Recommender systems need to mirror the complexity of the environment they are applied in. The more we know about what might benefit the user, the more objectives the recommender system has. In addition there may be multiple stakeholders - sellers, buyers, shareholders - in addition to legal and ethical constraints. Simultaneously optimizing for a multitude of objectives, correlated and not correlated, having the same scale or not, has proven difficult so far.
We introduce a stochastic multi-gradient descent approach to recommender systems (MGDRec) to solve this problem. We show that this exceeds state-of-the-art methods in traditional objective mixtures, like revenue and recall. Not only that, but through gradient normalization we can combine fundamentally different objectives, having diverse scales, into a single coherent framework. We show that uncorrelated objectives, like the proportion of quality products, can be improved alongside accuracy. Through the use of stochasticity, we avoid the pitfalls of calculating full gradients and provide a clear setting for its applicability.
University of Konstanz（康斯坦茨大学）；National University of Singapore（新加坡国立大学）；Google Inc.（谷歌公司）
In recent years, interest in recommender research has shifted from explicit feedback towards implicit feedback data. A diversity of complex models has been proposed for a wide variety of applications. Despite this, learning from implicit feedback is still computationally challenging. So far, most work relies on stochastic gradient descent (SGD) solvers which are easy to derive, but in practice challenging to apply, especially for tasks with many items. For the simple matrix factorization model, an efficient coordinate descent (CD) solver has been previously proposed. However, efficient CD appr…
Swisscom（瑞士电信）；Ecole Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；Symphony
Recommender systems research tends to evaluate model performance offline and on randomly sampled targets, yet the same systems are later used to predict user behavior sequentially from a fixed point in time. Simulating online recommender system performance is notoriously difficult and the discrepancy between online and offline behaviors is typically not accounted for in offline evaluations. This disparity permits weaknesses to go unnoticed until the model is deployed in a production setting. In this paper, we first demonstrate how omitting temporal context when evaluating recommender system pe…
Though recommender systems are defined by personalization, recent work has shown the importance of additional, beyond-accuracy objectives, such as fairness. Because users often expect their recommendations to be purely personalized, these new algorithmic objectives must be communicated transparently in a fairness-aware recommender system. While explanation has a long history in recommender systems research, there has been little work that attempts to explain systems that use a fairness objective. Even though the previous work in other branches of AI has explored the use of explanations as a to…
Symphony；Swisscom（瑞士电信）；Ecole Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
Multi-objective gradient methods are becoming the standard for solving multi-objective problems. Among others, they show promising results in developing multi-objective recommender systems with both correlated and conflicting objectives. Classic multi-gradient~descent usually relies on the combination of the gradients, not including the computation of first and second moments of the gradients. This leads to a brittle behavior and misses important areas in the solution space. In this work, we create a multi-objective model-agnostic Adamize method that leverages the benefits of the Adam optimize…
A recommender system generates personalized recommendations for a user by computing the preference score of items, sorting the items according to the score, and filtering top-K items with high scores. While sorting and ranking items are integral for this recommendation procedure, it is nontrivial to incorporate them in the process of end-to-end model training since sorting is nondifferentiable and hard to optimize with gradient descent. This incurs the inconsistency issue between existing learning objectives and ranking metrics of recommenders. In this work, we present DRM (differentiable rank…
Hong Kong University of Science and Technology（香港科技大学）；Shanghai Jiao Tong University（上海交通大学）；BNU-HKBU United International College（北京师范大学-香港浸会大学联合国际学院）
