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Markov Decision Problems (MDPs) provide a foundational framework for modelling sequential decision-making across diverse domains, guided by optimality criteria such as discounted and average rewards. However, these criteria have inherent…

"Classical" First Order (FO) algorithms of convex optimization, such as Mirror Descent algorithm or Nesterov's optimal algorithm of smooth convex optimization, are well known to have optimal (theoretical) complexity estimates which do not…

Mathematical optimization is a fundamental tool for decision-making in a wide range of applications. However, in many real-world scenarios, the parameters of the optimization problem are not known a priori and must be predicted from…

Distributed optimization is fundamental to modern machine learning applications like federated learning, but existing methods often struggle with ill-conditioned problems and face stability-versus-speed tradeoffs. We introduce fractional…

Robust optimization (RO) has emerged as one of the leading paradigms to efficiently model parameter uncertainty. The recent connections between RO and problems in statistics and machine learning domains demand for solving RO problems in…

Large language models (LLMs) continue to struggle with mathematical reasoning, and common post-training pipelines often reduce each generated solution to a binary outcome: correct or incorrect. This perspective is limiting in practice, as…

Optical computing holds promise for high-speed, energy-efficient information processing, with diffractive optical networks emerging as a flexible platform for implementing task-specific transformations. A challenge, however, is the…

Recent development of Deep Reinforcement Learning (DRL) has demonstrated superior performance of neural networks in solving challenging problems with large or even continuous state spaces. One specific approach is to deploy neural networks…

Distributionally robust optimization (DRO) is a widely used framework for optimizing objective functionals in the presence of both randomness and model-form uncertainty. A key step in the practical solution of many DRO problems is a…

A robust-to-dynamics optimization (RDO) problem is an optimization problem specified by two pieces of input: (i) a mathematical program (an objective function $f:\mathbb{R}^n\rightarrow\mathbb{R}$ and a feasible set…

Reinforcement Learning with Human Feedback (RLHF) has become crucial for aligning Large Language Models (LLMs) with human intent. However, existing offline RLHF approaches suffer from overoptimization, where language models degrade by…

While traditional Deep Learning (DL) optimization methods treat all training samples equally, Distributionally Robust Optimization (DRO) adaptively assigns importance weights to different samples. However, a significant gap exists between…

Complex design problems are common in the scientific and industrial fields. In practice, objective functions or constraints of these problems often do not have explicit formulas, and can be estimated only at a set of sampling points through…

We study the problem of deployment efficient reinforcement learning (RL) with linear function approximation under the \emph{reward-free} exploration setting. This is a well-motivated problem because deploying new policies is costly in…

The task of hyper-parameter optimization (HPO) is burdened with heavy computational costs due to the intractability of optimizing both a model's weights and its hyper-parameters simultaneously. In this work, we introduce a new class of HPO…

Large language models in the past have typically relied on some form of reinforcement learning with human feedback (RLHF) to better align model responses with human preferences. However, because of oft-observed instabilities when…

Derivative-free optimization (DFO) has recently gained a lot of momentum in machine learning, spawning interest in the community to design faster methods for problems where gradients are not accessible. While some attention has been given…

In recent years, Multifactorial Optimization (MFO) has gained a notable momentum in the research community. MFO is known for its inherent capability to efficiently address multiple optimization tasks at the same time, while transferring…

Metaheuristic algorithms are optimization methods that are inspired by real phenomena in nature or the behavior of living beings, e.g., animals, to be used for solving complex problems, as in engineering, energy optimization, health care,…

In this paper, we establish a distributed functional optimization (DFO) theory over time-varying networks. The vast majority of existing distributed optimization theories are developed based on Euclidean decision variables. However, for…