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Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to…

Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level…

Machine learning (ML) methods offer a wide range of configurable hyperparameters that have a significant influence on their performance. While accuracy is a commonly used performance objective, in many settings, it is not sufficient.…

Optimization lies at the heart of machine learning and signal processing. Contemporary approaches based on the stochastic gradient method are non-adaptive in the sense that their implementation employs prescribed parameter values that need…

Optimization of conflicting functions is of paramount importance in decision making, and real world applications frequently involve data that is uncertain or unknown, resulting in multi-objective optimization (MOO) problems of stochastic…

Multi-objective optimisation is regarded as one of the most promising ways for dealing with constrained optimisation problems in evolutionary optimisation. This paper presents a theoretical investigation of a multi-objective optimisation…

This paper gives a concise overview of evolutionary algorithms for multiobjective optimization. A substantial number of evolutionary computation methods for multiobjective problem solving has been proposed so far, and an attempt of unifying…

We consider multistage stochastic optimization problems involving multiple units. Each unit is a (small) control system. Static constraints couple units at each stage. We present a mix of spatial and temporal decompositions to tackle such…

Training a single model for multilingual, multi-task speech processing (MSP) is severely hampered by conflicting objectives between tasks like speech recognition and translation. While multi-objective optimization (MOO) aims to align…

Multi-material structural topology and shape optimization problems are formulated within a phase field approach. First-order conditions are stated and the relation of the necessary conditions to classical shape derivatives are discussed. An…

We present a multi-objective portfolio decision model that involves selecting both a portfolio of projects and a set of elements to allocate to each project. Our model includes a defined set of objectives to optimize, with projects…

We study the problem of optimizing nonlinear objective functions over bipartite matchings. While the problem is generally intractable, we provide several efficient algorithms for it, including a deterministic algorithm for maximizing convex…

We develop a quadratic regularization approach for the solution of high-dimensional multistage stochastic optimization problems characterized by a potentially large number of time periods/stages (e.g. hundreds), a high-dimensional resource…

This paper addresses the problem of approximating the set of all solutions for Multi-objective Markov Decision Processes. We show that in the vast majority of interesting cases, the number of solutions is exponential or even infinite. In…

Many real-world multi-objective optimisation problems rely on computationally expensive function evaluations. Multi-objective Bayesian optimisation (BO) can be used to alleviate the computation time to find an approximated set of Pareto…

We propose a model of Pareto optimization (multi-objective programming) in the context of a categorical theory of resources. We describe how to adapt multi-objective swarm intelligence algorithms to this categorical formulation.

Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently…

We consider a multi-objective risk-averse two-stage stochastic programming problem with a multivariate convex risk measure. We suggest a convex vector optimization formulation with set-valued constraints and propose an extended version of…

Real-world experiments involve batched & delayed feedback, non-stationarity, multiple objectives & constraints, and (often some) personalization. Tailoring adaptive methods to address these challenges on a per-problem basis is infeasible,…

This paper considers the problem of maximizing multiple linear functions over the probability simplex. A classification of feasible points is indicated. A necessary and sufficient condition for a member of each class to be an efficient…