Online Learning and Decision Making Under Generalized Linear Model with High-Dimensional Data

Xue Wang (), Mike Mingcheng Wei () and Tao Yao ()
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Xue Wang: DAMO Academy, Alibaba Group, Bellevue, Washington 98004
Mike Mingcheng Wei: Operations Management and Strategy, School of Management, University at Buffalo, Buffalo, New York 14260
Tao Yao: Data and Business Intelligence, Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai 20003, China

Management Science, 2025, vol. 71, issue 8, 6647-6665

Abstract: We propose a minimax concave penalized multiarmed bandit algorithm under the generalized linear model (G-MCP-Bandit) for decision-makers facing high-dimensional data in an online learning and decision-making environment. We demonstrate that in the data-rich regime, the G-MCP-Bandit algorithm attains the optimal cumulative regret in the sample size dimension and a tight bound in the covariate dimension and the significant covariate dimension. In the data-poor regime, the G-MCP-Bandit algorithm maintains a tight regret upper bound. In addition, we develop a local linear approximation method, the two-step weighted Lasso procedure, to identify the minimax concave penalty (MCP) estimator for the G-MCP-Bandit algorithm when samples are not independent and identically distributed. Under this procedure, the MCP estimator can match the oracle estimator with high probability and converge to the true parameters at the optimal convergence rate. Finally, through experiments based on both synthetic and real data sets, we show that the G-MCP-Bandit algorithm outperforms other benchmarking algorithms in terms of cumulative regret and that the benefits of the G-MCP-Bandit algorithm increase in the data’s sparsity level and the size of the decision set.

Keywords: multiarmed bandits; minimax concave penalty; high-dimensional data; online learning and decision making; generalized linear model (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:71:y:2025:i:8:p:6647-6665

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