Proof connects Gittins indices to Bayesian upper confidence bounds for patient agents.
problem Connecting Gittins indices to Bayesian upper confidence bounds for patient agents.
method Proof using Gaussian multi-armed bandit problem with discount factor γ.
result Gittins index equals γ-quantile of posterior mean plus vanishing error term.
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 O ( T ln 2 T ) O(\sqrt{T \ln^2 T}) O ( T ln 2 T ) cumulative regret under squared exponential kernel. Two batch Bayesian optimization algorithms with regret guarantees.
problem Efficiently optimizing multiple objectives in batch feedback settings.
method Gaussian process upper confidence bound and Thompson sampling approaches.
result Frequentist regret guarantees and numerical results.
The estimation of probabilities of default (PDs) for low default portfolios by means of upper confidence bounds is a well established procedure in many financial institutions. However, there are often discussions within the institutions or between institutions and supervisors about which confidence level to use for the…
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.
Bayesian methods improve drug discovery experiment design.
problem Optimizing drug screening experiments in high-dimensional data.
method Bayesian inference and optimisation with upper confidence bound algorithms, Thompson sampling, and sparse tree search.
result Sparse tree search techniques outperform other methods in drug toxicity screening.
Bayesian bandit algorithms with approximate inference improve regret bounds in stochastic linear bandits.
problem Theoretical justification for Bayesian bandit algorithms with approximate inference in stochastic linear bandits.
method Proposed a theoretical framework to analyze approximate inference impact and conducted frequentist regret analysis on LinTS and LinBUCB.
result LinTS and LinBUCB preserve their original regret upper bounds with larger constant terms in approximate inference settings.
New bounds for Bayesian bandits show prior improves performance.
problem Improving regret bounds for Bayesian bandits.
method Upper confidence bound algorithm with finite-time logarithmic regret bounds.
result Derives O ( c Δ log n ) O(c_Δ\log n) O ( c Δ log n ) and O ( c h log 2 n ) O(c_h \log^2 n) O ( c h log 2 n ) upper bounds for Bayesian bandits. 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.
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.
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 1 / δ 1/δ 1/ δ with probability δ δ δ . EBUCB framework achieves optimal regret with bounded approximate inference error.
problem Theoretical gap between practical performance and theoretical justification of Bayesian bandit algorithms with approximate inference.
method Enhanced Bayesian Upper Confidence Bound (EBUCB) framework that accommodates bandit problems with approximate inference.
result EBUCB achieves optimal regret order O ( log T ) O(\log T) O ( log T ) under certain conditions on inference error. This paper improves Bayesian optimization by using pseudo-points to enhance model accuracy.
problem Expensive black-box optimization problems, especially in parameter tuning and experimental design.
method Generates pseudo-points to improve Gaussian process models in Bayesian optimization.
result Cumulative regret can be generally upper bounded using the proposed framework.
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.
A hybrid model for Bayesian optimization handles mixed variables using MCTS for categorical and GP for continuous.
problem Optimizing functions with mixed variable types (continuous, integer, categorical).
method Merges MCTS for categorical and GP for continuous variables, integrates UCTS search strategy, and dynamically selects kernels.
result Hybrid models outperform traditional methods in Bayesian optimization.
UCB exploration improves best arm identification in fixed-budget settings.
problem Best arm identification in fixed-budget scenarios.
method Adaptive allocations based on upper confidence bounds (UCBs) with prior information learning.
result Empirically and theoretically efficient for Bayesian BAI problem with improved performance.
Standard acquisition functions are sufficient for asynchronous Bayesian optimization.
problem Redundant and repeated queries in asynchronous Bayesian optimization.
method Conceptual analysis and theoretical guarantees of standard acquisitions.
result Standard acquisition functions achieve theoretical guarantees equivalent to Thompson sampling in asynchronous settings.
New algorithm minimizes Bayesian regret in offline linear bandits.
problem Minimizing Bayesian regret in offline linear bandits.
method Proposes a new algorithm that directly minimizes upper bounds on Bayesian regret using conic optimization.
result Upper bounds are tight and guarantee superior performance compared to LCB.
