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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…
This paper considers optimal attack attention allocation on remote state estimation in multi-systems. Suppose there are $\mathtt{M}$ independent systems, each of which has a remote sensor monitoring the system and sending its local…
Multi-party multi-objective optimization problems (MPMOPs) require consensus among autonomous decision makers and therefore differ from flattened many-objective formulations. Existing runtime theory for multi-objective evolutionary…
To adapt large language models (LLMs) to ranking tasks, existing list-wise methods, represented by list-wise Direct Preference Optimization (DPO), focus on optimizing partial-order or full-order list ranking consistency for LLMs to enhance…
Machine learning algorithms in high-dimensional settings are highly susceptible to the influence of even a small fraction of structured outliers, making robust optimization techniques essential. In particular, within the…
Majorization-minimization algorithms consist of iteratively minimizing a majorizing surrogate of an objective function. Because of its simplicity and its wide applicability, this principle has been very popular in statistics and in signal…
Aligning Large Language Models (LLMs) with human preferences typically relies on external supervision, which faces critical limitations: human annotations are scarce and subjective, reward models are vulnerable to reward hacking, and…
We consider the problem of unconstrained minimization of a smooth objective function in $\R^n$ in a setting where only function evaluations are possible. While importance sampling is one of the most popular techniques used by machine…
In the context of Noisy Multi-Objective Optimization, dealing with uncertainties requires the decision maker to define some preferences about how to handle them, through some statistics (e.g., mean, median) to be used to evaluate the…
This paper presents a stochastic, model predictive control (MPC) algorithm that leverages short-term probabilistic forecasts for dispatching and rebalancing Autonomous Mobility-on-Demand systems (AMoD, i.e. fleets of self-driving vehicles).…
For the purpose of addressing the multi-objective optimal reactive power dispatch (MORPD) problem, a two-step approach is proposed in this paper. First of all, to ensure the economy and security of the power system, the MORPD model aiming…
Offline model-based optimization (MBO) seeks to discover high-performing designs using only a fixed dataset of past evaluations. Most existing methods rely on learning a surrogate model via regression and implicitly assume that good…
We consider a class of sequential decision-making problems under uncertainty that can encompass various types of supervised learning concepts. These problems have a completely observed state process and a partially observed modulation…
Out-of-Distribution (OOD) detection, i.e., identifying whether an input is sampled from a novel distribution other than the training distribution, is a critical task for safely deploying machine learning systems in the open world. Recently,…
We provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic…
Partially observable Markov decision processes (POMDPs) provide a modeling framework for autonomous decision making under uncertainty and imperfect sensing, e.g. robot manipulation and self-driving cars. However, optimal control of POMDPs…
Optimal control in non-stationary Markov decision processes (MDP) is a challenging problem. The aim in such a control problem is to maximize the long-term discounted reward when the transition dynamics or the reward function can change over…
The analysis of structure-preserving numerical methods for the Poisson--Nernst--Planck (PNP) system has attracted growing interests in recent years. In this work, we provide an optimal rate convergence analysis and error estimate for finite…
Motivated by applications arising from large scale optimization and machine learning, we consider stochastic quasi-Newton (SQN) methods for solving unconstrained convex optimization problems. The convergence analysis of the SQN methods,…
We study optimization problems in which a linear functional is maximized over probability measures that are dominated by a given measure according to an integral stochastic order in an arbitrary dimension. We show that the following four…