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We consider De Finetti's control problem for absolutely continuous strategies with control rates bounded by a concave function and prove that a generalized mean-reverting strategy is optimal. In order to solve this problem, we need to deal…
Evolutionary multi-objective algorithms have successfully been used in the context of Pareto optimization where a given constraint is relaxed into an additional objective. In this paper, we explore the use of 3-objective formulations for…
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…
Aligning large language models (LLMs) with human preferences is critical for enhancing LLMs' safety, helpfulness, humor, faithfulness, etc. Current reinforcement learning from human feedback (RLHF) mainly focuses on a fixed reward learned…
This paper deals with Pareto solutions of a nonsmooth fractional interval-valued multiobjective optimization. We first introduce four types of Pareto solutions of the considered problem by considering the lower-upper interval order relation…
In classic reinforcement learning (RL) and decision making problems, policies are evaluated with respect to a scalar reward function, and all optimal policies are the same with regards to their expected return. However, many real-world…
We present a review that unifies decision-support methods for exploring the solutions produced by multi-objective optimization (MOO) algorithms. As MOO is applied to solve diverse problems, approaches for analyzing the trade-offs offered by…
In the present paper, some aspects of the finite-dimensional theory of set-inclusive generalized equations are studied. Set-inclusive generalized equations are problems arising in several contexts of optimization and variational analysis,…
Most existing studies on evolutionary multi-objective optimization focus on approximating the whole Pareto-optimal front. Nevertheless, rather than the whole front, which demands for too many points (especially in a high-dimensional space),…
Modern machine learning tasks often require considering not just one but multiple objectives. For example, besides the prediction quality, this could be the efficiency, robustness or fairness of the learned models, or any of their…
A traditional and intuitively appealing Multi-Task Multiple Kernel Learning (MT-MKL) method is to optimize the sum (thus, the average) of objective functions with (partially) shared kernel function, which allows information sharing amongst…
For a control problem with multiple conflicting objectives, there exists a set of Pareto-optimal policies called the Pareto set instead of a single optimal policy. When a multi-objective control problem is continuous and complex,…
This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…
We consider a class of infinite-dimensional optimization problems in which a distributed vector-valued variable should pointwise almost everywhere take values from a given finite set $\mathcal{M}\subset\mathbb{R}^m$. Such hybrid…
This paper is devoted to general nonconvex problems of multiobjective optimization in Hilbert spaces. Based on Mordukhovich's limiting subgradients, we define a new notion of Pareto critical points for such problems, establish necessary…
In planning problems, it is often challenging to fully model the desired specifications. In particular, in human-robot interaction, such difficulty may arise due to human's preferences that are either private or complex to model.…
Many real world problems can be defined as optimisation problems in which the aim is to maximise an objective function. The quality of obtained solution is directly linked to the pertinence of the used objective function. However, designing…
Vector optimization problems are a generalization of multiobjective optimization in which the preference order is related to an arbitrary closed and convex cone, rather than the nonnegative octant. Due to its real life applications, it is…
The paper is devoted to the study of regularized versions of multiobjective optimization problems described by directionally Lipschitzian functions. Such regularizations appear in proximal-type algorithms of multiobjective optimization,…
This paper presents a convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems that are non-convex in the input norm, which is a…