Optimizing ARDL Models for Retail Sales Forecasting and Fair Pricing

Data-driven pricing is increasingly prevalent in sectors such as airlines, lending, insurance, and retail. By learning demand models from customer features and setting prices accordingly, these systems may generate discriminatory outcomes that raise fairness concerns. This leads to fundamental questions - how and where should systems incorporate fairness considerations in the pricing pipeline, and how does it ultimately affect societal outcomes? To answer these, we study a stylized model where a seller has a two-stage decision pipeline comprising linear demand model estimation followed by price optimization. The seller considers fairness notions in training loss, price, and demand, under both parity-wise and Rawlsian perspectives. We show that equalizing training loss across consumer groups leads to multiple solutions, which in turn can result in undesirable outcomes despite being a standard approach in fair machine learning. Focusing instead on fairness applied directly to prices or demand, we compare two strategies that enforce fairness in either the demand estimation stage or the price optimization stage. For parity-wise fairness, we characterize when each strategy yields higher social welfare under small fairness levels. We show that when market sizes and prices in the dataset are similar, imposing price fairness in the estimation stage is more beneficial to consumers, whereas imposing demand fairness in the optimization stage yields better consumer outcomes. For Rawlsian fairness, the two strategies coincide exactly. Lastly, we extend our model to alternate demand functions and conduct a case study using real-world vaccine pricing data.

We study the contextual dynamic pricing problem under non-stationarity, where a firm sells products to $T$ sequentially arriving consumers that behave according to an unknown demand model that can change over time. The demand model is assumed to be a generalized linear model (GLM), allowing for a feature vector in $\mathbb{R}^d$ that encodes products and consumer information. To achieve optimal revenue (i.e., least regret), the firm needs to learn and exploit the unknown GLMs while monitoring for potential changes. We propose a multiscale change-point detection based algorithm that achieves a regret of order $\widetilde{O}(\sqrt{s_TdT}\wedge\{V_T^{1/3}d^{1/3}T^{2/3}+\sqrt{dT}\})$, where $s_T$ is the number of piecewise stationary segments and $V_T$ is a newly defined notion of design-adjusted variation budget of model parameters. Our algorithm is adaptive and does not require knowing $s_T$ or $V_T$. Moreover, to our knowledge, this is the first dynamic pricing algorithm that is adaptive to the nature of changes and achieves the best-of-both-worlds rate, thus closing a long-standing gap in the literature. We remark that, due to the varying contexts, existing works in the adaptive non-stationary bandit literature cannot be applied to achieve optimality for contextual dynamic pricing. The regret is further accompanied with a newly constructed minimax lower bound, confirming the optimality of our algorithm (up to logarithmic factors). Extensive numerical experiments are conducted to illustrate the efficiency and robustness of the proposed algorithm in non-stationary dynamic pricing.

We study contextual dynamic pricing with arbitrary covariate sequences and bounded, possibly nonbinary purchase quantities. Demand follows a semiparametric surplus-index model with an unknown linear valuation parameter and an unknown Hölder-smooth response. We impose neither concavity nor strong unimodality on revenue and allow nonunique optimal prices. We develop a pilot-corrected layered decision-partitioning policy that combines directional pilot estimation, local polynomial learning, predictable data assignment, and global action elimination. Pilot correction removes the first-order effect of valuation-parameter error, while permanent labels enable concentration under adaptive sampling. The policy attains the minimax smoothness-dependent horizon rate up to logarithmic factors; a matching lower bound already holds for a constant-context binary-demand subclass.