On E-commerce platforms, new products often suffer from the cold-start problem: limited interaction data reduces their search visibility and hurts relevance ranking. To address this, we propose a simple yet effective behavior feature boosting method that leverages substitute relationships among products (BFS). BFS identifies substitutes—products that satisfy similar user needs—and aggregates their behavioral signals (e.g., clicks, add-to-carts, purchases, and ratings) to provide a warm start for new items. Incorporating these enriched signals into ranking models mitigates cold-start effects and improves relevance and competitiveness. Experiments on a large E-commerce platform, both offline and online, show that BFS significantly improves search relevance and product discovery for cold-start products. BFS is scalable and practical, improving user experience while increasing exposure for newly launched items in E-commerce search. The BFS-enhanced ranking model has been launched in production and has served customers since 2025.

This paper introduces MO-LightGBM, an open-source library built upon LightGBM, specifically designed to offer an integrated, versatile, and easily adaptable framework for Multi-objective Learning to Rank (MOLTR). MO-LightGBM supports diverse Multi-objective optimization (MOO) settings and incorporates 12 state-of-the-art optimization strategies. Its modular architecture enhances usability and flexibility, allowing researchers and practitioners to easily develop new MOO methodologies, perform rigorous comparisons with existing techniques, and effectively deploy MOO algorithms in practical ranking applications. We illustrate the utility of MO-LightGBM through a Bi-objective Learning to Rank example and present visualizations of the results. MO-LightGBM is available at https://github.com/amazon-science/MO-LightGBM.

Recently, multi-objective optimization (MOO) has gained attention for its broad applications in ML, operations research, and engineering. However, MOO algorithm design remains in its infancy and many existing MOO methods suffer from unsatisfactory convergence rate and sample complexity performance. To address this challenge, in this paper, we propose an algorithm called STIMULUS (**st**ochastic path-**i**ntegrated **mul**ti-gradient rec**u**rsive e**s**timator), a new and robust approach for solving MOO problems. Different from the traditional methods, STIMULUS introduces a simple yet powerful recursive framework for updating stochastic gradient estimates to improve convergence performance with low sample complexity. In addition, we introduce an enhanced version of \algns, termed \algmns, which incorporates a momentum term to further expedite convergence. We establish $\mathcal{O}(1/T)$ convergence rates of the proposed methods for non-convex settings and $\mathcal{O}(\exp{-\mu T})$ for strongly convex settings, where $T$ is the total number of iteration rounds. Additionally, we achieve the state-of-the-art $O\left(n+\sqrt{n}\epsilon^{-1}\right)$ sample complexities for non-convex settings and $\mathcal{O}\left(n+ \sqrt{n} \ln ({\mu/\epsilon})\right)$ for strongly convex settings, where $\epsilon>0$ is a desired stationarity error. Moreover, to alleviate the periodic full gradient evaluation requirement in STIMULUS and STIMULUS-M, we further propose enhanced versions with adaptive batching called STIMULUS$^+$/ STIMULUS-M$^+$ and provide their theoretical analysis.

In e-commerce recommender systems, providing product suggestions to customers that are often bought together, which is called “complementary recommendation,” not only improves customer experience but also boosts business impact. However, in practice, it is highly challenging to efficiently extract the complementary relations between the items due to noisy and low coverage of the co-purchased records in transaction datasets. To address these challenges, graph neural networks (GNN) have been increasingly adopted in complementary item recommendations thanks to their capabilities in integrating side-information and topological structures to extract these complex item relationships. However, most existing GNN-based methods fall short in learning better product complementary representation since they often utilize a simple one-to-one product-to-vector mapping strategy, which fails to describe the transitive logic of complementary items. To overcome this challenge, we propose a new GNN model called transitivity-encoded graph attention networks (TransGAT). To our knowledge, TransGAT is the first method that extends representation space by encoding the behavioral direction into embedding space in GNN and enabling mutual relationship extraction between complementary items. In order to better extract customer's intrinsic behavioral information, we further adopt the substitute information as the guidance by jointly learning complements and substitutes graphs and coupling them together. Moreover, several self-supervised data augmentation strategies are incorporated in our approach. Through evaluations on three real-world datasets, TransGAT consistently surpasses contemporary benchmarks, showcasing its prowess in complementary item recommendations.

