Kernel Single-Index Bandits: Estimation, Inference, and Learning

• URL: http://arxiv.org/abs/2603.18938v1
• Date: Thu, 19 Mar 2026 14:15:16 GMT
• Title: Kernel Single-Index Bandits: Estimation, Inference, and Learning
• Abstract summary: We study contextual bandits with finitely many actions in which the reward of each arm follows a single-index model.<n>We propose a kernelized $varepsilon$-greedy algorithm that combines Stein-based estimation of index parameters with inverse-propensity-weighted ridge regression.
• Score: 3.1109381260263853
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study contextual bandits with finitely many actions in which the reward of each arm follows a single-index model with an arm-specific index parameter and an unknown nonparametric link function. We consider a regime in which arms correspond to stable decision options and covariates evolve adaptively under the bandit policy. This setting creates significant statistical challenges: the sampling distribution depends on the allocation rule, observations are dependent over time, and inverse-propensity weighting induces variance inflation. We propose a kernelized $\varepsilon$-greedy algorithm that combines Stein-based estimation of the index parameters with inverse-propensity-weighted kernel ridge regression for the reward functions. This approach enables flexible semiparametric learning while retaining interpretability. Our analysis develops new tools for inference with adaptively collected data. We establish asymptotic normality for the single-index estimator under adaptive sampling, yielding valid confidence regions, and derive a directional functional central limit theorem for the RKHS estimator, which provides asymptotically valid pointwise confidence intervals. The analysis relies on concentration bounds for inverse-weighted Gram matrices together with martingale central limit theorems. We further obtain finite-time regret guarantees, including $\tilde{O}(\sqrt{T})$ rates under common-link Lipschitz conditions, showing that semiparametric structure can be exploited without sacrificing statistical efficiency. These results provide a unified framework for simultaneous learning and inference in single-index contextual bandits.

Related papers

• Universality of General Spiked Tensor Models [9.454986540713655]
  We study the rank-one spiked tensor model in the high-dimensional regime.<n>We show that their high-dimensional spectral behavior and statistical limits are robust to non-Gaussian noise.
  arXiv  Detail & Related papers  (2026-02-04T11:59:30Z)
• Statistical Inference under Adaptive Sampling with LinUCB [15.167069362020426]
  We show that the linear upper confidence bound (LinUCB) algorithm for linear bandits satisfies a property called stability.<n>We establish a central limit theorem for the LinUCB algorithm, establishing normality for the limiting distribution of the estimation error.
  arXiv  Detail & Related papers  (2025-11-28T21:48:18Z)
• Graph-based Clustering Revisited: A Relaxation of Kernel $k$-Means Perspective [73.18641268511318]
  We propose a graph-based clustering algorithm that only relaxes the orthonormal constraint to derive clustering results.<n>To ensure a doubly constraint into a gradient, we transform the non-negative constraint into a class probability parameter.
  arXiv  Detail & Related papers  (2025-09-23T09:14:39Z)
• Asymptotically Optimal Linear Best Feasible Arm Identification with Fixed Budget [55.938644481736446]
  We introduce a novel algorithm for best feasible arm identification that guarantees an exponential decay in the error probability.<n>We validate our algorithm through comprehensive empirical evaluations across various problem instances with different levels of complexity.
  arXiv  Detail & Related papers  (2025-06-03T02:56:26Z)
• Semiparametric conformal prediction [79.6147286161434]
  We construct a conformal prediction set accounting for the joint correlation structure of the vector-valued non-conformity scores.<n>We flexibly estimate the joint cumulative distribution function (CDF) of the scores.<n>Our method yields desired coverage and competitive efficiency on a range of real-world regression problems.
  arXiv  Detail & Related papers  (2024-11-04T14:29:02Z)
• Statistical Inference for Temporal Difference Learning with Linear Function Approximation [55.80276145563105]
  We investigate the statistical properties of Temporal Difference learning with Polyak-Ruppert averaging.<n>We make three theoretical contributions that improve upon the current state-of-the-art results.
  arXiv  Detail & Related papers  (2024-10-21T15:34:44Z)
• Likelihood Ratio Confidence Sets for Sequential Decision Making [51.66638486226482]
  We revisit the likelihood-based inference principle and propose to use likelihood ratios to construct valid confidence sequences. Our method is especially suitable for problems with well-specified likelihoods. We show how to provably choose the best sequence of estimators and shed light on connections to online convex optimization.
  arXiv  Detail & Related papers  (2023-11-08T00:10:21Z)
• Distribution Regression with Sliced Wasserstein Kernels [45.916342378789174]
  We propose the first OT-based estimator for distribution regression. We study the theoretical properties of a kernel ridge regression estimator based on such representation.
  arXiv  Detail & Related papers  (2022-02-08T15:21:56Z)
• Optimal variance-reduced stochastic approximation in Banach spaces [114.8734960258221]
  We study the problem of estimating the fixed point of a contractive operator defined on a separable Banach space. We establish non-asymptotic bounds for both the operator defect and the estimation error.
  arXiv  Detail & Related papers  (2022-01-21T02:46:57Z)
• From Optimality to Robustness: Dirichlet Sampling Strategies in Stochastic Bandits [0.0]
  We study a generic Dirichlet Sampling (DS) algorithm, based on pairwise comparisons of empirical indices computed with re-sampling of the arms' observations. We show that different variants of this strategy achieve provably optimal regret guarantees when the distributions are bounded and logarithmic regret for semi-bounded distributions with a mild quantile condition.
  arXiv  Detail & Related papers  (2021-11-18T14:34:21Z)
• Nonparametric Score Estimators [49.42469547970041]
  Estimating the score from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models. We provide a unifying view of these estimators under the framework of regularized nonparametric regression. We propose score estimators based on iterative regularization that enjoy computational benefits from curl-free kernels and fast convergence.
  arXiv  Detail & Related papers  (2020-05-20T15:01:03Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.