We consider applications involving a large set of instances of projecting points to polytopes. We develop an intuition guided by theoretical and empirical analysis to show that when these instances follow certain structures, a large majority of the projections lie on vertices of the polytopes. To do these projections efficiently we derive a vertex-oriented incremental algorithm to project a point onto any arbitrary polytope, as well as give specific algorithms to cater to simplex projection and polytopes where the unit box is cut by planes. Such settings are especially useful in web-scale applications such as optimal matching or allocation problems. Several such problems in internet marketplaces (e-commerce, ride-sharing, food delivery, professional services, advertising, etc.), can be formulated as Linear Programs (LP) with such polytope constraints that require a projection step in the overall optimization process. We show that in some of the very recent works, the polytopic projection is the most expensive step and our efficient projection algorithms help in gaining massive improvements in performance.

One of the most well-established applications of machine learning is in deciding what content to show website visitors. When observation data comes from high-velocity, user-generated data streams, machine learning methods perform a balancing act between model complexity, training time, and computational costs. Furthermore, when model freshness is critical, the training of models becomes time-constrained. Parallelized batch offline training, although horizontally scalable, is often not time-considerate or cost-effective. In this paper, we propose Lambda Learner, a new framework for training models by incremental updates in response to mini-batches from data streams. We show that the resulting model of our framework closely estimates a periodically updated model trained on offline data and outperforms it when model updates are time-sensitive. We provide theoretical proof that the incremental learning updates improve the loss-function over a stale batch model. We present a large-scale deployment on the sponsored content platform for a large social network, serving hundreds of millions of users across different channels (e.g., desktop, mobile). We address challenges and complexities from both algorithms and infrastructure perspectives, illustrate the system details for computation, storage, stream processing training data, and open-source the system.

We present the evolution of a large-scale content recommendation platform for LinkedIn Learning, serving 645M+ LinkedIn users across several different channels (e.g., desktop, mobile). We address challenges and complexities from both algorithms and infrastructure perspectives. We describe the progression from unsupervised models that exploit member similarity with course content, to supervised learning models leveraging member interactions with courses, and finally to hyper-personalized mixed-effects models with several million coefficients. For all the experiments, we include metric lifts achieved via online A/B tests and illustrate the trade-offs between computation and storage requirements.

This paper proposes a new unified optimization framework combining pay-per-click auctions and guaranteed delivery in sponsored search. Advertisers usually have different (and sometimes mixed) marketing goals: brand awareness and direct response. Different mechanisms are good at addressing different goals, e.g., guaranteed delivery was often used to build brand awareness and pay-per-click auctions was widely used for direct marketing. Our new method accommodates both in a unified framework, with the search engine revenue as an optimization objective. In this way, we can target a guaranteed number of ad clicks (or impressions) per campaign for advertisers willing to pay a premium and enable keyword auctions for all others. Specifically, we formulate this joint optimization problem using linear programming and a column generation strategy for efficiency. To select the best column (a ranked list of ads) given a query, we propose a novel dynamic programming algorithm that takes the special structure of the ad allocation and pricing mechanisms into account. We have tested the proposed framework and the algorithms on real ad data obtained from a commercial search engine. The results demonstrate that our proposed approach can outperform several baselines in guaranteeing the number of clicks for the given advertisers, and in increasing the total revenue for the search engine.

Popular methods for probabilistic topic modeling like the Latent Dirichlet Allocation (LDA, [1]) and Correlated Topic Models (CTM, [2]) share an important property, i.e., using a common set of topics to model all the data. This property can be too restrictive for modeling complex data entries where multiple fields of heterogeneous data jointly provide rich information about each object or event. We propose a new extension of the CTM method to enable modeling with multi-field topics in a global graphical structure, and a mean-field variational algorithm to allow joint learning of multinomial topic models from discrete data and Gaussian-style topic models for real-valued data. We conducted experiments with both simulated and real data, and observed that the multi-field CTM outperforms a conventional CTM in both likelihood maximization and perplexity reduction. A deeper analysis on the simulated data reveals that the superior performance is the result of successful discovery of the mapping among field-specific topics and observed data.

We describe a system for scheduling a conference based on incomplete information about available resources and scheduling constraints. We explain the representation of uncertain knowledge and related common-sense rules, which allow reasoning based on uncertain and partially missing data.