Traditional recommender systems are typically passive in that they try to adapt their recommendations to the user's historical interests. However, it is highly desirable for commercial applications, such as e-commerce, advertisement placement, and news portals, to be able to expand the users' interests so that they would accept items that they were not originally aware of or interested in to increase customer interactions. In this paper, we present Influential Recommender System (IRS), a new recommendation paradigm that aims to proactively lead a user to like a given objective item by progress…
École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
Recent studies have shown that providing personalized explanations alongside recommendations increases trust and perceived quality. Furthermore, it gives users an opportunity to refine the recommendations by critiquing parts of the explanations. On one hand, current recommender systems model the recommendation, explanation, and critiquing objectives jointly, but this creates an inherent trade-off between their respective performance. On the other hand, although recent latent linear critiquing approaches are built upon an existing recommender system, they suffer from computational inefficiency …
Predictive analytics systems are currently one of the most important areas of research and development within the Artificial Intelligence domain and particularly in Machine Learning. One of the "holy grails" of predictive analytics is the research and development of the "perfect" recommendation system. In our paper, we propose an advanced pipeline model for the multi-task objective of determining product complementarity, similarity and sales prediction using deep neural models applied to big-data sequential transaction systems. Our highly parallelized hybrid model pipeline consists of both uns…
University of Oxford（牛津大学）；Max Planck Institute for Mathematics in the Sciences（马克斯·普朗克数学与自然科学研究所）；Universität Bielefeld（比勒费尔德大学）；ETH Zurich（苏黎世联邦理工学院）
We prove the local convergence to minima and estimates on the rate of convergence for the stochastic gradient descent method in the case of not necessarily globally convex nor contracting objective functions. In particular, the results are applicable to simple objective functions arising in machine learning.
VinAI Research（VinAI研究院）；Monash University（莫纳什大学）；University of Texas, Austin（德克萨斯大学奥斯汀分校）
Sampling from an unnormalized target distribution is an essential problem with many applications in probabilistic inference. Stein Variational Gradient Descent (SVGD) has been shown to be a powerful method that iteratively updates a set of particles to approximate the distribution of interest. Furthermore, when analysing its asymptotic properties, SVGD reduces exactly to a single-objective optimization problem and can be viewed as a probabilistic version of this single-objective optimization problem. A natural question then arises: "Can we derive a probabilistic version of the multi-objective …
Factorization machines (FMs) are a powerful tool for regression and classification in the context of sparse observations, that has been successfully applied to collaborative filtering, especially when side information over users or items is available. Bayesian formulations of FMs have been proposed to provide confidence intervals over the predictions made by the model, however they usually involve Markov-chain Monte Carlo methods that require many samples to provide accurate predictions, resulting in slow training in the context of large-scale data. In this paper, we propose a variational form…
LensKit is an open-source toolkit for building, researching, and learning about recommender systems. First released in 2010 as a Java framework, it has supported diverse published research, small-scale production deployments, and education in both MOOC and traditional classroom settings. In this paper, I present the next generation of the LensKit project, re-envisioning the original tool's objectives as flexible Python package for supporting recommender systems research and development. LensKit for Python (LKPY) enables researchers and students to build robust, flexible, and reproducible exper…
We study convergence properties of Stochastic Gradient Descent (SGD) for convex objectives without assumptions on smoothness or strict convexity. We consider the question of establishing that with high probability the objective evaluated at the candidate minimizer returned by SGD is close to the minimal value of the objective. We compare this result concerning the final candidate minimzer (i.e. the final model parameters learned after all gradient steps) to the online learning techniques of [Zin03] that take a rolling average of the model parameters at the different steps of SGD.
