Related papers: Introduction to Interpolation-Based Optimization

Direct Preference Optimization (DPO) guides large language models (LLMs) to generate recommendations aligned with user historical behavior distributions by minimizing preference alignment loss. However, our systematic empirical research and…

Bayesian optimization (BO) is a successful methodology to optimize black-box functions that are expensive to evaluate. While traditional methods optimize each black-box function in isolation, there has been recent interest in speeding up BO…

Direct Preference Optimization (DPO) is a widely adopted offline algorithm for preference-based reinforcement learning from human feedback (RLHF), designed to improve training simplicity and stability by redefining reward functions.…

Bilevel optimization recently has received tremendous attention due to its great success in solving important machine learning problems like meta learning, reinforcement learning, and hyperparameter optimization. Extending single-agent…

We consider the problem of optimizing the sum of a smooth, nonconvex function for which derivatives are unavailable, and a convex, nonsmooth function with easy-to-evaluate proximal operator. Of particular focus is the case where the smooth…

In this paper, we propose a trigonometric-interpolation approach for solutions of second order nonlinear ODEs with mixed boundary conditions. The method interpolates secondary derivative $y''$ of a target solution $y$ by a trigonometric…

Direct Preference Optimization (DPO) improves the alignment of large language models (LLMs) with human values by training directly on human preference datasets, eliminating the need for reward models. However, due to the presence of…

Multi-objective optimization is a widely studied problem in diverse fields, such as engineering and finance, that seeks to identify a set of non-dominated solutions that provide optimal trade-offs among competing objectives. However, the…

We study reinforcement learning in hybrid discrete-continuous action spaces, such as settings where the discrete component selects a regime (or index) and the continuous component optimizes within it -- a structure common in robotics,…

Optimizing an expensive-to-query function is a common task in science and engineering, where it is beneficial to keep the number of queries to a minimum. A popular strategy is Bayesian optimization (BO), which leverages probabilistic models…

We develop novel integrated learning and optimization (ILO) methodologies to solve economic dispatch (ED) and DC optimal power flow (DCOPF) problems for better economic operation. The optimization problem for ED is formulated with load…

Aligning Large Language Models (LLMs) with human preferences is crucial for safe and effective AI interactions. While popular methods like Direct Preference Optimization (DPO) have simplified alignment, they remain sensitive to data noise…

Decentralized policy optimization has been commonly used in cooperative multi-agent tasks. However, since all agents are updating their policies simultaneously, from the perspective of individual agents, the environment is non-stationary,…

Bayesian optimization (BO) is a prominent approach to optimizing expensive-to-evaluate black-box functions. The massive computational capability of edge devices such as mobile phones, coupled with privacy concerns, has led to a surging…

Gasoline blending scheduling uses resource allocation and operation sequencing to meet a refinery's production requirements. The presence of nonlinearity, integer constraints, and a large number of decision variables adds complexity to this…

We provide first the functional analysis background required for reduced order modeling and present the underlying concepts of reduced basis model reduction. The projection-based model reduction framework under affinity assumptions,…

Bayesian Optimization (BO) is a widely used approach for blackbox optimization that leverages a Gaussian process (GP) model and an acquisition function to guide future sampling. While effective in low-dimensional settings, BO faces…

Bayesian optimization (BO) is a widely-used sequential method for zeroth-order optimization of complex and expensive-to-compute black-box functions. The existing BO methods assume that the function evaluation (feedback) is available to the…

We consider the problem of minimizing a high-dimensional objective function, which may include a regularization term, using (possibly noisy) evaluations of the function. Such optimization is also called derivative-free, zeroth-order, or…

In this note, we present a derivative-free trust-region (TR) algorithm for reliability based optimization (RBO) problems. The proposed algorithm consists of solving a set of subproblems, in which simple surrogate models of the reliability…