LIBO optimizes repeated bandit tasks without prior knowledge or regret.
problem Optimizing repeated bandit tasks without prior knowledge or regret.
method LIBO sequentially meta-learns a kernel to adapt to the environment and solve tasks with the latest estimate.
result LIBO achieves sublinear lifelong regret, converging to oracle performance as more tasks are solved.
Algorithm adapts to non-stationary rewards without prior knowledge.
problem Optimizing decisions in non-stationary environments without prior knowledge of changes.
method Optimization-based algorithm that restarts when non-stationarity is detected.
result Achieves tighter dynamic regret bound and is nearly minimax optimal.
Paper tackles non-stationary kernelized bandits with near-optimal algorithm.
problem Minimizing regret in a time-varying reward function.
method Near-optimal algorithm with a novel restarting phased elimination with random permutation (R-PERP).
result Regret upper bound matches the lower bound, making the algorithm near-optimal.
Unified analysis of kernel-based and locally adaptive bandit optimization methods.
problem Performance of bandit optimization algorithms in RKHS functions.
method Investigates the relationship between kernel regularity and algorithmic performance, characterizing spectral properties of various kernels.
result Unified framework for analyzing kernel-based and locally adaptive bandit algorithms, deriving explicit regret bounds.
Kernel ε ε ε -Greedy optimizes multi-armed bandits with covariates for sub-linear regret.
problem Optimizing multi-armed bandits with covariates in a reproducing kernel Hilbert space.
method Online weighted kernel ridge regression estimator for mean reward function estimation.
result Achieves sub-linear regret rate and optimal T \sqrt{T} T regret rate under margin condition. Bayesian optimization improved for biased data.
problem Adversarial bias in observations, especially hidden confounders.
method Reduction to dueling bandits, information-directed sampling (IDS).
result First efficient kernelized algorithm with regret guarantees.
A batched Gaussian Process bandit optimization method achieves near-optimal regret bounds.
problem Black-box optimization with limited function evaluations.
method Batched Gaussian Process bandit optimization algorithm.
result Achieves near-optimal cumulative regret bound of O ∗ ( T γ T ) O^\ast(\sqrt{Tγ_T}) O ∗ ( T γ T ) using O ( log log T ) O(\log\log T) O ( log log T ) batches. Algorithm optimizes collaborative learning among distributed clients using kernel-based bandits.
problem Optimizing personalized objectives in a distributed system with limited global information.
method Kernel-based bandit framework with surrogate Gaussian process models, sparse approximations.
result Order-optimal regret performance (up to polylogarithmic factors) and reduced communication overhead.
Study on adaptivity to kernel regularity in bandit problems.
problem Adaptation to unknown kernel regularity in continuum-armed bandit problems.
method Derive adaptivity lower bound and verify with minimax non-adaptive kernelised bandit algorithms.
result Impossibility of achieving optimal cumulative regret in different RKHSs with varying regularities.
This paper tackles open problem of tight bounds for KBs with Bernoulli rewards.
problem Open problem of tight bounds for Kernelized Bandits with Bernoulli rewards.
method Focus on Bernoulli model, not subgaussian noise, and optimize function in RKHS.
result Open problem remains unsolved in this context.
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.
Improved guarantees for misspecified kernelized bandit optimization.
problem Misspecification in kernelized bandit optimization.
method Localization and domain splitting techniques.
result Logarithmic or polylogarithmic growth of misspecification amplification.
Kernel-based bandit is an extensively studied black-box optimization problem, in which the objective function is assumed to live in a known reproducing kernel Hilbert space. While nearly optimal regret bounds (up to logarithmic factors) are established in the noisy setting, surprisingly, less is known about the noise-f…
Paper proposes no-regret algorithms for private GP bandit optimization.
problem Private Gaussian process bandit optimization.
method Combines uniform kernel approximator with random perturbations for differentially private GP bandit algorithms.
result Provable no-regret algorithms for stationary kernel functions in two DP settings.
Algorithm reduces regret in distributed kernel bandits with shared randomness.
problem Minimizing regret in collaborative function maximization.
method Uniform exploration at local agents and shared randomness with central server.
result Achieves optimal regret order with sublinear communication cost.
