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Dual Instrumental Method for Confounded Kernelized Bandits

arXiv 2209.03224 ↗First posted 7 Sep 2022cs.LG cs.AI stat.MLcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 19 of its 49 references that are in the map. First posted on arXiv 7 Sep 2022.

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References · 19

  1. 2016Kernel Mean Embedding of Distributions: A Review and Beyondcited by 360
  2. 2020A Survey on Causal Inferencecited by 202
  3. 2020Beyond UCB: Optimal and Efficient Contextual Bandits with Regression Oraclescited by 195
  4. 2013Finite-Time Analysis of Kernelised Contextual Banditscited by 177
  5. 2019Kernel Instrumental Variable Regressioncited by 118
  6. 2020Bypassing the Monster: A Faster and Simpler Optimal Algorithm for Contextual Bandits under Realizabilitycited by 114
  7. 2016Causal Bandits: Learning Good Interventions via Causal Inferencecited by 100
  8. 2017Lower Bounds on Regret for Noisy Gaussian Process Bandit Optimizationcited by 77
  9. 2019Nearly Minimax-Optimal Regret for Linearly Parameterized Banditscited by 54
  10. 2021Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restrictioncited by 54
  11. 2020Bandit optimisation of functions in the Mat'ern kernel RKHScited by 40
  12. 2021Deep Proxy Causal Learning and its Application to Confounded Bandit Policy Evaluationcited by 39
7 more
  1. 2020Provably Efficient Neural Estimation of Structural Equation Model: An Adversarial Approachcited by 31
  2. 2019Beyond Least-Squares: Fast Rates for Regularized Empirical Risk Minimization through Self-Concordancecited by 28
  3. 2017Estimation Considerations in Contextual Banditscited by 22
  4. 2020Bandits with Partially Observable Confounded Datacited by 22
  5. 2017Instrument-Armed Banditscited by 10
  6. 2019Bayesian Deconditional Kernel Mean Embeddingscited by 6
  7. 2022Efficient Kernel UCB for Contextual Banditscited by 3

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