Linear Bandits with Partially Observable Features

• URL: http://arxiv.org/abs/2502.06142v1
• Date: Mon, 10 Feb 2025 04:15:38 GMT
• Title: Linear Bandits with Partially Observable Features
• Authors: Wonyoung Kim, Sungwoo Park, Garud Iyengar, Assaf Zeevi, Min-hwan Oh,
• Abstract summary: We introduce a novel linear bandit problem with partially observable features, resulting in partial reward information and spurious estimates.<n>Without proper address for latent part, regret possibly grows linearly in decision horizon $T$, as their influence on rewards are unknown.<n>We propose a novel analysis to handle the latent features and an algorithm that achieves sublinear regret.
• Score: 35.08645010112184
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We introduce a novel linear bandit problem with partially observable features, resulting in partial reward information and spurious estimates. Without proper address for latent part, regret possibly grows linearly in decision horizon $T$, as their influence on rewards are unknown. To tackle this, we propose a novel analysis to handle the latent features and an algorithm that achieves sublinear regret. The core of our algorithm involves (i) augmenting basis vectors orthogonal to the observed feature space, and (ii) introducing an efficient doubly robust estimator. Our approach achieves a regret bound of $\tilde{O}(\sqrt{(d + d_h)T})$, where $d$ is the dimension of observed features, and $d_h$ is the unknown dimension of the subspace of the unobserved features. Notably, our algorithm requires no prior knowledge of the unobserved feature space, which may expand as more features become hidden. Numerical experiments confirm that our algorithm outperforms both non-contextual multi-armed bandits and linear bandit algorithms depending solely on observed features.

