Congyuan Duan

Congyuan Duan, Jingyang Li, Dong Xia

Is it possible to make online decisions when personalized covariates are unavailable? We take a collaborative-filtering approach for decision-making based on collective preferences. By assuming low-dimensional latent features, we formulate the covariate-free decision-making problem as a matrix completion bandit. We propose a policy learning procedure that combines an $\varepsilon$-greedy policy for decision-making with an online gradient descent algorithm for bandit parameter estimation. Our novel two-phase design balances policy learning accuracy and regret performance. For policy inference, we develop an online debiasing method based on inverse propensity weighting and establish its asymptotic normality. Our methods are applied to data from the San Francisco parking pricing project, revealing intriguing discoveries and outperforming the benchmark policy.

Congyuan Duan, Wanteng Ma, Jiashuo Jiang et al.

This paper investigates regret minimization, statistical inference, and their interplay in high-dimensional online decision-making based on the sparse linear context bandit model. We integrate the $\varepsilon$-greedy bandit algorithm for decision-making with a hard thresholding algorithm for estimating sparse bandit parameters and introduce an inference framework based on a debiasing method using inverse propensity weighting. Under a margin condition, our method achieves either $O(T^{1/2})$ regret or classical $O(T^{1/2})$-consistent inference, indicating an unavoidable trade-off between exploration and exploitation. If a diverse covariate condition holds, we demonstrate that a pure-greedy bandit algorithm, i.e., exploration-free, combined with a debiased estimator based on average weighting can simultaneously achieve optimal $O(\log T)$ regret and $O(T^{1/2})$-consistent inference. We also show that a simple sample mean estimator can provide valid inference for the optimal policy's value. Numerical simulations and experiments on Warfarin dosing data validate the effectiveness of our methods.