This paper provides the first sample complexity lower bounds for the estimation of simple diffusion models, including the Bass model (used in modeling consumer adoption) and the SIR model (used in modeling epidemics). We show that one cannot hope to learn such models until quite late in the diffusion. Specifically, we show that the time required to collect a number of observations that exceeds our sample complexity lower bounds is large. For Bass models with low innovation rates, our results imply that one cannot hope to predict the eventual number of adopting customers until one is at least two-thirds of the way to the time at which the rate of new adopters is at its peak. In a similar vein, our results imply that in the case of an SIR model, one cannot hope to predict the eventual number of infections until one is approximately two-thirds of the way to the time at which the infection rate has peaked. This lower bound in estimation further translates into a lower bound in regret for decision-making in epidemic interventions. Our results formalize the challenge of accurate forecasting and highlight the importance of incorporating additional data sources. To this end, we analyze the benefit of a seroprevalence study in an epidemic, where we characterize the size of the study needed to improve SIR model estimation. Extensive empirical analyses on product adoption and epidemic data support our theoretical findings.

We describe the current content moderation strategy employed by Meta to remove policy-violating content from its platforms. Meta relies on both handcrafted and learned risk models to flag potentially violating content for human review. Our approach aggregates these risk models into a single ranking score, calibrating them to prioritize more reliable risk models. A key challenge is that violation trends change over time, affecting which risk models are most reliable. Our system additionally handles production challenges such as changing risk models and novel risk models. We use a contextual bandit to update the calibration in response to such trends. Our approach increases Meta's top-line metric for measuring the effectiveness of its content moderation strategy by 13%.

Personalization and recommendations are now accepted as core competencies in just about every online setting, ranging from media platforms to e-commerce to social networks. While the challenge of estimating user preferences has garnered significant attention, the operational problem of using such preferences to construct personalized offer sets to users is still a challenge, particularly in modern settings where a massive number of items and a millisecond response time requirement mean that even enumerating all of the items is impossible. Faced with such settings, existing techniques are either (a) entirely heuristic with no principled justification, or (b) theoretically sound, but simply too slow to work. Thus motivated, we propose an algorithm for personalized offer set optimization that runs in time sub-linear in the number of items while enjoying a uniform performance guarantee. Our algorithm works for an extremely general class of problems and models of user choice that includes the mixed multinomial logit model as a special case. We achieve a sub-linear runtime by leveraging the dimensionality reduction from learning an accurate latent factor model, along with existing sub-linear time approximate near neighbor algorithms. Our algorithm can be entirely data-driven, relying on samples of the user, where a `sample' refers to the user interaction data typically collected by firms. We evaluate our approach on a massive content discovery dataset from Outbrain that includes millions of advertisements. Results show that our implementation indeed runs fast and with increased performance relative to existing fast heuristics.

In this paper, we consider a novel variant of the multi-armed bandit (MAB) problem, \emph{MAB with cost subsidy}, which models many real-life applications where the learning agent has to pay to select an arm and is concerned about optimizing cumulative costs and rewards. We present two applications, \emph{intelligent SMS routing problem} and \emph{ad audience optimization problem} faced by a number of businesses (especially online platforms) and show how our problem uniquely captures key features of these applications. We show that naive generalizations of existing MAB algorithms like Upper Confidence Bound and Thompson Sampling do not perform well for this problem. We then establish fundamental lower bound of $\Omega(K^{1/3} T^{2/3})$ on the performance of any online learning algorithm for this problem, highlighting the hardness of our problem in comparison to the classical MAB problem (where $T$ is the time horizon and $K$ is the number of arms). We also present a simple variant of \textit{explore-then-commit} and establish near-optimal regret bounds for this algorithm. Lastly, we perform extensive numerical simulations to understand the behavior of a suite of algorithms for various instances and recommend a practical guide to employ different algorithms.

We study the problem of modeling purchase of multiple items and utilizing it to display optimized recommendations, which is a central problem for online e-commerce platforms. Rich personalized modeling of users and fast computation of optimal products to display given these models can lead to significantly higher revenues and simultaneously enhance the end user experience. We present a parsimonious multi-purchase family of choice models called the BundleMVL-K family, and develop a binary search based iterative strategy that efficiently computes optimized recommendations for this model. This is one of the first attempts at operationalizing multi-purchase class of choice models. We characterize structural properties of the optimal solution, which allow one to decide if a product is part of the optimal assortment in constant time, reducing the size of the instance that needs to be solved computationally. We also establish the hardness of computing optimal recommendation sets. We show one of the first quantitative links between modeling multiple purchase behavior and revenue gains. The efficacy of our modeling and optimization techniques compared to competing solutions is shown using several real world datasets on multiple metrics such as model fitness, expected revenue gains and run-time reductions. The benefit of taking multiple purchases into account is observed to be $6-8\%$ in relative terms for the Ta Feng and UCI shopping datasets when compared to the MNL model for instances with $\sim 1500$ products. Additionally, across $8$ real world datasets, the test log-likelihood fits of our models are on average $17\%$ better in relative terms. The simplicity of our models and the iterative nature of our optimization technique allows practitioners meet stringent computational constraints while increasing their revenues in practical recommendation applications at scale.