RIKEN AIP（理化学研究所先进智能项目中心）；Fujitsu Limited（富士通有限公司）；Tokyo Institute of Technology（东京工业大学）；KLab Inc.（KLab株式会社）
In this paper, we propose a strategy to construct a multi-objective optimization algorithm from a single-objective optimization algorithm by using the Bézier simplex model. Also, we extend the stability of optimization algorithms in the sense of Probability Approximately Correct (PAC) learning and define the PAC stability. We prove that it leads to an upper bound on the generalization with high probability. Furthermore, we show that multi-objective optimization algorithms derived from a gradient descent-based single-objective optimization algorithm are PAC stable. We conducted numerical experi…
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究所）；Université Grenoble Alpes（格勒诺布尔阿尔卑斯大学）
In this thesis, we focus on the design of an automatic algorithms that provide personalized ranking by adapting to the current conditions. To demonstrate the empirical efficiency of the proposed approaches we investigate their applications for decision making in recommender systems and energy systems domains. For the former, we propose novel algorithm called SAROS that take into account both kinds of feedback for learning over the sequence of interactions. The proposed approach consists in minimizing pairwise ranking loss over blocks constituted by a sequence of non-clicked items followed by t…
Geodesic Gradient Descent: A Generic and Learning-rate-free Optimizer on Objective Function-induced Manifolds
School of Information Science and Engineering, Hebei University of Science and Technology（信息科学与工程学院，河北科技大学）；School of Computer Science and Engineering, University of Electronic Science and Technology of China（计算机科学与工程学院，电子科技大学）；International Institute of Next Generation Internet, Macau University of Science and Technology（下一代互联网国际研究院，澳门科技大学）
Local Entropy Search over Descent Sequences for Bayesian Optimization
Institute for Data Science in Mechanical Engineering, RWTH Aachen University, Germany（机械工程数据科学研究所，亚琛工业大学，德国）；Learning Systems and Robotics Lab, Technical University of Munich, Germany（学习系统与机器人实验室，慕尼黑技术大学，德国）
University of Southern California（南加州大学）；University College London（伦敦大学学院）；Polytechnic University of Bari（巴里理工大学）
Recently, there has been a rising awareness that when machine learning (ML) algorithms are used to automate choices, they may treat/affect individuals unfairly, with legal, ethical, or economic consequences. Recommender systems are prominent examples of such ML systems that assist users in making high-stakes judgments. A common trend in the previous literature research on fairness in recommender systems is that the majority of works treat user and item fairness concerns separately, ignoring the fact that recommender systems operate in a two-sided marketplace. In this work, we present an optimi…
Simons Institute for the Theory of Computing（西蒙斯计算理论研究所）；University of California, Berkeley（加州大学伯克利分校）；University of California, Los Angeles（加州大学洛杉矶分校）
Although the optimization objectives for learning neural networks are highly non-convex, gradient-based methods have been wildly successful at learning neural networks in practice. This juxtaposition has led to a number of recent studies on provable guarantees for neural networks trained by gradient descent. Unfortunately, the techniques in these works are often highly specific to the particular setup in each problem, making it difficult to generalize across different settings. To address this drawback in the literature, we propose a unified non-convex optimization framework for the analysis o…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；ETH Zurich（苏黎世联邦理工学院）；EPFL（洛桑联邦理工学院）
Two popular examples of first-order optimization methods over linear spaces are coordinate descent and matching pursuit algorithms, with their randomized variants. While the former targets the optimization by moving along coordinates, the latter considers a generalized notion of directions. Exploiting the connection between the two algorithms, we present a unified analysis of both, providing affine invariant sublinear $\mathcal{O}(1/t)$ rates on smooth objectives and linear convergence on strongly convex objectives. As a byproduct of our affine invariant analysis of matching pursuit, our rates…
King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
We present a new perspective on the celebrated Sinkhorn algorithm by showing that is a special case of incremental/stochastic mirror descent. In order to see this, one should simply plug Kullback-Leibler divergence in both mirror map and the objective function. Since the problem has unbounded domain, the objective function is neither smooth nor it has bounded gradients. However, one can still approach the problem using the notion of relative smoothness, obtaining that the stochastic objective is 1-relative smooth. The discovered equivalence allows us to propose 1) new methods for optimal trans…
