Beyond the Full Slate: Evaluating MNL Algorithms on All Slates

Multinomial logit models (MNLs) are ubiquitous in machine learning, particularly in recommendation systems. While these models are typically evaluated using global metrics over a full catalog of items (such as $\ell_2$-error), practical applications often involve making predictions on small, curated subsets or ``slates'' of items. A model that minimizes global error may nevertheless yield very poor predictions on specific sub-universes. Yet, evaluating performance across all possible subsets remains computationally challenging. In this paper, we present a set of new efficient algorithms to evaluate the small-slate performance of MNL models. Using these tools, we conduct an empirical study comparing standard non-adaptive and adaptive learning algorithms. We demonstrate that while methods that compute the Maximum Likelihood Estimate (MLE) suffer from poor worst-case performance on small slates, specialized adaptive algorithms that dynamically sample difficult subsets can mitigate this issue. Conversely, we find that non-adaptive algorithms often achieve competitive average-case performance; we provide a theoretical model explaining this phenomenon. We conclude with recommendations for practitioners regarding when to utilize adaptive sampling based on the specific robustness requirements of their application.