Online Regularization towards Always-Valid High-Dimensional Dynamic Pricing

Abstract

We propose a novel online regularization scheme for revenue-maximization in high-dimensional dynamic pricing algorithms. The online regularization scheme equips the proposed optimistic online regularized maximum likelihood pricing (OORMLP) algorithm with three major advantages: encode market noise knowledge into pricing process optimism; empower online statistical learning with alwaysvalidity over all decision points; envelop prediction error process with time-uniform non-asymptotic oracle inequalities. This type of non-asymptotic inference results allows us to design safer and more robust dynamic pricing algorithms in practice. In theory, the proposed OORMLP algorithm exploits the sparsity structure of highdimensional models and obtains a logarithmic regret in a decision horizon. These theoretical advances are made possible by proposing an optimistic online LASSO procedure that resolves dynamic pricing problems at the process level, based on a novel use of non-asymptotic martingale concentration. In experiments, we evaluate OORMLP in different synthetic pricing problem settings and observe that OORMLP performs better than RMLP proposed in [13].Preprint. Under review.

Policy Optimization Using Semi-parametric Models for Dynamic Pricing

“…A common and natural choice is to model the market value of the product at time t as a linear function of its features x t plus some market noise z t , i.e. v t = θ x t + z t where θ is some unknown parameter (Qiang and Bayati, 2016;Javanmard, 2017;Miao et al, 2019;Javanmard and Nazerzadeh, 2019;Ban and Keskin, 2020;Wang et al, 2020;Tang et al, 2020;Golrezaei et al, 2020). Under this setting, for 'truthful' buyers whose decision is based on comparing v t and offered price p t , the demand curve can be expressed as a generalized linear model given feature covariates x t , where the link function is closely related to the distribution of the market noise z t (see (2.3) for a detailed reasoning).…”

“…They prove that the greedy iterative least squares (GILS) algorithm achieves a regret upper bound of O d (log T ), where O d is the order that hides logarithmic terms and the dimensionality of feature d, and provide a matching lower bound under their setting. Miao et al (2019) and Ban and Keskin (2020) consider a generalized linear model with known link, while Javanmard and Nazerzadeh (2019) and Wang et al (2020) study the same problem with high dimensional sparse parameters. The algorithms are usually a combination of statistical estimation procedures and online learning techniques.…”

Rate-Optimal Contextual Online Matching Bandit

“…Bandit algorithms (Bubeck and Cesa-Bianchi, 2012;Lattimore and Szepesvári, 2020) and reinforcement learning (Sutton and Barto, 2018) are modern strategies to solve sequential decision making problems. They have received recent attentions in statistics community for business and scientific applications including dynamic pricing (Wang et al, 2020;Chen, Simchi-Levi and Wang, 2021;Chen, Miao and Wang, 2021;Wang et al, 2021), online decision making (Shi et al, 2020;Chen, Lu and Song, 2021;Chen et al, 2022), dynamic treatment regimes (Qi and Liu, 2018;Luckett et al, 2019;Qi et al, 2020;Qi, Miao and Zhang, 2021), and online causal effect in two-sided market (Shi et al, 2022b).…”