For strongly convex objectives that are smooth, the classical theory of gradient descent ensures linear convergence relative to the number of gradient evaluations. An analogous nonsmooth theory is challenging. Even when the objective is smooth at every iterate, the corresponding local models are unstable and the number of cutting planes invoked by traditional remedies is difficult to bound, leading to convergences guarantees that are sublinear relative to the cumulative number of gradient evaluations. We instead propose a multipoint generalization of the gradient descent iteration for local op…
University of Science and Technology of China（中国科学技术大学）；Georgia Institute of Technology（佐治亚理工学院）
This article suggests that deterministic Gradient Descent, which does not use any stochastic gradient approximation, can still exhibit stochastic behaviors. In particular, it shows that if the objective function exhibit multiscale behaviors, then in a large learning rate regime which only resolves the macroscopic but not the microscopic details of the objective, the deterministic GD dynamics can become chaotic and convergent not to a local minimizer but to a statistical distribution. A sufficient condition is also established for approximating this long-time statistical limit by a rescaled Gib…
Eindhoven University of Technology（埃因霍温理工大学）；Northwestern University（西北大学）；DePaul University（德保罗大学）；University of Colorado Boulder（科罗拉多大学博尔德分校）
Fairness is a critical system-level objective in recommender systems that has been the subject of extensive recent research. A specific form of fairness is supplier exposure fairness where the objective is to ensure equitable coverage of items across all suppliers in recommendations provided to users. This is especially important in multistakeholder recommendation scenarios where it may be important to optimize utilities not just for the end-user, but also for other stakeholders such as item sellers or producers who desire a fair representation of their items. This type of supplier fairness is…
LLM-Assisted Reranking to Operationalize Nuanced Objectives in Recommender Systems
Department of Communication, University of California, Los Angeles, CA 90095（通信系，加州大学洛杉矶分校，CA 90095）；Department of Computer and Information Science, University of Pennsylvania, Philadelphia, PA 19104（计算机与信息科学系，宾夕法尼亚大学，Philadelphia, PA 19104）；Amenenberg School of Communication, University of Pennsylvania, Philadelphia, PA 19104（安纳伯格通信学院，宾夕法尼亚大学，Philadelphia, PA 19104）；Operations, Information, and Decisions Department, University of Pennsylvania, Philadelphia, PA 19104（运营、信息与决策系，宾夕法尼亚大学，Philadelphia, PA 19104）
Ill-posed linear inverse problems appear in many scientific setups, and are typically addressed by solving optimization problems, which are composed of data fidelity and prior terms. Recently, several works have considered a back-projection (BP) based fidelity term as an alternative to the common least squares (LS), and demonstrated excellent results for popular inverse problems. These works have also empirically shown that using the BP term, rather than the LS term, requires fewer iterations of optimization algorithms. In this paper, we examine the convergence rate of the projected gradient d…
University of Pennsylvania（宾夕法尼亚大学）；Washington University in St. Louis（华盛顿大学圣路易斯分校）
Local optimization presents a promising approach to expensive, high-dimensional black-box optimization by sidestepping the need to globally explore the search space. For objective functions whose gradient cannot be evaluated directly, Bayesian optimization offers one solution -- we construct a probabilistic model of the objective, design a policy to learn about the gradient at the current location, and use the resulting information to navigate the objective landscape. Previous work has realized this scheme by minimizing the variance in the estimate of the gradient, then moving in the direction…
Predicting conversion rate (e.g., the probability that a user will purchase an item) is a fundamental problem in machine learning based recommender systems. However, accurate conversion labels are revealed after a long delay, which harms the timeliness of recommender systems. Previous literature concentrates on utilizing early conversions to mitigate such a delayed feedback problem. In this paper, we show that post-click user behaviors are also informative to conversion rate prediction and can be used to improve timeliness. We propose a generalized delayed feedback model (GDFM) that unifies bo…
Learning from the Descent Direction: Adaptive Gradient Descent under One-Sided Hölder Regularity
Weierstrass Institute for Applied Analysis and Stochastics（魏尔斯特拉斯应用分析与随机研究所）；Physikalisch-Technische Bundesanstalt (PTB)（德国联邦物理技术研究院）；Technical University of Berlin（柏林工业大学）
University of California, Berkeley（加利福尼亚大学伯克利分校）；Facebook AI Research（Facebook人工智能研究（Facebook AI Research））
We prove that stochastic gradient descent efficiently converges to the global optimizer of the maximum likelihood objective of an unknown linear time-invariant dynamical system from a sequence of noisy observations generated by the system. Even though the objective function is non-convex, we provide polynomial running time and sample complexity bounds under strong but natural assumptions. Linear systems identification has been studied for many decades, yet, to the best of our knowledge, these are the first polynomial guarantees for the problem we consider.