A new algorithm for differential privacy in kernelized contextual bandits reduces error rate.
problem Joint differential privacy in kernelized contextual bandits.
method Proposes a novel algorithm with a specific error rate and privacy parameter dependence.
result Achieves an error rate of $\mathcal{O}\left(\sqrt{\frac{γ_T}{T}} + \frac{γ_T}{T \varepsilon}
ight)$ after T T T queries. New algorithm optimizes noisy function evaluations with delayed feedback.
problem Optimizing unknown functions from noisy, delayed feedback.
method Kernel bandit problem with stochastically delayed feedback.
result Proposes an algorithm with improved regret bound for non-smooth kernels.
New method tackles confounded bandit problems with dual instrumental variables.
problem Confounded contextual bandit problems where noise affects both contexts and rewards.
method Dual instrumental variable regression applied to reproducing kernel Hilbert spaces.
result Near-optimal convergence rate and computationally efficient algorithms proved.
New algorithm reduces regret for kernelized bandits by adapting to specific problem instances.
problem Efficiently learning the optimizer of an unknown function in RKHS with noisy oracle.
method Instance-dependent regret analysis and a new minimax near-optimal algorithm.
result New algorithm achieves better performance on specific problem instances.
New algorithm optimizes resource allocation in non-stationary networks.
problem Optimal resource allocation in non-stationary RMABs is computationally hard.
method Sliding-Window Online Whittle (SW-Whittle) policy for non-stationary transition kernels.
result Sub-linear dynamic regret achieved with unknown variation budget.
Kernel method improves cooperative decision-making among agents.
problem Cooperative multi-agent decision making with contextual information.
method Proposed extsc{Coop-KernelUCB} algorithm for near-optimal per-agent regret.
result Near-optimal bounds on per-agent regret with efficient computation and communication.
Meta-KeL learns kernels from offline data to improve sequential decision-making.
problem Adaptive confidence sets for prediction functions in sequential decision-making tasks.
method Meta-KeL: meta-learning a kernel from offline data; structured sparsity estimator for unknown kernel combinations.
result Valid confidence sets that become as tight as those given the true unknown kernel with increasing offline data.
The paper refines and extends batched kernelized bandits, improving regret bounds and introducing a robust setting.
problem Optimizing black-box functions with noisy batches in Reproducing Kernel Hilbert Space.
method Refined and extended existing regret bounds, including adaptive batch sizes and robust optimization.
result Improved regret bounds for batched kernelized bandits, showing optimal number of batches and adaptive batch sizes.
Improved GP bandit algorithms for noiseless, varying noise, and RKHS norms.
problem Minimizing regret in Gaussian process bandits with unknown reward functions.
method New upper bound on maximum posterior variance, refined MVR and PE algorithms.
result Optimal regret bounds for noiseless, varying noise, and RKHS norms.
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.
A new algorithm tackles adversarial linear contextual bandits using kernelized loss functions.
problem Online learning in adversarial linear contextual bandits with flexible loss functions.
method Proposes a computationally efficient algorithm using an optimistically biased estimator for reproducing kernel Hilbert space loss functions.
result Achieves near-optimal regret guarantees under polynomial and exponential eigendecay assumptions.
Paper establishes lower bounds for non-stationary kernelized bandits.
problem Optimizing functions with noisy observations in non-stationary scenarios.
method Develops algorithm-independent lower bounds for time-varying functions under total variation constraints.
result First algorithm-independent lower bounds for time-varying kernelized bandits.
New algorithm uses GNNs to optimize rewards in graph-structured data.
problem Optimizing rewards in molecule design with graph-structured data.
method Embedding permutation invariance into GNNs and using GNTK for regret bounds.
result First GNN confidence bound and phased-elimination algorithm with sublinear regret.
New algorithms use neural networks to minimize regret in contextual bandits.
problem Minimizing regret in sequential decisions with side information.
method Proposes NN-UCB and NTK-UCB algorithms using neural networks.
result Proves sublinear regret bounds for contextual bandits.
MAXMINLCB optimizes unknown target functions with preference feedback using a Stackelberg game approach.
problem Optimizing unknown target functions with pairwise comparisons and human feedback.
method MAXMINLCB, a zero-sum Stackelberg game, balances exploration and exploitation.
result MAXMINLCB consistently outperforms existing algorithms with a rate-optimal regret guarantee.
The paper improves bounds on regret in Gaussian process bandits.
problem Sequential optimization of expensive, possibly non-convex functions with noisy feedback.
method Analyzes maximal information gain and decay rates of GP kernel eigenvalues to improve regret bounds.
result General bounds on maximal information gain and improved regret bounds for various settings, including Matérn kernels.
