Classification, recommendation, and ranking problems often involve competing goals with additional constraints (e.g., to satisfy fairness or diversity criteria). Such optimization problems are quite challenging, often involving non-convex functions along with considerations of user preferences in balancing trade-offs. Pareto solutions represent optimal frontiers for jointly optimizing multiple competing objectives. A major obstacle for frequently used linear-scalarization strategies is that the resulting optimization problem might not always converge to a global optimum. Furthermore, such methods only return one solution point per run. A Pareto solution set is a subset of all such global optima over multiple runs for different trade-off choices. Therefore, a Pareto front can only be guaranteed with multiple runs of the linear-scalarization problem, where all runs converge to their respective global optima. Consequently, extracting a Pareto front for practical problems is computationally intractable with substantial computational overheads, limited scalability, and reduced accuracy. We propose a robust, low cost, two-stage, hybrid neural Pareto optimization approach that is accurate and scales (compute space and time) with data dimensions, as well as number of functions and constraints. The first stage (neural network) efficiently extracts a weak Pareto front, using Fritz-John conditions as the discriminator, with no assumptions of convexity on the objectives or constraints. The second stage (efficient Pareto filter) extracts the strong Pareto optimal subset given the weak front from stage 1. Fritz-John conditions provide us with theoretical bounds on approximation error between the true and network extracted weak Pareto front. Numerical experiments demonstrates the accuracy and efficiency on a canonical set of benchmark problems and a fairness optimization task from prior works.
We present Parallel Feasible Pareto Frontier Entropy Search ($\{\text{PF}\}^2$ES) -- a novel information-theoretic acquisition function for multi-objective Bayesian optimization supporting unknown constraints and batch query. Due to the complexity of characterizing the mutual information between candidate evaluations and (feasible) Pareto frontiers, existing approaches must either employ crude approximations that significantly hamper their performance or rely on expensive inference schemes that substantially increase the optimization's computational overhead. By instead using a variational low…
We propose a surrogate-assisted reference vector adaptation (SRVA) method to solve expensive multi- and many-objective optimization problems with various Pareto front shapes. SRVA is coupled with a multi-objective Bayesian optimization (MBO) algorithm using reference vectors for scalarization of objective functions. The Kriging surrogate models for MBO is used to estimate the Pareto front shape and generate adaptive reference vectors uniformly distributed on the estimated Pareto front. We combine SRVA with expected improvement of penalty-based boundary intersection as an infill criterion for M…
Groupe PSA（标致雪铁龙集团）；CNRS（法国国家科学研究中心）；École Nationale Supérieure des Mines de Saint-Étienne（圣艾蒂安国立高等矿业学校）
Optimizing nonlinear systems involving expensive computer experiments with regard to conflicting objectives is a common challenge. When the number of experiments is severely restricted and/or when the number of objectives increases, uncovering the whole set of Pareto optimal solutions is out of reach, even for surrogate-based approaches: the proposed solutions are sub-optimal or do not cover the front well. As non-compromising optimal solutions have usually little point in applications, this work restricts the search to solutions that are close to the Pareto front center. The article starts by…
Multi-objective optimization (MOO) problems are prevalent in machine learning. These problems have a set of optimal solutions, called the Pareto front, where each point on the front represents a different trade-off between possibly conflicting objectives. Recent MOO methods can target a specific desired ray in loss space however, most approaches still face two grave limitations: (i) A separate model has to be trained for each point on the front; and (ii) The exact trade-off must be known before the optimization process. Here, we tackle the problem of learning the entire Pareto front, with the …