Bayesian sequence prediction is a simple technique for predicting future symbols sampled from an unknown measure on infinite sequences over a countable alphabet. While strong bounds on the expected cumulative error are known, there are only limited results on the distribution of this error. We prove tight high-probabil…
Bayes-UCBVI tackles reinforcement learning with a new upper confidence bound method.
problem Optimizing exploration in reinforcement learning without bonuses.
method Bayes-UCBVI uses a quantile of a Q-value function posterior as an upper confidence bound.
result Proves a regret bound of order O ~ ( H 3 S A T ) \widetilde{O}(\sqrt{H^3SAT}) O ( H 3 S A T ) for tabular reinforcement learning. Bayesian optimisation tackles uncertain inputs in noisy function evaluations.
problem Optimizing functions with uncertain query locations and noisy outcomes.
method Proposes a UCB algorithm for BO with uncertain inputs, using Gaussian process models.
result Theoretical and experimental results show the proposed algorithm outperforms conventional methods.
Upper and lower bounds on regret for noisy optimization of Brownian motion.
problem Optimizing a one-dimensional Brownian motion with noisy observations.
method Upper bound uses confidence bounds and Markov property; lower bound uses hypothesis testing reduction.
result Upper and lower bounds are tight up to a factor of O ( ( log T ) 1.5 ) O((\log T)^{1.5}) O (( log T ) 1.5 ) . BILBO optimizes bilevel problems without repeated lower-level optimizations.
problem Challenges in bilevel optimization, especially in noisy, constrained, and derivative-free settings.
method BILevel Bayesian Optimization (BILBO) that optimizes both levels simultaneously, using confidence-bounds and function query selection.
result Theoretical and empirical evidence of BILBO's effectiveness on various problems.
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.
The paper honors Lai's contributions to multi-armed bandits and establishes new regret bounds.
problem Improving regret bounds in multi-armed bandit problems.
method Establishes non-asymptotic regret bounds for upper confidence bound indices.
result New regret bounds match Lai-Robbins lower bound.
Bayesian optimisation improves with fully-Bayesian treatment of hyperparameters.
problem Overconfident model predictions in BO due to ignoring hyperparameter uncertainty.
method Investigate FBBO using three approximate inference schemes compared to maximum likelihood approach.
result FBBO using EI with an ARD kernel leads to best performance in noise-free setting.
This paper proposes a DGP approach with UCBs for point target tracking over WSNs.
problem Uncertainty quantification in distributed machine learning-based tracking over WSNs.
method Distributed Gaussian process (DGP) approach with upper confidence bounds (UCBs).
result UCBs provide 88% and 42% higher probability of encompassing true target states in X and Y coordinates, respectively.
OFVF uses Bayesian plausibility sets for robust exploration in reinforcement learning.
problem Exploration in reinforcement learning, especially in poorly understood states and actions.
method Bayesian approach with plausibility sets constructed based on sensible value functions.
result OFVF constructs tighter optimistic estimates for exploration, leading to robust policies.
New method uses random decompositions for high-dimensional Bayesian optimization.
problem Learning accurate decompositions for high-dimensional black-box functions.
method Data-independent random tree-based decomposition sampling.
result Random decomposition upper-confidence bound algorithm (RDUCB) yields significant empirical gains.
Bayesian optimisation's mean function choice affects convergence speed.
problem The choice of mean function in Bayesian optimisation impacts convergence speed.
method Empirical investigation of 8 mean functions on 10 synthetic and 2 real-world problems.
result Using a constant mean function equal to the worst observed quality value promotes faster convergence.
In the field of reinforcement learning there has been recent progress towards safety and high-confidence bounds on policy performance. However, to our knowledge, no practical methods exist for determining high-confidence policy performance bounds in the inverse reinforcement learning setting---where the true reward fun…
A new differentiable UCB algorithm for linear bandits learns adaptive confidence bounds.
problem Inability of UCB to strike optimal exploration-exploitation due to confidence bounds.
method Proposes a differentiable linear bandit algorithm and a gradient estimator for learning adaptive confidence bounds.
result Achieves a i l d e O ( β ^ d T ) ilde{\mathcal{O}}(\hatβ\sqrt{dT}) i l d e O ( β ^ d T ) upper bound of T T T -round regret. Unified framework for active learning problems using information theory.
problem Combining level set estimation and Bayesian optimization.
method Information-theoretic criterion and acquisition function.
result Unified framework achieves state-of-the-art performance.