Related papers

• Neural Variance-aware Dueling Bandits with Deep Representation and Shallow Exploration [6.287267171078442]
  We propose variance-aware algorithms that leverage neural networks to approximate nonlinear utility functions.<n>We establish theoretical guarantees showing that our algorithms achieve sublinear cumulative average regret of order $bigollt(d sqrtsum_t=1T sigma_t2 + sqrtdTrt),$ for sufficiently wide neural networks.
  arXiv  Detail & Related papers  (2025-06-02T01:58:48Z)
• Sparse Linear Bandits with Blocking Constraints [22.01704171400845]
  We investigate the high-dimensional sparse linear bandits problem in a data-poor regime.<n>We show novel offline statistical guarantees of the lasso estimator for the linear model.<n>We propose a meta-algorithm based on corralling that does not need knowledge of optimal sparsity parameter $k$ at minimal cost to regret.
  arXiv  Detail & Related papers  (2024-10-26T01:42:03Z)
• Variance-Dependent Regret Bounds for Non-stationary Linear Bandits [52.872628573907434]
  We propose algorithms that utilize the variance of the reward distribution as well as the $B_K$, and show that they can achieve tighter regret upper bounds. We introduce two novel algorithms: Restarted Weighted$textOFUL+$ and Restarted $textSAVE+$. Notably, when the total variance $V_K$ is much smaller than $K$, our algorithms outperform previous state-of-the-art results on non-stationary linear bandits under different settings.
  arXiv  Detail & Related papers  (2024-03-15T23:36:55Z)
• Contextual Bandits with Stage-wise Constraints [41.29604168314892]
  We study contextual bandits in the presence of a stage-wise constraint when the constraint must be satisfied both with high probability and in expectation.<n>We propose an upper-confidence bound algorithm for the problem and prove a $T$-round regret bound for it.<n>We extend our results to the case where the reward and cost functions are both non-linear.
  arXiv  Detail & Related papers  (2024-01-15T23:58:21Z)
• Learning Adversarial Low-rank Markov Decision Processes with Unknown Transition and Full-information Feedback [30.23951525723659]
  We study the low-rank MDPs with adversarially changed losses in the full-information feedback setting. We propose a policy optimization-based algorithm POLO, and we prove that it attains the $widetildeO(Kfrac56Afrac12dln (1+M)/ (1-gamma)2)$ regret guarantee.
  arXiv  Detail & Related papers  (2023-11-14T03:12:43Z)
• Variance-Aware Regret Bounds for Stochastic Contextual Dueling Bandits [53.281230333364505]
  This paper studies the problem of contextual dueling bandits, where the binary comparison of dueling arms is generated from a generalized linear model (GLM) We propose a new SupLinUCB-type algorithm that enjoys computational efficiency and a variance-aware regret bound $tilde Obig(dsqrtsum_t=1Tsigma_t2 + dbig)$. Our regret bound naturally aligns with the intuitive expectation in scenarios where the comparison is deterministic, the algorithm only suffers from an $tilde O(d)$ regret.
  arXiv  Detail & Related papers  (2023-10-02T08:15:52Z)
• Optimal Horizon-Free Reward-Free Exploration for Linear Mixture MDPs [60.40452803295326]
  We propose a new reward-free algorithm for learning linear Markov decision processes (MDPs) At the core of our algorithm is uncertainty-weighted value-targeted regression with exploration-driven pseudo-reward. We show that our algorithm only needs to explore $tilde O( d2varepsilon-2)$ episodes to find an $varepsilon$-optimal policy.
  arXiv  Detail & Related papers  (2023-03-17T17:53:28Z)
• Exploration in Linear Bandits with Rich Action Sets and its Implications for Inference [23.364534479492715]
  We show that the minimum eigenvalue of the expected matrix grows as $Omega(sqrtn) whenever the expected cumulative regret of the algorithm is $sqrtn)$. We apply our result to two practical scenarios -- emphmodel selection and emphclustering in linear bandits.
  arXiv  Detail & Related papers  (2022-07-23T20:25:07Z)
• Misspecified Gaussian Process Bandit Optimization [59.30399661155574]
  Kernelized bandit algorithms have shown strong empirical and theoretical performance for this problem. We introduce a emphmisspecified kernelized bandit setting where the unknown function can be $epsilon$--uniformly approximated by a function with a bounded norm in some Reproducing Kernel Hilbert Space (RKHS) We show that our algorithm achieves optimal dependence on $epsilon$ with no prior knowledge of misspecification.
  arXiv  Detail & Related papers  (2021-11-09T09:00:02Z)
• Adapting to Misspecification in Contextual Bandits [82.55565343668246]
  We introduce a new family of oracle-efficient algorithms for $varepsilon$-misspecified contextual bandits. We obtain the first algorithm that achieves the optimal $O(dsqrtT + varepsilonsqrtdT)$ regret bound for unknown misspecification level.
  arXiv  Detail & Related papers  (2021-07-12T21:30:41Z)
• Budgeted and Non-budgeted Causal Bandits [2.9005223064604078]
  Learning good interventions in a causal graph can be modelled as a multi-armed bandit problem with side-information. We propose an algorithm to minimize simple regret that optimally trades-off observations and interventions based on the cost of intervention. Our results are experimentally validated and compared to the best-known bounds in the current literature.
  arXiv  Detail & Related papers  (2020-12-13T13:31:14Z)
• High-Dimensional Sparse Linear Bandits [67.9378546011416]
  We derive a novel $Omega(n2/3)$ dimension-free minimax regret lower bound for sparse linear bandits in the data-poor regime. We also prove a dimension-free $O(sqrtn)$ regret upper bound under an additional assumption on the magnitude of the signal for relevant features.
  arXiv  Detail & Related papers  (2020-11-08T16:48:11Z)
• Stochastic Linear Bandits with Protected Subspace [51.43660657268171]
  We study a variant of the linear bandit problem wherein we optimize a linear objective function but rewards are accrued only to an unknown subspace. In particular, at each round, the learner must choose whether to query the objective or the protected subspace alongside choosing an action. Our algorithm, derived from the OFUL principle, uses some of the queries to get an estimate of the protected space.
  arXiv  Detail & Related papers  (2020-11-02T14:59:39Z)
• Sparsity-Agnostic Lasso Bandit [27.383079108028074]
  We consider a contextual bandit problem where the dimension $d$ of the feature vectors is potentially large. All existing algorithms for sparse bandits require a priori knowledge of the value of the sparsity index $s_$. We propose an algorithm that does not require prior knowledge of the sparsity index $s_$ and establish tight regret bounds on its performance under mild conditions.
  arXiv  Detail & Related papers  (2020-07-16T17:24:12Z)
• Stochastic Linear Bandits Robust to Adversarial Attacks [117.665995707568]
  We provide two variants of a Robust Phased Elimination algorithm, one that knows $C$ and one that does not. We show that both variants attain near-optimal regret in the non-corrupted case $C = 0$, while incurring additional additive terms respectively. In a contextual setting, we show that a simple greedy algorithm is provably robust with a near-optimal additive regret term, despite performing no explicit exploration and not knowing $C$.
  arXiv  Detail & Related papers  (2020-07-07T09:00:57Z)
• Contextual Linear Bandits under Noisy Features: Towards Bayesian Oracles [65.9694455739978]
  We study contextual linear bandit problems under feature uncertainty, where the features are noisy and have missing entries. Our analysis reveals that the optimal hypothesis can significantly deviate from the underlying realizability function, depending on the noise characteristics. This implies that classical approaches cannot guarantee a non-trivial regret bound.
  arXiv  Detail & Related papers  (2017-03-03T21:39:56Z)

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.