ID-based embeddings are widely used in web-scale online recommendation systems. However, their susceptibility to overfitting, particularly due to the long-tail nature of data distributions, often limits training to a single epoch, a phenomenon known as the "one-epoch problem." This challenge has driven research efforts to optimize performance within the first epoch by enhancing convergence speed or feature sparsity. In this study, we introduce a novel two-stage training strategy that incorporates a pre-training phase using a minimal model with contrastive loss, enabling broader data coverage for the embedding system. Our offline experiments demonstrate that multi-epoch training during the pre-training phase does not lead to overfitting, and the resulting embeddings improve online generalization when fine-tuned for more complex downstream recommendation tasks. We deployed the proposed system in live traffic at Pinterest, achieving significant site-wide engagement gains.

Sequential models that encode user activity for next action prediction have become a popular design choice for building web-scale personalized recommendation systems. Traditional methods of sequential recommendation either utilize end-to-end learning on realtime user actions, or learn user representations separately in an offline batch-generated manner. This paper (1) presents Pinterest's ranking architecture for Homefeed, our personalized recommendation product and the largest engagement surface; (2) proposes TransAct, a sequential model that extracts users' short-term preferences from their realtime activities; (3) describes our hybrid approach to ranking, which combines end-to-end sequential modeling via TransAct with batch-generated user embeddings. The hybrid approach allows us to combine the advantages of responsiveness from learning directly on realtime user activity with the cost-effectiveness of batch user representations learned over a longer time period. We describe the results of ablation studies, the challenges we faced during productionization, and the outcome of an online A/B experiment, which validates the effectiveness of our hybrid ranking model. We further demonstrate the effectiveness of TransAct on other surfaces such as contextual recommendations and search. Our model has been deployed to production in Homefeed, Related Pins, Notifications, and Search at Pinterest.

Probabilistic inference in pairwise Markov Random Fields (MRFs), i.e. computing the partition function or computing a MAP estimate of the variables, is a foundational problem in probabilistic graphical models. Semidefinite programming relaxations have long been a theoretically powerful tool for analyzing properties of probabilistic inference, but have not been practical owing to the high computational cost of typical solvers for solving the resulting SDPs. In this paper, we propose an efficient method for computing the partition function or MAP estimate in a pairwise MRF by instead exploiting a recently proposed coordinate-descent-based fast semidefinite solver. We also extend semidefinite relaxations from the typical binary MRF to the full multi-class setting, and develop a compact semidefinite relaxation that can again be solved efficiently using the solver. We show that the method substantially outperforms (both in terms of solution quality and speed) the existing state of the art in approximate inference, on benchmark problems drawn from previous work. We also show that our approach can scale to large MRF domains such as fully-connected pairwise CRF models used in computer vision.

Modularity maximization has been a fundamental tool for understanding the community structure of a network, but the underlying optimization problem is nonconvex and NP-hard to solve. State-of-the-art algorithms like the Louvain or Leiden methods focus on different heuristics to help escape local optima, but they still depend on a greedy step that moves node assignment locally and is prone to getting trapped. In this paper, we propose a new class of low-cardinality algorithm that generalizes the local update to maximize a semidefinite relaxation derived from max-k-cut. This proposed algorithm is scalable, empirically achieves the global semidefinite optimality for small cases, and outperforms the state-of-the-art algorithms in real-world datasets with little additional time cost. From the algorithmic perspective, it also opens a new avenue for scaling-up semidefinite programming when the solutions are sparse instead of low-rank.

This paper proposes a new algorithm for solving MAX2SAT problems based on combining search methods with semidefinite programming approaches. Semidefinite programming techniques are well-known as a theoretical tool for approximating maximum satisfiability problems, but their application has traditionally been very limited by their speed and randomized nature. Our approach overcomes this difficult by using a recent approach to low-rank semidefinite programming, specialized to work in an incremental fashion suitable for use in an exact search algorithm. The method can be used both within complete or incomplete solver, and we demonstrate on a variety of problems from recent competitions. Our experiments show that the approach is faster (sometimes by orders of magnitude) than existing state-of-the-art complete and incomplete solvers, representing a substantial advance in search methods specialized for MAX2SAT problems.

Integrating logical reasoning within deep learning architectures has been a major goal of modern AI systems. In this paper, we propose a new direction toward this goal by introducing a differentiable (smoothed) maximum satisfiability (MAXSAT) solver that can be integrated into the loop of larger deep learning systems. Our (approximate) solver is based upon a fast coordinate descent approach to solving the semidefinite program (SDP) associated with the MAXSAT problem. We show how to analytically differentiate through the solution to this SDP and efficiently solve the associated backward pass. We demonstrate that by integrating this solver into end-to-end learning systems, we can learn the logical structure of challenging problems in a minimally supervised fashion. In particular, we show that we can learn the parity function using single-bit supervision (a traditionally hard task for deep networks) and learn how to play 9x9 Sudoku solely from examples. We also solve a “visual Sudoku” problem that maps images of Sudoku puzzles to their associated logical solutions by combining our MAXSAT solver with a traditional convolutional architecture. Our approach thus shows promise in integrating logical structures within deep learning.

State-of-the-art first- and second-order optimization methods are able to achieve either fast global linear convergence rates or quadratic convergence, but not both of them. In this work, we propose an interpolation between first- and second-order methods for regularized empirical risk minimization that exploits the problem structure to efficiently combine multiple update directions. Our method attains both optimal global linear convergence rate for first-order methods, and local quadratic convergence. Experimental results show that our method outperforms state-of-the-art first- and second-order optimization methods in terms of the number of data accesses, while is competitive in training time.

Distributed optimization has become an important research topic for dealing with extremely large volume of data available in the Internet companies nowadays. Additional machines make computation less expensive, but inter-machine communication becomes prominent in the optimization process, and efficient optimization methods should reduce the amount of the communication in order to achieve shorter overall running time. In this work, we utilize the advantages of the recently proposed, theoretically fast-convergent common-directions method, but tackle its main drawback of excessive spatial and computational costs to propose a limited-memory algorithm. The result is an efficient, linear-convergent optimization method for paraliel/distributed optimization. We further discuss how our method can exploit the problem structure to efficiently train regularized empirical risk minimization (ERM) models. Experimental results show that our method outperforms state-of-the-art distributed optimization methods for ERM problems.

This paper develops an approach for efficiently solving general convex optimization problems specified as disciplined convex programs (DCP), a common general-purpose modeling framework. Specifically we develop an algorithm based upon fast epigraph projections, projections onto the epigraph of a convex function, an approach closely linked to proximal operator methods. We show that by using these operators, we can solve any disciplined convex program without transforming the problem to a standard cone form, as is done by current DCP libraries. We then develop a large library of efficient epigraph projection operators, mirroring and extending work on fast proximal algorithms, for many common convex functions. Finally, we evaluate the performance of the algorithm, and show it often achieves order of magnitude speedups over existing general-purpose optimization solvers.