Robust algorithm optimizes corrupted Gaussian process bandits.
problem Sequential optimization of corrupted, expensive reward functions.
method Robust GP Phased Elimination (RGP-PE) algorithm.
result Algorithm balances robustness to corruptions with exploration and exploitation.
NeurWIN learns Whittle indices for restless bandits using deep reinforcement learning.
problem Finding optimal solutions for restless bandits with complex transition kernels.
method NeurWIN uses a neural network to learn Whittle indices, leveraging the Whittle indices' mathematical properties.
result NeurWIN outperforms other RL algorithms in solving three recently studied restless bandit problems.
VOGP efficiently identifies Pareto optimal solutions in black-box vector optimization.
problem Black-box vector optimization with incomplete order relations.
method VOGP is an adaptive elimination algorithm using Gaussian process bandits.
result VOGP achieves theoretical guarantees with sample complexity bounds.
Unified framework for multi-user bandits using Laplacian kernels.
problem Multi-user contextual bandits with graph-related users and non-linear rewards.
method Joint penalty combining graph smoothness and individual roughness in a unified RKHS.
result Unified multi-user RKHS and effective dimension for regret bounds.
New method tackles high-dimensional contextual bandits with flexible kernel models.
problem Maximizing rewards in decision-making scenarios with many features.
method Introduces stochastic assumptions and no-regret learning for Gaussian kernels.
result Achieves no-regret learning even with feature dimensions growing with samples.
In this paper, we consider the problem of sequentially optimizing a black-box function f f f based on noisy samples and bandit feedback. We assume that f f f is smooth in the sense of having a bounded norm in some reproducing kernel Hilbert space (RKHS), yielding a commonly-considered non-Bayesian form of Gaussian process …
New algorithms tackle RKHS bandits with reduced complexity and improved performance.
problem Adversarial and stochastic RKHS bandit problems with high computational complexity.
method Combining approximation theory with misspecified linear bandit methods.
result First general algorithm for adversarial RKHS bandit problem.
Investigates sequential problems on graph structures and large action spaces.
problem Sequential decision-making on graph structures and large action spaces.
method Spectral bandits, side observations, influence maximization, kernel bandits, polymatroid bandits, function optimization, infinitely many-arms bandits.
result Contributions to graph and structured bandits.
Optimal mixtures of generative models outperform individual models on image datasets.
problem Selecting the best single model from a group of trained generative models.
method Formulated a quadratic optimization problem and proposed the Mixture-UCB algorithm for efficient selection.
result Mixture of generative models achieves better evaluation scores than individual models on benchmark datasets.
New algorithm reduces neural net error in contextual bandits.
problem Neural contextual bandits with general activation functions.
method Proposed an efficient algorithm with sublinear regret bound.
result Demonstrated provably sublinear regret bound in finite regime.
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.
We study the regret minimization problem in the novel setting of generalized kernelized bandits (GKBs), where we optimize an unknown function f ∗ f^* f ∗ belonging to a reproducing kernel Hilbert space (RKHS) having access to samples generated by an exponential family (EF) reward model whose mean is a non-linear function $μ(…
Kernelized bandit algorithm tackles adaptive contextual bandits with single-index models.
problem Adaptive contextual bandits with single-index models and unknown link functions.
method Kernelized ε-greedy algorithm combining Stein-based index estimation and kernel ridge regression for reward functions.
result Unified framework for simultaneous learning and inference in single-index contextual bandits.
IDS algorithm optimizes sequential decisions in various monitoring settings.
problem Optimizing sequential decisions in complex monitoring scenarios.
method Information-directed sampling (IDS) algorithm for linear partial monitoring.
result IDS achieves nearly worst-case rate optimality in finite-action games.
Optimal simple regret bound for Gaussian Process bandits.
problem Sequential optimization of expensive-to-evaluate functions.
method Proved a bound on simple regret for pure exploration algorithms.
result Order optimal bound on simple regret for Gaussian Process bandits.
New algorithms estimate function levels with near-optimal efficiency.
problem Estimating points where an unknown function exceeds a given threshold.
method Relates to adaptive experimental design methods for linear bandits in RKHS.
result Proves nearly optimal sample complexity bounds for level set estimation.
Improved regret bounds for linear bandits with heavy-tailed rewards.
problem Stochastic linear bandits with heavy-tailed rewards.
method Elimination-based algorithm guided by experimental design.
result Regret bound of \(\tilde{\mathcal{O}}(d^\frac{1+3ε}{2(1+ε)} T^\frac{1}{1+ε})\) for \(ε\in (0,1)\).