Multi-objective optimization (MOO) is a prevalent challenge for Deep Learning, however, there exists no scalable MOO solution for truly deep neural networks. Prior work either demand optimizing a new network for every point on the Pareto front, or induce a large overhead to the number of trainable parameters by using hyper-networks conditioned on modifiable preferences. In this paper, we propose to condition the network directly on these preferences by augmenting them to the feature space. Furthermore, we ensure a well-spread Pareto front by penalizing the solutions to maintain a small angle t…
Centrum Wiskunde & Informatica（荷兰国家数学与计算机科学研究所）；Leiden University Medical Center（莱顿大学医学中心）；Delft University of Technology（代尔夫特理工大学）
Real-world problems are often multi-objective with decision-makers unable to specify a priori which trade-off between the conflicting objectives is preferable. Intuitively, building machine learning solutions in such cases would entail providing multiple predictions that span and uniformly cover the Pareto front of all optimal trade-off solutions. We propose a novel approach for multi-objective training of neural networks to approximate the Pareto front during inference. In our approach, the neural networks are trained multi-objectively using a dynamic loss function, wherein each network's los…
Improving Pareto Front Learning via Multi-Sample Hypernetworks
College of Engineering and Computer Science, VinUniversity（VinUniversity工程与计算机科学学院）；School of Applied Mathematics and Informatics, Hanoi University of Science and Technology（河内科技大学应用数学与信息学院）
Divide and Conquer: Provably Unveiling the Pareto Front with Multi-Objective Reinforcement Learning
Vrije Universiteit Brussel（布鲁塞尔自由大学）；Université de Montréal（蒙特利尔大学）；Mila - Quebec AI Institute（米拉-魁北克人工智能研究所）；University of Galway（戈尔韦大学）；City of Amsterdam（阿姆斯特丹市）；Utrecht University（乌得勒支大学）
Kyushu Sangyo University（九州产业大学）；KLab Inc.（KLab公司）；RIKEN（理化学研究所）；Tokyo Institute of Technology（东京工业大学）
A multi-objective optimization problem is $C^r$ weakly simplicial if there exists a $C^r$ surjection from a simplex onto the Pareto set/front such that the image of each subsimplex is the Pareto set/front of a subproblem, where $0\leq r\leq \infty$. This property is helpful to compute a parametric-surface approximation of the entire Pareto set and Pareto front. It is known that all unconstrained strongly convex $C^r$ problems are $C^{r-1}$ weakly simplicial for $1\leq r \leq \infty$. In this paper, we show that all unconstrained strongly convex problems are $C^0$ weakly simplicial. The usefuln…
A Two-Phase Adaptive Balanced Penalty Method for Controllable Pareto Front Learning under Split Feasibility Conditions
Faculty of Applied Mathematics and Informatics, Hanoi University of Science and Technology（应用数学与信息技术学院，河内科学技术大学）；College of Engineering and Computer Science, VinUniversity（工程与计算机科学学院，Vin大学）
School of Software Engineering, South China University of Technology（华南理工大学软件学院）；Weixin Group, Tencent（腾讯微信事业群）；Tencent AI Lab, Tencent（腾讯AI实验室）
Designing feasible and effective architectures under diverse computation budgets incurred by different applications/devices is essential for deploying deep models in practice. Existing methods often perform an independent architecture search for each target budget, which is very inefficient yet unnecessary. Moreover, the repeated independent search manner would inevitably ignore the common knowledge among different search processes and hamper the search performance. To address these issues, we seek to train a general architecture generator that automatically produces effective architectures fo…
University of Melbourne（墨尔本大学）；University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）
Algorithmic fairness seeks to identify and correct sources of bias in machine learning algorithms. Confoundingly, ensuring fairness often comes at the cost of accuracy. We provide formal tools in this work for reconciling this fundamental tension in algorithm fairness. Specifically, we put to use the concept of Pareto optimality from multi-objective optimization and seek the fairness-accuracy Pareto front of a neural network classifier. We demonstrate that many existing algorithmic fairness methods are performing the so-called linear scalarization scheme which has severe limitations in recover…
Variational Model Merging for Pareto Front Estimation in Multitask Finetuning
RIKEN Center for AI Project, Japan（日本人工智能研究中心（AI项目））；Ubiquitous Knowledge Processing Lab (UKP Lab), Department of Computer Science, Technical University of Darmstadt and National Research Center for Applied Cybersecurity ATHENE, Germany（大众知识处理实验室（UKP实验室），计算机科学系，达姆施塔特技术大学和应用网络安全国家研究中心ATHENE，德国）
