Calibrating Sales Forecasts in a Pandemic Using Competitive Online Nonparametric Regression

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 nonparametric regression method. Specifically, the method takes the future COVID-19 case estimates, which can be simulated via the susceptible-infectious-removed (SIR) epidemic model as an input, and outputs the level of calibration for the baseline sales forecast generated by AB InBev. 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, we derive our algorithm by minimizing regret, which is the difference between the squared euro2-norm associated with labels generated by the algorithm and labels generated by an adversary and the squared euro2-norm associated with labels generated by the best isotonic (nondecreasing) 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 (possibly non-i.i.d. and even adversarial). We demonstrate the performances of our algorithm on both synthetic and AB InBev's data sets of three different markets (each corresponds to a country) from March 2020 to March 2021. The AB InBev's numerical experiments show that our method is capable of reducing the forecast error in terms of weighted mean absolute percentage error (WMAPE) and mean squared error (MSE) by more than 37% for the company.