Related papers: Using first-order information in Direct Multisearc…

Reinforcement learning is about learning agent models that make the best sequential decisions in unknown environments. In an unknown environment, the agent needs to explore the environment while exploiting the collected information, which…

Solutions to multi-objective optimization problems can generally not be compared or ordered, due to the lack of orderability of the single objectives. Furthermore, decision-makers are often made to believe that scaled objectives can be…

Meshless methods approximate operators in a specific node as a weighted sum of values in its neighbours. Higher order approximations of derivatives provide more accurate solutions with better convergence characteristics, but they come at…

Real-world multiobjective optimization problems usually involve conflicting objectives that change over time, which requires the optimization algorithms to quickly track the Pareto optimal front (POF) when the environment changes. In recent…

Multi-material design optimization problems can, after discretization, be solved by the iterative solution of simpler sub-problems which approximate the original problem at an expansion point to first order. In particular, models…

In a wide range of applications it is desirable to optimally control a dynamical system with respect to concurrent, potentially competing goals. This gives rise to a multiobjective optimal control problem where, instead of computing a…

Derivative-free - or zeroth-order - optimization (DFO) has gained recent attention for its ability to solve problems in a variety of application areas, including machine learning, particularly involving objectives which are stochastic…

While recent advances in preference learning have enhanced alignment in human feedback, mathematical reasoning remains a persistent challenge. We investigate how data diversification strategies in preference optimization can improve the…

Neural Architecture Search (NAS) aims to automate the discovery of high-performing deep neural network architectures. Traditional objective-based NAS approaches typically optimize a certain performance metric (e.g., prediction accuracy),…

The paper discusses derivative-free optimization (DFO), which involves minimizing a function without access to gradients or directional derivatives, only function evaluations. Classical DFO methods, which mimic gradient-based methods, such…

To acquire a new skill, humans learn better and faster if a tutor, based on their current knowledge level, informs them of how much attention they should pay to particular content or practice problems. Similarly, a machine learning model…

In this paper, we will provide an introduction to the derivative-free optimization algorithms which can be potentially applied to train deep learning models. Existing deep learning model training is mostly based on the back propagation…

Determining optimal well placements and controls are two important tasks in oil field development. These problems are computationally expensive, nonconvex, and contain multiple optima. The practical solution of these problems require…

Many modern machine learning applications, such as multi-task learning, require finding optimal model parameters to trade-off multiple objective functions that may conflict with each other. The notion of the Pareto set allows us to focus on…

Estimation of density derivatives is a versatile tool in statistical data analysis. A naive approach is to first estimate the density and then compute its derivative. However, such a two-step approach does not work well because a good…

This paper presents an algorithm for solving multiobjective optimization problems involving composite functions, where we minimize a quadratic model that approximates $F(x) - F(x^k)$ and that can be derivative-free. We establish theoretical…

Derivative-free algorithms seek the minimum of a given function based only on function values queried at appropriate points. Although these methods are widely used in practice, their performance is known to worsen as the problem dimension…

In the context of the optimization of rotating electric machines, many different objective functions are of interest and considering this during the optimization is of crucial importance. While evolutionary algorithms can provide a Pareto…

We introduce Direct Value Optimization (DVO), an innovative reinforcement learning framework for enhancing large language models in complex reasoning tasks. Unlike traditional methods relying on preference labels, DVO utilizes value signals…

Multi-objective optimization aims at finding trade-off solutions to conflicting objectives. These constitute the Pareto optimal set. In the context of expensive-to-evaluate functions, it is impossible and often non-informative to look for…