Gaussian process bandits.
method Study lenient regret notions and introduce algorithms for finding good actions.
result Upper and lower bounds on lenient regret for GP-UCB and elimination algorithms.
A Domain-Shrinking based Bayesian Optimization Algorithm with Order-Optimal Regret Performancestat.ML
Bayesian optimization algorithm reduces regret with efficient region pruning.
problem Sequential optimization of unknown functions in high-dimensional spaces.
method Gaussian process-based, domain shrinking through tree-based region pruning.
result Order-optimal regret performance with reduced computational complexity.
New algorithm optimizes noisy, potentially corrupted functions.
problem Optimizing unknown functions with noisy bandit feedback, especially when evaluations are corrupted.
method Fast-Slow GP-UCB algorithm, combining robust and non-robust evaluations, enlarged confidence bounds.
result Theoretical analysis upper bounds cumulative regret, showing dependencies on corruption level and kernel.
Inexact acquisition solutions in BO lead to sublinear cumulative regret.
problem Inexact maximization of acquisition functions in Bayesian optimization.
method Define inaccuracy measure, establish cumulative regret bounds for GP-UCB and GP-TS.
result Inexact BO algorithms can achieve sublinear cumulative regret under appropriate inaccuracy conditions.
How can we efficiently gather information to optimize an unknown function, when presented with multiple, mutually dependent information sources with different costs? For example, when optimizing a robotic system, intelligently trading off computer simulations and real robot testings can lead to significant savings. Exi…
Bayesian optimization is a sample-efficient method for finding a global optimum of an expensive-to-evaluate black-box function. A global solution is found by accumulating a pair of query point and its function value, repeating these two procedures: (i) modeling a surrogate function; (ii) maximizing an acquisition funct…
New tighter confidence bounds for sequential kernel regression.
problem Quantifying uncertainty in sequential learning algorithms.
method Martingale tail inequalities and conic programming.
result New confidence bounds are tighter than existing ones.
Enhanced Gaussian process models accelerate optimization and posterior approximation.
problem Improving the accuracy and speed of Gaussian process models for optimization and inference.
method Introduces a random exploration step to classical GP-UCB algorithms, facilitating faster convergence.
result New algorithms achieve nearly optimal convergence rates and provide bounds for Hellinger distance.
New algorithm reduces online hyperparameter optimization costs.
problem High cost of evaluating validation examples in online HPO.
method Modeling online HPO as a time-varying Bayesian optimization problem, proposing a costly feedback setting.
result Cost-efficient GP-UCB algorithm reaches human expert-level performance.
We consider black box optimization of an unknown function in the nonparametric Gaussian process setting when the noise in the observed function values can be heavy tailed. This is in contrast to existing literature that typically assumes sub-Gaussian noise distributions for queries. Under the assumption that the unknow…
Bayesian optimization (BO) is a powerful paradigm for derivative-free global optimization of a black-box objective function (BOF) that is expensive to evaluate. However, the overhead of BO can still be prohibitive for problems with highly expensive function evaluations. In this paper, we investigate how to reduce the r…
Monotonicity helps in safely optimizing unknown functions.
problem Sequentially maximizing an unknown function with safety constraints.
method Gaussian process with monotonicity assumption, inspired by GP-UCB and SafeOpt.
result The proposed M-SafeUCB algorithm achieves theoretical guarantees and safety.