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.
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.
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.
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.
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. 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.
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. 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.
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.
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.
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.
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.
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.
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.
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.
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.
New method clusters items with bandit feedback without parametric assumptions.
problem Clustering with noisy observations from unknown distributions.
method Kernel-based approach to nonparametric clustering with bandit feedback.
result Adaptive algorithm with theoretical guarantees for unknown signal-to-noise ratio.
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.
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.
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.
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.
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.
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. 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 algorithm for differential private kernel bandits with improved regret bounds.
problem Contextual bandits with differential privacy constraints.
method Proposes a private kernel-ridge regression estimator using random projections.
result Achieves state-of-the-art cumulative regret bounds in both joint and local models of differential privacy.
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.
We consider the problem of optimising functions in the reproducing kernel Hilbert space (RKHS) of a Matérn kernel with smoothness parameter ν ν ν over the domain [ 0 , 1 ] d [0,1]^d [ 0 , 1 ] d under noisy bandit feedback. Our contribution, the π π π -GP-UCB algorithm, is the first practical approach with guaranteed sublinear regret for all $ν>1…
NK bandits improve performance on nonlinear tasks.
problem Improving performance on nonlinear sequential decision tasks.
method Proposed NK bandits using neural kernels to guide policies.
result NK bandits achieve state-of-the-art performance.
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.
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.
Study pure exploration in high-dimensional feature spaces using adaptive embeddings.
problem Overcoming the curse of dimensionality in pure exploration bandits.
method Adaptive embedding of feature representations into lower-dimensional spaces, carefully dealing with model misspecification.
result Sample complexity guarantees that depend on the effective dimension of feature spaces in kernel or neural representations.
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.
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.
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.
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.
Eluder dimension and information gain are equivalent for reproducing kernel Hilbert spaces.
problem Complexity measures in bandit and reinforcement learning.
method Equivalence of eluder dimension and information gain for reproducing kernel Hilbert spaces.
result Eluder dimension and information gain are equivalent for reproducing kernel Hilbert spaces.
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 consider online learning for minimizing regret in unknown, episodic Markov decision processes (MDPs) with continuous states and actions. We develop variants of the UCRL and posterior sampling algorithms that employ nonparametric Gaussian process priors to generalize across the state and action spaces. When the trans…
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.
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 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.
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(…
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.
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…
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.
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.
Explearn learns to explain predictions using Gaussian Processes.
problem Learning to explain predictions effectively.
method Gaussian Processes-based contextual bandits.
result Guaranteed convergence with high probability.