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In this work, we propose a novel method to tackle the problem of multiobjective optimization under parameteric uncertainties, by considering the Conditional Pareto Sets and Conditional Pareto Fronts. Based on those quantities we can define…

Optimization and Control · Mathematics 2026-01-15 Victor Trappler , Céline Helbert , Rodolphe Le Riche

Multi-objective optimization (MOO) problems require balancing competing objectives, often under constraints. The Pareto optimal solution set defines all possible optimal trade-offs over such objectives. In this work, we present a novel…

Machine Learning · Computer Science 2022-04-19 Soumyajit Gupta , Gurpreet Singh , Raghu Bollapragada , Matthew Lease

Optimization problems have been the subject of statistical physics approximations. A specially relevant and general scenario is provided by optimization methods considering tradeoffs between cost and efficiency, where optimal solutions…

Statistical Mechanics · Physics 2015-09-16 Luís F. Seoane , Ricard V. Solé

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…

Machine Learning · Computer Science 2021-10-20 Timo M. Deist , Monika Grewal , Frank J. W. M. Dankers , Tanja Alderliesten , Peter A. N. Bosman

Deep learning models form one of the most powerful machine learning models for the extraction of important features. Most of the designs of deep neural models, i.e., the initialization of parameters, are still manually tuned. Hence,…

Machine Learning · Computer Science 2023-05-18 Mrittika Chakraborty , Wreetbhas Pal , Sanghamitra Bandyopadhyay , Ujjwal Maulik

An important challenge in multi-objective reinforcement learning is obtaining a Pareto front of policies to attain optimal performance under different preferences. We introduce Iterated Pareto Referent Optimisation (IPRO), which decomposes…

Machine Learning · Computer Science 2025-02-07 Willem Röpke , Mathieu Reymond , Patrick Mannion , Diederik M. Roijers , Ann Nowé , Roxana Rădulescu

Design problems in industrial engineering often involve a large number of design variables with multiple objectives, under complex nonlinear constraints. The algorithms for multiobjective problems can be significantly different from the…

Optimization and Control · Mathematics 2013-03-27 Xin-She Yang

Deep reinforcement learning (DRL) has recently shown its success in tackling complex combinatorial optimization problems. When these problems are extended to multiobjective ones, it becomes difficult for the existing DRL approaches to…

Artificial Intelligence · Computer Science 2022-02-15 Zizhen Zhang , Zhiyuan Wu , Hang Zhang , Jiahai Wang

We propose a novel framework for optimizing injection strategies in large-scale CO$_2$ storage combining multi-agent models with multi-objective optimization, and reservoir simulation. We investigate whether agents should form coalitions…

Numerical Analysis · Mathematics 2024-06-13 Per Pettersson , Sebastian Krumscheid , Sarah Gasda

Multiobjective combinatorial optimization (MOCO) problems can be found in many real-world applications. However, exactly solving these problems would be very challenging, particularly when they are NP-hard. Many handcrafted heuristic…

Machine Learning · Computer Science 2022-05-10 Xi Lin , Zhiyuan Yang , Qingfu Zhang

Prior work in multi-objective reinforcement learning typically uses linear reward scalarization with fixed weights, which provably fails to capture non-convex Pareto fronts and thus yields suboptimal results. This limitation becomes…

Machine Learning · Computer Science 2026-04-01 Yining Lu , Zilong Wang , Shiyang Li , Xin Liu , Changlong Yu , Qingyu Yin , Zhan Shi , Zixuan Zhang , Meng Jiang

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…

Machine Learning · Computer Science 2021-04-27 Aviv Navon , Aviv Shamsian , Gal Chechik , Ethan Fetaya

Many machine learning tasks aim to find models that work well not for a single, but for a group of criteria, often opposing ones. One such example is imbalanced data classification, where, on the one hand, we want to achieve the best…

Machine Learning · Computer Science 2025-11-18 Szymon Wojciechowski , Michał Woźniak

Post-training of LLMs with RLHF, and subsequently preference optimization algorithms such as DPO, IPO, etc., made a big difference in improving human alignment. However, all such techniques can only work with a single (human) objective. In…

Machine Learning · Computer Science 2025-05-19 Akhil Agnihotri , Rahul Jain , Deepak Ramachandran , Zheng Wen

To date, the multi-objective optimization literature has mainly focused on conflicting objectives, studying the Pareto front, or requiring users to balance tradeoffs. Yet, in machine learning practice, there are many scenarios where such…

Machine Learning · Computer Science 2025-03-05 Yonathan Efroni , Ben Kretzu , Daniel Jiang , Jalaj Bhandari , Zheqing , Zhu , Karen Ullrich

In multiobjective optimisation, a set of scalable test problems with a variety of features allow researchers to investigate and evaluate the abilities of different optimisation algorithms, and thus can help them to design and develop more…

Neural and Evolutionary Computing · Computer Science 2022-08-24 Liangli Zhen , Miqing Li , Ran Cheng , Dezhong Peng , Xin Yao

A novel method, the Pareto Envelope Augmented with Reinforcement Learning (PEARL), has been developed to address the challenges posed by multi-objective problems, particularly in the field of engineering where the evaluation of candidate…

Machine Learning · Computer Science 2024-03-19 Paul Seurin , Koroush Shirvan

The goal of multi-objective optimization is to understand optimal trade-offs between competing objective functions by finding the Pareto front, i.e., the set of all Pareto optimal solutions, where no objective can be improved without…

Multi-objective optimization (MOO) arises in many real-world applications where trade-offs between competing objectives must be carefully balanced. In the offline setting, where only a static dataset is available, the main challenge is…

Machine Learning · Computer Science 2026-02-16 Jatan Shrestha , Santeri Heiskanen , Kari Hepola , Severi Rissanen , Pekka Jääskeläinen , Joni Pajarinen

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…

Machine Learning · Computer Science 2021-10-15 Michael Ruchte , Josif Grabocka
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