Efficient Simple Regret Algorithms for Stochastic Contextual Bandits

• URL: http://arxiv.org/abs/2601.21167v1
• Date: Thu, 29 Jan 2026 02:09:13 GMT
• Title: Efficient Simple Regret Algorithms for Stochastic Contextual Bandits
• Authors: Shuai Liu, Alireza Bakhtiari, Alex Ayoub, Botao Hao, Csaba Szepesvári,
• Abstract summary: We study contextual logistic bandits under the simple regret objective.<n>We propose the first algorithm that achieves simple regret $tildemathcalO(d/sqrtT)$.<n>We also introduce a new variant of Thompson Sampling tailored to the simple-regret setting.
• Score: 32.5817931126341
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study stochastic contextual logistic bandits under the simple regret objective. While simple regret guarantees have been established for the linear case, no such results were previously known for the logistic setting. Building on ideas from contextual linear bandits and self-concordant analysis, we propose the first algorithm that achieves simple regret $\tilde{\mathcal{O}}(d/\sqrt{T})$. Notably, the leading term of our regret bound is free of the constant $κ= \mathcal O(\exp(S))$, where $S$ is a bound on the magnitude of the unknown parameter vector. The algorithm is shown to be fully tractable when the action set is finite. We also introduce a new variant of Thompson Sampling tailored to the simple-regret setting. This yields the first simple regret guarantee for randomized algorithms in stochastic contextual linear bandits, with regret $\tilde{\mathcal{O}}(d^{3/2}/\sqrt{T})$. Extending this method to the logistic case, we obtain a similarly structured Thompson Sampling algorithm that achieves the same regret bound -- $\tilde{\mathcal{O}}(d^{3/2}/\sqrt{T})$ -- again with no dependence on $κ$ in the leading term. The randomized algorithms, as expected, are cheaper to run than their deterministic counterparts. Finally, we conducted a series of experiments to empirically validate these theoretical guarantees.

Related papers

• Exploration via Feature Perturbation in Contextual Bandits [33.46701416812218]
  We propose a simple strategy for contextual bandits that injects randomness directly into feature inputs.<n>Remarkably, this algorithm achieves $tildemathcalO(dsqrtT)$ worst-case regret bound for generalized linear contextual bandits.
  arXiv  Detail & Related papers  (2025-10-20T10:32:48Z)
• p-Mean Regret for Stochastic Bandits [52.828710025519996]
  We introduce a simple, unified UCB-based algorithm that achieves novel $p$-mean regret bounds.<n>Our framework encompasses both average cumulative regret and Nash regret as special cases.
  arXiv  Detail & Related papers  (2024-12-14T08:38:26Z)
• Tangential Randomization in Linear Bandits (TRAiL): Guaranteed Inference and Regret Bounds [1.03590082373586]
  We propose and analyze TRAiL, a regret-optimal forced exploration algorithm for linear bandits. TraiL ensures a $Omega(sqrtT)$ growth in the inference quality, measured via the minimum eigenvalue of the design (regressor) matrix. We characterize an $Omega(sqrtT)$ minimax lower bound for any algorithm on the expected regret.
  arXiv  Detail & Related papers  (2024-11-19T01:08:13Z)
• Efficient Frameworks for Generalized Low-Rank Matrix Bandit Problems [61.85150061213987]
  We study the generalized low-rank matrix bandit problem, proposed in citelu2021low under the Generalized Linear Model (GLM) framework. To overcome the computational infeasibility and theoretical restrain of existing algorithms, we first propose the G-ESTT framework. We show that G-ESTT can achieve the $tildeO(sqrt(d_1+d_2)3/2Mr3/2T)$ bound of regret while G-ESTS can achineve the $tildeO
  arXiv  Detail & Related papers  (2024-01-14T14:14:19Z)
• Revisiting Weighted Strategy for Non-stationary Parametric Bandits [82.1942459195896]
  This paper revisits the weighted strategy for non-stationary parametric bandits. We propose a refined analysis framework, which produces a simpler weight-based algorithm. Our new framework can be used to improve regret bounds of other parametric bandits.
  arXiv  Detail & Related papers  (2023-03-05T15:11:14Z)
• Squeeze All: Novel Estimator and Self-Normalized Bound for Linear Contextual Bandits [18.971564419292893]
  We propose a linear contextual bandit algorithm with $O(sqrtdTlog T)$ regret bound, where $d$ is the dimension of contexts and $T$ is the time horizon. Our proposed algorithm is equipped with a novel estimator in which exploration is embedded through explicit randomization.
  arXiv  Detail & Related papers  (2022-06-11T02:43:17Z)
• No Regrets for Learning the Prior in Bandits [30.478188057004175]
  $tt AdaTS$ is a Thompson sampling algorithm that adapts sequentially to bandit tasks. $tt AdaTS$ is a fully-Bayesian algorithm that can be implemented efficiently in several classes of bandit problems.
  arXiv  Detail & Related papers  (2021-07-13T15:51:32Z)
• Randomized Exploration for Reinforcement Learning with General Value Function Approximation [122.70803181751135]
  We propose a model-free reinforcement learning algorithm inspired by the popular randomized least squares value iteration (RLSVI) algorithm. Our algorithm drives exploration by simply perturbing the training data with judiciously chosen i.i.d. scalar noises. We complement the theory with an empirical evaluation across known difficult exploration tasks.
  arXiv  Detail & Related papers  (2021-06-15T02:23:07Z)
• Non-stationary Linear Bandits Revisited [26.082923174615495]
  Non-stationary linear bandits are a variant of linear bandits with a time-varying underlying regression parameter. We prove an $widetildeO(T3/4(1+P_T)1/4)$ dynamic regret for these algorithms, slightly worse than the rate as was anticipated.
  arXiv  Detail & Related papers  (2021-03-09T10:07:17Z)
• Thresholded Lasso Bandit [70.17389393497125]
  Thresholded Lasso bandit is an algorithm that estimates the vector defining the reward function as well as its sparse support. We establish non-asymptotic regret upper bounds scaling as $mathcalO( log d + sqrtT )$ in general, and as $mathcalO( log d + sqrtT )$ under the so-called margin condition.
  arXiv  Detail & Related papers  (2020-10-22T19:14:37Z)
• Impact of Representation Learning in Linear Bandits [83.17684841392754]
  We study how representation learning can improve the efficiency of bandit problems. We present a new algorithm which achieves $widetildeO(TsqrtkN + sqrtdkNT)$ regret, where $N$ is the number of rounds we play for each bandit.
  arXiv  Detail & Related papers  (2020-10-13T16:35:30Z)
• Stochastic Bandits with Linear Constraints [69.757694218456]
  We study a constrained contextual linear bandit setting, where the goal of the agent is to produce a sequence of policies. We propose an upper-confidence bound algorithm for this problem, called optimistic pessimistic linear bandit (OPLB)
  arXiv  Detail & Related papers  (2020-06-17T22:32:19Z)
• Low-Rank Generalized Linear Bandit Problems [19.052901817304743]
  In a low-rank linear bandit problem, the reward of an action is the inner product between the action and an unknown low-rank matrix $Theta*$. We propose an algorithm based on a novel combination of online-to-confidence-set conversioncitepabbasi2012online and the exponentially weighted average forecaster constructed by a covering of low-rank matrices.
  arXiv  Detail & Related papers  (2020-06-04T15:30:14Z)

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.