Deep Learning-Based Causal Inference for Large-Scale Combinatorial Experiments: Theory and Empirical Evidence

Large-scale online platforms launch hundreds of randomized experiments (also known as A/B tests) every day to iterate their operations and marketing strategies. The combinations of these treatments are typically not exhaustively tested, which triggers an important question of both academic and practical interest. Without observing the outcomes of all treatment combinations, how does one estimate the causal effect of any treatment combination and identify the optimal treatment combination? We develop a novel framework combining deep learning and doubly robust estimation to estimate the causal effect of any treatment combination for each user on the platform when observing only a small subset of treatment combinations. Our proposed framework (called debiased deep learning ( DeDL )) exploits Neyman orthogonality and combines interpretable and flexible structural layers in deep learning. We show theoretically that this framework yields efficient, consistent, and asymptotically normal estimators under mild assumptions, thus allowing for identifying the best treatment combination when observing only a few combinations. To empirically validate our method, we collaborated with a large-scale video-sharing platform and implemented our framework for three experiments involving three treatments, where each combination of treatments is tested. When observing only a subset of treatment combinations, our DeDL approach significantly outperforms other benchmarks to accurately estimate and infer the average treatment effect of any treatment combination and to identify the optimal treatment combination. This paper was accepted by Vivek Farias, data science. Funding: R. Zhang is grateful for financial support from the Hong Kong Research Grants Council General Research Fund [Grants 14502722, 14503224, and 14504123]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2024.04625 .