We revisit the classical online portfolio selection problem. It is widely assumed that a trade-off between computational complexity and regret is unavoidable, with Cover's Universal Portfolios algorithm, SOFT-BAYES and ADA-BARRONS currently constituting its state-of-the-art Pareto frontier. In this paper, we present the first efficient algorithm, BISONS, that obtains polylogarithmic regret with memory and per-step running time requirements that are polynomial in the dimension, displacing ADA-BARRONS from the Pareto frontier. Additionally, we resolve a COLT 2020 open problem by showing that a c…
SPREAD: Sampling-based Pareto front Refinement via Efficient Adaptive Diffusion
Department of Computer Science, TU Dortmund University（计算机科学系，多特蒙德技术大学）；Lamarr Institute for Machine Learning and Artificial Intelligence（拉马尔机器学习与人工智能研究所）
Osaka University（大阪大学）；Japan Fine Ceramics Center（日本精细陶瓷中心）；Nagoya Institute of Technology（名古屋工业大学）；National Institute for Material Science（国立材料科学研究所）
This paper studies an entropy-based multi-objective Bayesian optimization (MBO). The entropy search is successful approach to Bayesian optimization. However, for MBO, existing entropy-based methods ignore trade-off among objectives or introduce unreliable approximations. We propose a novel entropy-based MBO called Pareto-frontier entropy search (PFES) by considering the entropy of Pareto-frontier, which is an essential notion of the optimality of the multi-objective problem. Our entropy can incorporate the trade-off relation of the optimal values, and further, we derive an analytical formula w…
MAP: Low-compute Model Merging with Amortized Pareto Fronts via Quadratic Approximation
University of Pennsylvania（宾夕法尼亚大学）；MILA（蒙特利尔人工智能研究院）；ServiceNow（ServiceNow公司）；Amazon AGI（亚马逊人工智能实验室）；Université de Montréal（蒙特利尔大学）；HKUST（香港科技大学）；University of Florida（佛罗里达大学）
Recent progress in model selection raises the question of the fundamental limits of these techniques. Under specific scrutiny has been model selection for general contextual bandits with nested policy classes, resulting in a COLT2020 open problem. It asks whether it is possible to obtain simultaneously the optimal single algorithm guarantees over all policies in a nested sequence of policy classes, or if otherwise this is possible for a trade-off $α\in[\frac{1}{2},1)$ between complexity term and time: $\ln(|Π_m|)^{1-α}T^α$. We give a disappointing answer to this question. Even in the purely st…
Performance optimization of deep learning models is conducted either manually or through automatic architecture search, or a combination of both. On the other hand, their performance strongly depends on the target hardware and how successfully the models were trained. We propose to use a multi-dimensional Pareto frontier to re-define the efficiency measure of candidate deep learning models, where several variables such as training cost, inference latency, and accuracy play a relative role in defining a dominant model. Furthermore, a random version of the multi-dimensional Pareto frontier is in…
Most content-based image retrieval systems consider either one single query, or multiple queries that include the same object or represent the same semantic information. In this paper we consider the content-based image retrieval problem for multiple query images corresponding to different image semantics. We propose a novel multiple-query information retrieval algorithm that combines the Pareto front method (PFM) with efficient manifold ranking (EMR). We show that our proposed algorithm outperforms state of the art multiple-query retrieval algorithms on real-world image databases. We attribut…
Lehigh University（理海大学）；The Ohio State University（俄亥俄州立大学）；Drake University（德雷克大学）；Cornell University（康奈尔大学）
Multiple-objective optimization (MOO) aims to simultaneously optimize multiple conflicting objectives and has found important applications in machine learning, such as minimizing classification loss and discrepancy in treating different populations for fairness. At optimality, further optimizing one objective will necessarily harm at least another objective, and decision-makers need to comprehensively explore multiple optima (called Pareto front) to pinpoint one final solution. We address the efficiency of finding the Pareto front. First, finding the front from scratch using stochastic multi-g…
Learning Heterogeneous Performance-Fairness Trade-offs in Federated Learning
Department of Computer Science and Engineering and the Research Institute of Trustworthy Autonomous Systems at Southern University of Science and Technology（计算机科学与工程系和可信自主系统研究 institute at 南方科技大学）
