Related papers: Exact Solution to Data-Driven Inverse Optimization…

We introduce a new algorithm to solve constrained nonlinear optimal control problem, with an emphasis on low-thrust trajectory in highly nonlinear dynamics. The algorithm, dubbed Pontryagin-Bellman Differential Dynamic Programming (PDDP),…

Projected Gradient Descent denotes a class of iterative methods for solving optimization programs. Its applicability to convex optimization programs has gained significant popularity for its intuitive implementation that involves only…

Equipping a deep model the abaility of few-shot learning, i.e., learning quickly from only few examples, is a core challenge for artificial intelligence. Gradient-based meta-learning approaches effectively address the challenge by learning…

Many problems encountered in science and engineering can be formulated as estimating a low-rank object (e.g., matrices and tensors) from incomplete, and possibly corrupted, linear measurements. Through the lens of matrix and tensor…

We consider a discrete optimization formulation for learning sparse classifiers, where the outcome depends upon a linear combination of a small subset of features. Recent work has shown that mixed integer programming (MIP) can be used to…

Designing faster algorithms for solving Mixed-Integer Linear Programming (MILP) problems is highly desired across numerous practical domains, as a vast array of complex real-world challenges can be effectively modeled as MILP formulations.…

We study the problem of computing an optimal policy of an infinite-horizon discounted constrained Markov decision process (constrained MDP). Despite the popularity of Lagrangian-based policy search methods used in practice, the oscillation…

Asynchronous stochastic gradient descent (SGD) enables scalable distributed training but suffers from gradient staleness. Existing mitigation strategies, such as delay-adaptive learning rates and staleness-aware filtering, typically…

In this paper, we develop a new optimization framework for the least squares learning problem via fully connected neural networks or physics-informed neural networks. The gradient descent sometimes behaves inefficiently in deep learning…

Many real-world optimization problems contain parameters that are unknown before deployment time, either due to stochasticity or to lack of information (e.g., demand or travel times in delivery problems). A common strategy in such cases is…

The efficient allocation of human resources is a critical concern in software development and other industries. This paper introduces a rigorous mathematical methodology for task assignment, employing Mixed Integer Linear Programming (MILP)…

Data-driven evolutionary multi-objective optimization (EMO) has been recognized as an effective approach for multi-objective optimization problems with expensive objective functions. The current research is mainly developed for problems…

We study the sequential decision making problem of maximizing the expected total reward while satisfying a constraint on the expected total utility. We employ the natural policy gradient method to solve the discounted infinite-horizon…

First-order algorithms have been popular for solving convex and non-convex optimization problems. A key assumption for the majority of these algorithms is that the gradient of the objective function is globally Lipschitz continuous, but…

Learning Markov decision processes (MDPs) in the presence of the adversary is a challenging problem in reinforcement learning (RL). In this paper, we study RL in episodic MDPs with adversarial reward and full information feedback, where the…

Mixed-Integer Linear Programming (MILP) plays an important role across a range of scientific disciplines and within areas of strategic importance to society. The MILP problems, however, suffer from combinatorial complexity. Because of…

Shape optimization approaches to inverse design offer low-dimensional, physically-guided parameterizations of structures by representing them as combinations of shape primitives. However, on discretized rectilinear simulation grids,…

We study the problem of non-convex optimization using Stochastic Gradient Langevin Dynamics (SGLD). SGLD is a natural and popular variation of stochastic gradient descent where at each step, appropriately scaled Gaussian noise is added. To…

Inspection planning is concerned with computing the shortest robot path to inspect a given set of points of interest (POIs) using the robot's sensors. This problem arises in a wide range of applications from manufacturing to medical…

Direct Preference Optimization (DPO) has been proposed as a promising alternative to Proximal Policy Optimization (PPO) based Reinforcement Learning with Human Feedback (RLHF). However, empirical evaluations consistently reveal suboptimal…