Reinforcement learning with multiple, potentially conflicting objectives is pervasive in real-world applications, while this problem remains theoretically under-explored. This paper tackles the multi-objective reinforcement learning (MORL) problem and introduces an innovative actor-critic algorithm named MOAC which finds a policy by iteratively making trade-offs among conflicting reward signals. Notably, we provide the first analysis of finite-time Pareto-stationary convergence and corresponding sample complexity in both discounted and average reward settings. Our approach has two salient features: (a) MOAC mitigates the cumulative estimation bias resulting from finding an optimal common gradient descent direction out of stochastic samples. This enables provable convergence rate and sample complexity guarantees independent of the number of objectives; (b) With proper momentum coefficient, MOAC initializes the weights of individual policy gradients using samples from the environment, instead of manual initialization. This enhances the practicality and robustness of our algorithm. Finally, experiments conducted on a real-world dataset validate the effectiveness of our proposed method.

Learning to Rank (LTR) technique is ubiquitous in Information Retrieval systems, especially in search ranking applications. The relevance labels used to train ranking models are often noisy measurements of human behavior, such as product ratings in product searches. This results in non-unique ground truth rankings and ambiguity. To address this, Multi-Label LTR (MLLTR) is used to train models using multiple relevance criteria, capturing conflicting but important goals, such as product quality and purchase likelihood for improved revenue in product searches. This research leverages Multi-Objective Optimization (MOO) in MLLTR and employs modern MOO algorithms to solve the problem. A general framework is proposed to combine label information to characterize trade-offs among goals, and allows for the use of gradient-based MOO algorithms. We test the proposed framework on four publicly available LTR datasets and one E-commerce dataset to show its efficacy.

In Learning-to-Rank (LTR) problems, the task of delivering relevant search results and allocating fair exposure to items of a protected group can conflict. Previous works in Fair LTR have attempted to resolve this by combining the objectives of relevant ranking and fair ranking into a single linear combination, but this approach is limited by the nonconvexity of the objective functions and can result in suboptimal relevance in ranking outputs. To address this, we propose a solution using Multi-Objective Optimization (MOO) algorithms. We extend these algorithms to querywise MOO to reduce the exposure disparity, not only on average but also at the query level. Interestingly, for moderate fairness requirements, it improves the relevance of ranking instead of deteriorating. We attribute this improvement to the benefits of multi-task learning and study the effect of fair ranking on the relevant ranking task. Moreover, we significantly improve the computational efficiency compared to previous methods by using the Gumbel max trick to sample the Plackett-Luce distribution. We evaluate our proposed methods on three real-world datasets and show their improvement in relevance ranking over state-of-the-art solutions.

In recent years, multi-objective optimization (MOO) emerges as a foundational problem underpinning many multi-agent multi-task learning applications. However, existing algorithms in MOO literature remain limited to centralized learning settings, which do not satisfy the distributed nature and data privacy needs of such multi-agent multi-task learning applications. This motivates us to propose a new federated multi-objective learning (FMOL) framework with multiple clients distributively and collaboratively solving an MOO problem while keeping their training data private. Notably, our FMOL framework allows a different set of objective functions across different clients to support a wide range of applications, which advances and generalizes the MOO formulation to the federated learning paradigm for the first time. For this FMOL framework, we propose two new federated multi-objective optimization (FMOO) algorithms called federated multi-gradient descent averaging (FMGDA) and federated stochastic multi-gradient descent averaging (FSMGDA). Both algorithms allow local updates to significantly reduce communication costs, while achieving the {\em same} convergence rates as those of their algorithmic counterparts in the single-objective federated learning. Our extensive experiments also corroborate the efficacy of our proposed FMOO algorithms.

Multi-objective optimization (MOO) and multi-task learning (MTL) have gained much popularity with prevalent use cases such as production model development of regression / classification / ranking models with MOO, and training deep learning models with MTL. Despite the long history of research in MOO, its application to machine learning requires development of solution strategy, and algorithms have recently been developed to solve specific problems such as discovery of any Pareto optimal (PO) solution, and that with a particular form of preference. In this paper, we develop a novel and generic framework to discover a PO solution with multiple forms of preferences. It allows us to formulate a generic MOO / MTL problem to express a preference, which is solved to achieve both alignment with the preference and PO, at the same time. Specifically, we apply the framework to solve the weighted Chebyshev problem and an extension of that. The former is known as a method to discover the Pareto front, the latter helps to find a model that outperforms an existing model with only one run. Experimental results demonstrate not only the method achieves competitive performance with existing methods, but also it allows us to achieve the performance from different forms of preferences.

