Large scale multi-objective optimization: Theoretical and practical challenges

Multi-objective optimization (MOO) is a well-studied problem for several important recommendation problems. While multiple approaches have been proposed, in this work, we focus on using constrained optimization formulations (e.g., quadratic and linear programs) to formulate and solve MOO problems. This approach can be used to pick desired operating points on the trade-off curve between multiple objectives. It also works well for internet applications which serve large volumes of online traffic, by working with Lagrangian duality formulation to connect dual solutions (computed offline) with the primal solutions (computed online). We identify some key limitations of this approach -- namely the inability to handle user and item level constraints, scalability considerations and variance of dual estimates introduced by sampling processes. We propose solutions for each of the problems and demonstrate how through these solutions we significantly advance the state-of-the-art in this realm. Our proposed methods can exactly handle user and item (and other such local) constraints, achieve a $100\times$ scalability boost over existing packages in R and reduce variance of dual estimates by two orders of magnitude.Comment: 10 pages, 2 figures, KDD'16 Submitted Versio

Constrained Multi-Slot Optimization for Ranking Recommendations

Ranking items to be recommended to users is one of the main problems in large scale social media applications. This problem can be set up as a multi-objective optimization problem to allow for trading off multiple, potentially conflicting objectives (that are driven by those items) against each other. Most previous approaches to this problem optimize for a single slot without considering the interaction effect of these items on one another. In this paper, we develop a constrained multi-slot optimization formulation, which allows for modeling interactions among the items on the different slots. We characterize the solution in terms of problem parameters and identify conditions under which an efficient solution is possible. The problem formulation results in a quadratically constrained quadratic program (QCQP). We provide an algorithm that gives us an efficient solution by relaxing the constraints of the QCQP minimally. Through simulated experiments, we show the benefits of modeling interactions in a multi-slot ranking context, and the speed and accuracy of our QCQP approximate solver against other state of the art methods.Comment: 12 Pages, 6 figure

A Real-Time Whole Page Personalization Framework for E-Commerce

E-commerce platforms consistently aim to provide personalized recommendations to drive user engagement, enhance overall user experience, and improve business metrics. Most e-commerce platforms contain multiple carousels on their homepage, each attempting to capture different facets of the shopping experience. Given varied user preferences, optimizing the placement of these carousels is critical for improved user satisfaction. Furthermore, items within a carousel may change dynamically based on sequential user actions, thus necessitating online ranking of carousels. In this work, we present a scalable end-to-end production system to optimally rank item-carousels in real-time on the Walmart online grocery homepage. The proposed system utilizes a novel model that captures the user's affinity for different carousels and their likelihood to interact with previously unseen items. Our system is flexible in design and is easily extendable to settings where page components need to be ranked. We provide the system architecture consisting of a model development phase and an online inference framework. To ensure low-latency, various optimizations across these stages are implemented. We conducted extensive online evaluations to benchmark against the prior experience. In production, our system resulted in an improvement in item discovery, an increase in online engagement, and a significant lift on add-to-carts (ATCs) per visitor on the homepage