Online Policy Learning and Inference by Matrix Completion
This addresses covariate-free decision-making for applications like collaborative filtering, though it appears incremental as it builds on existing bandit and matrix completion techniques.
The paper tackles the problem of making online decisions without personalized covariates by formulating it as a matrix completion bandit, proposing a two-phase policy learning procedure and an online debiasing method for inference. The approach outperforms benchmarks when applied to San Francisco parking pricing data.
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.