Today, recommender systems have played an increasingly important role in shaping our experiences of digital environments and social interactions. However, as recommender systems become ubiquitous in our society, recent years have also witnessed significant fairness concerns for recommender systems. Specifically, studies have shown that recommender systems may inherit or even amplify biases from historical data, and as a result, provide unfair recommendations. To address fairness risks in recommender systems, most of the previous approaches to date are focused on modifying either the existing training data samples or the deployed recommender algorithms, but unfortunately with limited degrees of success. In this paper, we propose a new approach called fair recommendation with optimized antidote data (FairRoad), which aims to improve the fairness performances of recommender systems through the construction of a small and carefully crafted antidote dataset. Toward this end, we formulate our antidote data generation task as a mathematical optimization problem, which minimizes the unfairness of the targeted recommender systems while not disrupting the deployed recommendation algorithms. Extensive experiments show that our proposed antidote data generation algorithm significantly improve the fairness of recommender systems with a small amounts of antidote data.

In this paper, we propose a framework to make the text clustering process, as a whole, efficient. In a real text clustering task, an analyst usually has some expectation on the results in mind. However, a single run of a clustering algorithm on the preprocessed data would not satisfy the expectation. Then the analyst faces labor-intensive trials for improving the results that involve repetitive feature refinement and parameter tuning. We develop the Iterative and Interactive Metric Learning System (IIMLS) for addressing the challenge. Specifically, IIMLS allows analysts to input feedback on a current clustering result. Given the feedback, IIMLS optimizes metric in the feature space so that the clustering algorithm applied with the refined metric would reflect the feedback. As a byproduct, learned metric may be used for a similar dataset. Illustrative examples on a real-world dataset show IIMLS can dramatically improve efficiency of a text clustering task. The learned ¿knowledge¿, or the metric, is visualized for gaining insights of the optimized feature metric.

Kernel partial least squares (KPLS) has been known as a generic kernel regression method and proven to be competitive with other kernel regression methods such as support vector machines for regression (SVM) and kernel ridge regression. Kernel boosted latent features (KBLF) is a variant of KPLS for any differentiable convex loss functions. It provides a more flexible framework for various predictive modeling tasks such as classification with logistic loss and robust regression with L1 norm loss, etc. However, KPLS and KBLF solutions are dense and thus not suitable for large-scale computations. Sparsification of KPLS solutions has been studied for dual and primal forms. For dual sparsity, it requires solving a nonlinear optimization problem at every iteration step and its computational burden limits its applicability to general regression tasks.In this paper, we propose simple heuristics to approximate sparse solutions for KPLS and the framework is also applied for sparsifying KBLF solutions. The algorithm provides an interesting "path" from a maximum residual criterion based algorithm with orthogonality conditions to the dense KPLS/KBLF. With the orthogonality, it differentiates itself from many existing forward selection-type algorithms. The computational advantage is illustrated by benchmark datasets and comparison to SVM is done.

Support Vector Machines and other kernel methods have proven to be very effective for nonlinear inference. Practical issues are how to select the type of kernel including any parameters and how to deal with the computational issues caused by the fact that the kernel matrix grows quadratically with the data. Inspired by ensemble and boosting methods like MART, we propose the Multiple Additive Regression Kernels (MARK) algorithm to address these issues. MARK considers a large (potentially infinite) library of kernel matrices formed by different kernel functions and parameters. Using gradient boosting/column generation, MARK constructs columns of the heterogeneous kernel matrix (the base hypotheses) on the fly and then adds them into the kernel ensemble. Regularization methods such as used in SVM, kernel ridge regression, and MART, are used to prevent overfitting. We investigate how MARK is applied to heterogeneous kernel ridge regression. The resulting algorithm is simple to implement and efficient. Kernel parameter selection is handled within MARK. Sampling and "weak" kernels are used to further enhance the computational efficiency of the resulting additive algorithm. The user can incorporate and potentially extract domain knowledge by restricting the kernel library to interpretable kernels. MARK compares very favorably with SVM and kernel ridge regression on several benchmark datasets.

We develop a fully-automated pattern search methodology for model selection of support vector machines (SVMs) for regression and classification. Pattern search (PS) is a derivative-free optimization method suitable for low-dimensional optimization problems for which it is difficult or impossible to calculate derivatives. This methodology was motivated by an application in drug design in which regression models are constructed based on a few high-dimensional exemplars. Automatic model selection in such underdetermined problems is essential to avoid overfitting and overestimates of generalization capability caused by selecting parameters based on testing results. We focus on SVM model selection for regression based on leave-one-out (LOO) and cross-validated estimates of mean squared error, but the search strategy is applicable to any model criterion. Because the resulting error surface produces an extremely noisy map of the model quality with many local minima, the resulting generalization capacity of any single local optimal model illustrates high variance. Thus several locally optimal SVM models are generated and then bagged or averaged to produce the final SVM. This strategy of pattern search combined with model averaging has proven to be very effective on benchmark tests and in high-variance drug design domains with high potential of overfitting.