In this paper, we study the statistical limits in terms of Sobolev norms of gradient descent for solving inverse problem from randomly sampled noisy observations using a general class of objective functions. Our class of objective functions includes Sobolev training for kernel regression, Deep Ritz Methods (DRM), and Physics Informed Neural Networks (PINN) for solving elliptic partial differential equations (PDEs) as special cases. We consider a potentially infinite-dimensional parameterization of our model using a suitable Reproducing Kernel Hilbert Space and a continuous parameterization of …
Southern University of Science and Technology（南方科技大学）；Wuhan University（武汉大学）
Stochastic gradient descent (SGD) is a popular and efficient method with wide applications in training deep neural nets and other nonconvex models. While the behavior of SGD is well understood in the convex learning setting, the existing theoretical results for SGD applied to nonconvex objective functions are far from mature. For example, existing results require to impose a nontrivial assumption on the uniform boundedness of gradients for all iterates encountered in the learning process, which is hard to verify in practical implementations. In this paper, we establish a rigorous theoretical f…
Stochastic gradient descent (SGD) type optimization schemes are fundamental ingredients in a large number of machine learning based algorithms. In particular, SGD type optimization schemes are frequently employed in applications involving natural language processing, object and face recognition, fraud detection, computational advertisement, and numerical approximations of partial differential equations. In mathematical convergence results for SGD type optimization schemes there are usually two types of error criteria studied in the scientific literature, that is, the error in the strong sense …
In this paper, we propose and analyze algorithms for zeroth-order optimization of non-convex composite objectives, focusing on reducing the complexity dependence on dimensionality. This is achieved by exploiting the low dimensional structure of the decision set using the stochastic mirror descent method with an entropy alike function, which performs gradient descent in the space equipped with the maximum norm. To improve the gradient estimation, we replace the classic Gaussian smoothing method with a sampling method based on the Rademacher distribution and show that the mini-batch method copes…
Convergence of the gradient descent algorithm has been attracting renewed interest due to its utility in deep learning applications. Even as multiple variants of gradient descent were proposed, the assumption that the gradient of the objective is Lipschitz continuous remained an integral part of the analysis until recently. In this work, we look at convergence analysis by focusing on a property that we term as concavifiability, instead of Lipschitz continuity of gradients. We show that concavifiability is a necessary and sufficient condition to satisfy the upper quadratic approximation which i…
Recommender systems can be characterized as software solutions that provide users convenient access to relevant content. Traditionally, recommender systems research predominantly focuses on developing machine learning algorithms that aim to predict which content is relevant for individual users. In real-world applications, however, optimizing the accuracy of such relevance predictions as a single objective in many cases is not sufficient. Instead, multiple and often competing objectives have to be considered, leading to a need for more research in multi-objective recommender systems. We can di…
One of the most essential parts of any recommender system is personalization-- how acceptable the recommendations are from the user's perspective. However, in many real-world applications, there are other stakeholders whose needs and interests should be taken into account. In this work, we define the problem of multistakeholder recommendation and we focus on finding algorithms for a special case where the recommender system itself is also a stakeholder. In addition, we will explore the idea of incremental incorporation of system-level objectives into recommender systems over time to tackle the…
