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Reinforcement Learning with Verifiable Rewards (RLVR) has achieved remarkable success in improving autoregressive models, especially in domains requiring correctness like mathematical reasoning and code generation. However, directly…

Safe reinforcement learning (safe RL) aims to respect safety requirements while optimizing long-term performance. In many practical applications, however, the problem involves an infinite number of constraints, known as semi-infinite safe…

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as an important paradigm for unlocking reasoning capabilities in large language models, exemplified by the success of OpenAI o1 and DeepSeek-R1. Currently, Group Relative…

Interval linear programming provides a tool for solving real-world optimization problems under interval-valued uncertainty. Instead of approximating or estimating crisp input data, the coefficients of an interval program may perturb…

Direct Preference Optimisation (DPO) has emerged as a powerful method for aligning Large Language Models (LLMs) with human preferences, offering a stable and efficient alternative to approaches that use Reinforcement learning via Human…

One of the most influential results in neural network theory is the universal approximation theorem [1, 2, 3] which states that continuous functions can be approximated to within arbitrary accuracy by single-hidden-layer feedforward neural…

We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an…

This paper focuses on optimization problems constrained by Parametric Variational Inequalities (PVI) defined on a moving set. Unlike most existing works on mathematical programs with equilibrium constraints, the equilibrium constraints have…

We introduce a novel kind of robustness in linear programming. A solution x* is called robust optimal if for all realizations of objective functions coefficients and constraint matrix entries from given interval domains there are…

The alignment of large language models (LLMs) with human preferences remains a key challenge. While post-training techniques like Reinforcement Learning from Human Feedback (RLHF) and Direct Preference Optimization (DPO) have achieved…

Reinforcement Learning (RL) has made significant strides in various domains, and policy gradient methods like Proximal Policy Optimization (PPO) have gained popularity due to their balance in performance, training stability, and…

Learning to optimize (L2O) is an emerging approach that leverages machine learning to develop optimization methods, aiming at reducing the laborious iterations of hand engineering. It automates the design of an optimization method based on…

This paper establishes comprehensive stability results for quasi-variational inequalities (QVIs) under monotone perturbations of the governing operator. We prove strong convergence of both minimal and maximal solutions when sequences of…

Regularization techniques are crucial to improving the generalization performance and training efficiency of deep neural networks. Many deep learning algorithms rely on weight decay, dropout, batch/layer normalization to converge faster and…

The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…

Linear programming (LP) relaxation is a standard technique for solving hard combinatorial optimization (CO) problems. Here we present a gradient descent algorithm which exploits the special structure of some LP relaxations induced by CO…

We study the problem of policy optimization (PO) with linear temporal logic (LTL) constraints. The language of LTL allows flexible description of tasks that may be unnatural to encode as a scalar cost function. We consider LTL-constrained…

As Large Language Models (LLMs) demonstrate remarkable capabilities learned from vast corpora, concerns regarding data privacy and safety are receiving increasing attention. LLM unlearning, which aims to remove the influence of specific…

Unconstrained Online Linear Optimization (OLO) is a practical problem setting to study the training of machine learning models. Existing works proposed a number of potential-based algorithms, but in general the design of these potential…

The rapid development of large language model (LLM) alignment algorithms has resulted in a complex and fragmented landscape, with limited clarity on the effectiveness of different methods and their inter-connections. This paper introduces…