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Minimax Concave Penalized Multi-Armed Bandit Model with High-Dimensional Covariates
xue wang · Mingcheng Wei · Tao Yao

Fri Jul 13 09:15 AM -- 12:00 PM (PDT) @ Hall B #141

In this paper, we propose a Minimax Concave Penalized Multi-Armed Bandit (MCP-Bandit) algorithm for a decision-maker facing high-dimensional data with latent sparse structure in an online learning and decision-making process. We demonstrate that the MCP-Bandit algorithm asymptotically achieves the optimal cumulative regret in sample size T, O(log T), and further attains a tighter bound in both covariates dimension d and the number of significant covariates s, O(s^2 (s + log d). In addition, we develop a linear approximation method, the 2-step Weighted Lasso procedure, to identify the MCP estimator for the MCP-Bandit algorithm under non-i.i.d. samples. Using this procedure, the MCP estimator matches the oracle estimator with high probability. Finally, we present two experiments to benchmark our proposed the MCP-Bandit algorithm to other bandit algorithms. Both experiments demonstrate that the MCP-Bandit algorithm performs favorably over other benchmark algorithms, especially when there is a high level of data sparsity or when the sample size is not too small.

Author Information

Mike Wei (University at Buffalo)
Tao Yao (penn state university)

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