Fraunhofer Center for Machine Learning（弗劳恩霍夫机器学习中心）；Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM（弗劳恩霍夫技术与经济数学研究所ITWM）
We present a novel adaptive optimization algorithm for black-box multi-objective optimization problems with binary constraints on the foundation of Bayes optimization. Our method is based on probabilistic regression and classification models, which act as a surrogate for the optimization goals and allow us to suggest multiple design points at once in each iteration. The proposed acquisition function is intuitively understandable and can be tuned to the demands of the problems at hand. We also present a novel ellipsoid truncation method to speed up the expected hypervolume calculation in a stra…
The Pennsylvania State University（宾夕法尼亚州立大学）；Microsoft Bing（微软必应）
As algorithmic decision-making systems are becoming more pervasive, it is crucial to ensure such systems do not become mechanisms of unfair discrimination on the basis of gender, race, ethnicity, religion, etc. Moreover, due to the inherent trade-off between fairness measures and accuracy, it is desirable to learn fairness-enhanced models without significantly compromising the accuracy. In this paper, we propose Pareto efficient Fairness (PEF) as a suitable fairness notion for supervised learning, that can ensure the optimal trade-off between overall loss and other fairness criteria. The propo…
Fudan University（复旦大学）；University of Texas at Dallas（德克萨斯大学达拉斯分校）
Pareto Front (PF) modeling is essential in decision making problems across all domains such as economics, medicine or engineering. In Operation Research literature, this task has been addressed based on multi-objective optimization algorithms. However, without learning models for PF, these methods cannot examine whether a new provided point locates on PF or not. In this paper, we reconsider the task from Data Mining perspective. A novel projection based active Gaussian process regression (P- aGPR) method is proposed for efficient PF modeling. First, P- aGPR chooses a series of projection space…
C-MORL: Multi-Objective Reinforcement Learning through Efficient Discovery of Pareto Front
University of Oxford（牛津大学）；The Hong Kong University of Science and Technology（香港科学与技术大学）；Queen Mary University of London（伦敦大学玛丽女王学院）；Microsoft Research Asia（微软亚洲研究院）；Peking University（北京大学）；University of Alberta（阿尔伯塔大学）
The Chinese University of Hong Kong（香港中文大学）；Intel Corporation（英特尔公司）；Cadence Design Systems（楷登电子系统公司）
In spite of maturity to the modern electronic design automation (EDA) tools, optimized designs at architectural stage may become sub-optimal after going through physical design flow. Adder design has been such a long studied fundamental problem in VLSI industry yet designers cannot achieve optimal solutions by running EDA tools on the set of available prefix adder architectures. In this paper, we enhance a state-of-the-art prefix adder synthesis algorithm to obtain a much wider solution space in architectural domain. On top of that, a machine learning-based design space exploration methodology…
RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program（理化学研究所跨学科理论与数学科学项目）；RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）；Keio University（庆应义塾大学）；Fujitsu Limited（富士通株式会社）；Tokyo Institute of Technology（东京工业大学）；KLab Inc.（KLab株式会社）
Bézier simplex fitting algorithms have been recently proposed to approximate the Pareto set/front of multi-objective continuous optimization problems. These new methods have shown to be successful at approximating various shapes of Pareto sets/fronts when sample points exactly lie on the Pareto set/front. However, if the sample points scatter away from the Pareto set/front, those methods often likely suffer from over-fitting. To overcome this issue, in this paper, we extend the Bézier simplex model to a probabilistic one and propose a new learning algorithm of it, which falls into the framewor…
Alibaba Group（阿里巴巴集团）；Beijing Institute of Technology（北京理工大学）；Weill Cornell Medicine（威尔康奈尔医学院）
In this paper, we focus on learning effective entity matching models over multi-source large-scale data. For real applications, we relax typical assumptions that data distributions/spaces, or entity identities are shared between sources, and propose a Relaxed Multi-source Large-scale Entity-matching (RMLE) problem. Challenges of the problem include 1) how to align large-scale entities between sources to share information and 2) how to mitigate negative transfer from joint learning multi-source data. What's worse, one practical issue is the entanglement between both challenges. Specifically, in…
