Calibrating Sales Forecast in a Pandemic: Random-Design Online Isotonic Regression

Abstract

Motivated by our collaboration with Anheuser-Busch InBev (AB InBev), a consumer packaged goods (CPG) company, we consider the problem of forecasting sales under the coronavirus disease 2019 (COVID-19) pandemic. Our approach combines non-parametric regression, game theory, and pandemic modeling to develop a data-driven competitive online non-parametric regression method. Specifically, the method takes the future COVID-19 cases estimates, which can be simulated via the SIR (i.e., Susceptible-Infectious-Removed) epidemic model, as an input, and outputs the level of calibration for the baseline sales forecast generated by AB InBev's offline learning algorithm. In generating the calibration level, we focus on an online learning setting, where our algorithm sequentially predicts the label (i.e., the level of calibration) of a random covariate (i.e., the current number of active cases) given past observations and the generative process (i.e., the SIR epidemic model) of future covariates. To provide robust performance guarantee for every sequence of data (each corresponds to a different market of AB InBev's), we derive our algorithm by minimizing regret, which is the difference between the squared l_2-norm associated with labels generated by the algorithm and labels generated by an adversary and the squared l_2-norm associated with labels generated by the best isotonic (non-decreasing) function in hindsight and the adversarial labels. We develop a computationally-efficient algorithm that attains the minimax-optimal regret over all possible choices of the labels. We demonstrate the performances of our algorithm on both synthetic and AB InBev’s datasets (from March 2020 to March 2021) of three different geographical regions . The AB InBev’s numerical experiments show that our method is capable of reducing the forecasting error in terms of WMAPE (i.e., weighted mean absolute percentage error) and MSE (i.e., mean squared error) by more than 49\% for the company.