Online Policy Learning and Inference by Matrix Completion

• URL: http://arxiv.org/abs/2404.17398v1
• Date: Fri, 26 Apr 2024 13:19:27 GMT
• Title: Online Policy Learning and Inference by Matrix Completion
• Authors: Congyuan Duan, Jingyang Li, Dong Xia,
• Abstract summary: We formulate the problem as a matrix completion bandit (MCB) We explore the $epsilon$-greedy bandit and the online gradient descent descent. A faster decaying exploration yields smaller regret but learns the optimal policy less accurately.
• Score: 12.527541242185404
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Making online decisions can be challenging when features are sparse and orthogonal to historical ones, especially when the optimal policy is learned through collaborative filtering. We formulate the problem as a matrix completion bandit (MCB), where the expected reward under each arm is characterized by an unknown low-rank matrix. The $\epsilon$-greedy bandit and the online gradient descent algorithm are explored. Policy learning and regret performance are studied under a specific schedule for exploration probabilities and step sizes. A faster decaying exploration probability yields smaller regret but learns the optimal policy less accurately. We investigate an online debiasing method based on inverse propensity weighting (IPW) and a general framework for online policy inference. The IPW-based estimators are asymptotically normal under mild arm-optimality conditions. Numerical simulations corroborate our theoretical findings. Our methods are applied to the San Francisco parking pricing project data, revealing intriguing discoveries and outperforming the benchmark policy.

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