Dual Instrumental Method for Confounded Kernelized Bandits

• URL: http://arxiv.org/abs/2209.03224v1
• Date: Wed, 7 Sep 2022 15:25:57 GMT
• Title: Dual Instrumental Method for Confounded Kernelized Bandits
• Authors: Xueping Gong and Jiheng Zhang
• Abstract summary: The contextual bandit problem is a framework with wide applications in various fields. We propose a confounded bandit problem where the noise becomes a latent confounder that affects both contexts and rewards. We show that a dual instrumental variable regression can correctly identify the true reward function.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The contextual bandit problem is a theoretically justified framework with wide applications in various fields. While the previous study on this problem usually requires independence between noise and contexts, our work considers a more sensible setting where the noise becomes a latent confounder that affects both contexts and rewards. Such a confounded setting is more realistic and could expand to a broader range of applications. However, the unresolved confounder will cause a bias in reward function estimation and thus lead to a large regret. To deal with the challenges brought by the confounder, we apply the dual instrumental variable regression, which can correctly identify the true reward function. We prove the convergence rate of this method is near-optimal in two types of widely used reproducing kernel Hilbert spaces. Therefore, we can design computationally efficient and regret-optimal algorithms based on the theoretical guarantees for confounded bandit problems. The numerical results illustrate the efficacy of our proposed algorithms in the confounded bandit setting.

Related papers

• Neural Dueling Bandits [58.90189511247936]
  We use a neural network to estimate the reward function using preference feedback for the previously selected arms. We then extend our theoretical results to contextual bandit problems with binary feedback, which is in itself a non-trivial contribution.
  arXiv  Detail & Related papers  (2024-07-24T09:23:22Z)
• $\alpha$-Fair Contextual Bandits [10.74025233418392]
  Contextual bandit algorithms are at the core of many applications, including recommender systems, clinical trials, and optimal portfolio selection. One of the most popular problems studied in the contextual bandit literature is to maximize the sum of the rewards in each round. In this paper, we consider the $alpha$-Fairtextual Con Bandits problem, where the objective is to maximize the global $alpha$-fair utility function.
  arXiv  Detail & Related papers  (2023-10-22T03:42:59Z)
• 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)
• On Kernelized Multi-Armed Bandits with Constraints [16.102401271318012]
  We study a bandit problem with a general unknown reward function and a general unknown constraint function. We propose a general framework for both algorithm performance analysis. We demonstrate the superior performance of our proposed algorithms via numerical experiments.
  arXiv  Detail & Related papers  (2022-03-29T14:02:03Z)
• Versatile Dueling Bandits: Best-of-both-World Analyses for Online Learning from Preferences [28.79598714109439]
  We study the problem of $K$-armed dueling bandit for both and adversarial environments. We first propose a novel reduction from any (general) dueling bandits to multi-armed bandits. Our algorithm is also the first to achieve an optimal $O(sum_i = 1K fraclog TDelta_i)$ regret bound against the Condorcet-winner benchmark.
  arXiv  Detail & Related papers  (2022-02-14T13:37:23Z)
• Deep Hierarchy in Bandits [51.22833900944146]
  Mean rewards of actions are often correlated. To maximize statistical efficiency, it is important to leverage these correlations when learning. We formulate a bandit variant of this problem where the correlations of mean action rewards are represented by a hierarchical Bayesian model.
  arXiv  Detail & Related papers  (2022-02-03T08:15:53Z)
• Optimal Gradient-based Algorithms for Non-concave Bandit Optimization [76.57464214864756]
  This work considers a large family of bandit problems where the unknown underlying reward function is non-concave. Our algorithms are based on a unified zeroth-order optimization paradigm that applies in great generality. We show that the standard optimistic algorithms are sub-optimal by dimension factors.
  arXiv  Detail & Related papers  (2021-07-09T16:04:24Z)
• Efficient First-Order Contextual Bandits: Prediction, Allocation, and Triangular Discrimination [82.52105963476703]
  A recurring theme in statistical learning, online learning, and beyond is that faster convergence rates are possible for problems with low noise. First-order guarantees are relatively well understood in statistical and online learning. We show that the logarithmic loss and an information-theoretic quantity called the triangular discrimination play a fundamental role in obtaining first-order guarantees.
  arXiv  Detail & Related papers  (2021-07-05T19:20:34Z)
• Corruption-Tolerant Gaussian Process Bandit Optimization [130.60115798580136]
  We consider the problem of optimizing an unknown (typically non-producing) function with a bounded norm. We introduce an algorithm based on Fast-Slow GP-UCB based on "fast but non-robust" and "slow" We argue that certain dependencies cannot be required depending on the corruption level.
  arXiv  Detail & Related papers  (2020-03-04T09:46:58Z)
• Bandit algorithms to emulate human decision making using probabilistic distortions [20.422725678982726]
  We formulate two sample multi-armed bandit problems with distorted probabilities on the reward distributions. We consider the aforementioned problems in the regret minimization as well as best arm identification framework for multi-armed bandits.
  arXiv  Detail & Related papers  (2016-11-30T17:37:51Z)

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.