A new stopping criterion for active learning based on deterministic generalization bounds.
problem Determining the optimal stopping point for active learning when data acquisition is costly.
method The proposed stopping criterion is based on the difference in expected generalization errors and hypothesis testing, derived from PAC-Bayesian theory.
result The proposed stopping criterion effectively stops active learning by combining an upper bound with a statistical test.
Proposes a method to handle missing inputs in Bayesian optimization.
problem Missing values in historical data and function evaluations.
method Impute missing values using probability distributions and develop a new acquisition function.
result Improves performance of Bayesian optimization by handling missing inputs effectively.
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 O ( T 1 / 4 ) O(T^{1/4}) O ( T 1/4 ) and O ( T 1 / 7 ) O(T^{1/7}) O ( T 1/7 ) corruptions with possibly infinite magnitude. Adapts Bayesian optimization for uncertain outcomes using stochastic sampling.
problem Optimizing with uncertain or stochastic outcomes in scientific and engineering problems.
method Proposes SSBO, a new framework that handles uncertainty and myopic decision making.
result SSBO techniques effectively optimize standard and applied problems.
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.
Bayesian model for energy-efficient EV navigation.
problem Limited battery capacity in electric vehicles.
method Bayesian modeling and online learning framework with exploration strategies.
result Established rigorous regret bounds for Thompson Sampling.
A new method optimizes material discovery by balancing exploration and exploitation.
problem Substantial experimental costs and lengthy development periods in material discovery.
method Threshold-Driven UCB-EI Bayesian Optimization (TDUE-BO) method.
result TDUE-BO significantly outperforms traditional BO methods in material discovery.
One-bit feedback suffices for a bandit problem's optimal strategy.
problem Optimal strategy for multi-armed bandit problem with limited feedback.
method Coding and decoding schemes for one-bit feedback to mimic full-reward feedback.
result Regret ratio approaches 1 with one-bit feedback.
Enhances RL with function approximation, improving regret bounds.
problem Improving exploration in reinforcement learning with function approximation.
method Prior-dependent Bayesian regret bound for PSRL with linear mixture MDPs, using value-targeted model learning and variance reduction.
result Established an upper bound of O ( d H 3 T log T ) {\mathcal{O}}(d\sqrt{H^3 T \log T}) O ( d H 3 T log T ) for PSRL. A new upper bound for variational inference improves the efficiency of Bayesian deep learning.
problem Improving variational inference in Bayesian deep learning.
method Presented a new upper bound (EUBO) for evidence, derived from KL-divergence and log marginal likelihood, and used SGD for optimization.
result The new upper bound (EUBO) is tighter than previous methods and outperforms state-of-the-art results in Bayesian neural networks.
Bayesian model for energy consumption helps electric vehicles navigate efficiently.
problem Limited battery capacity in electric vehicles makes energy efficient navigation challenging.
method Developed an online learning framework using Bayesian models and exploration strategies like Thompson Sampling.
result Established rigorous regret bounds for Thompson Sampling in both single-agent and multi-agent settings.
UCB-RS uses RS to improve UCB for online advertising.
problem Improving recommendation in online advertising.
method UCB-RS, combining UCB with recommendation system.
result UCB-RS outperforms other reinforcement learning methods in RecoGym.
New algorithm improves best arm identification in Bayesian settings.
problem Finding the arm with the highest mean in unknown distributions.
method Developed a variant of successive elimination algorithm.
result Achieved optimal performance in Bayesian setting with logarithmic gap.
WS-KDE provides robust confidence bounds for stochastic functions.
problem Optimizing time-consuming black-box functions with stochastic outputs.
method Wilson Score Kernel Density Estimation (WS-KDE) for Bayesian optimization.
result WS-KDE provides reliable confidence bounds for any stochastic function.
Paper bounds prediction error for misspecified Gaussian process models.
problem Guaranteeing model confidence for nonparametric Gaussian process regression.
method Derives an upper bound for mean square prediction error using pseudo-concave optimization.
result Upper bound for mean square prediction error of misspecified models.