arXiv:2606. 00002v1 Announce Type: new Abstract: Mixed-Integer Linear Programming (MILP) decision engines routinely output nominally optimal plans for high-stakes industrial systems.
arXiv:2608. 02343v1 Announce Type: cross Abstract: Many operational problems are constrained sequential decision processes with large, combinatorial action spaces and interdependent feasibility constraints.
arXiv:2607. 07762v1 Announce Type: new Abstract: Modern machine learning (ML) increasingly relies on complex models whose behavior is difficult to characterize beyond empirical performance metrics.
arXiv:2404. 03578v3 Announce Type: replace Abstract: The sim-to-real gap, which represents the disparity between training and testing environments, poses a significant challenge in reinforcement learning (RL).
arXiv:2608. 03562v1 Announce Type: new Abstract: Reinforcement learning (RL) with general utility extends classic RL by optimizing an arbitrary utility functional of the policy-induced occupancy measure, thereby enabling a broader range of applications.
Mixed-Integer Linear Programming (MILP) is a fundamental problem class in operations research and combinatorial optimization, with broad applications to industrial decision-making. Owing to their NP-hardness, however, modern solvers may struggle to find high-quality solutions for challenging MILP instances within practical time limits.
arXiv:2510. 07750v3 Announce Type: replace-cross Abstract: Robust optimization safeguards decisions against uncertainty by optimizing against worst-case scenarios, yet their effectiveness hinges on a prespecified robustness level that is often chosen ad hoc, leading to either insufficient protection or overly conservative and costly solutions.
Robust Nash Alignment introduces a game-theoretic framework that seeks a policy with a high worst-case win rate against both an adversarial competitor and any preference kernel within an ambiguity set around a nominal preference. The authors propose a four-player primal-dual proxy game and an optimistic mirror descent-ascent algorithm to efficiently optimize this robust objective, proving convergence guarantees and demonstrating improved performance in controlled tabular games and LLM alignment experiments.
The paper presents a unified taxonomy that classifies machine‑learning and artificial‑intelligence applications according to mathematical programming paradigms such as linear, quadratic, mixed‑integer, conic, bilevel, and others. It standardizes notation, identifies key inputs, decision variables, and principal formulations for each application, and discusses structural properties, solution strategies, and limitations. The authors compare tractability, relaxation quality, decomposition, approximation guarantees, and scalability across paradigms, emphasizing that mathematical programming serves as a disciplined interface between predictions and constrained decisions rather than a universal modeling claim.
arXiv:2608. 19953v1 Announce Type: new Abstract: Mixed-Integer Linear Programming (MILP) is a fundamental problem class in operations research and combinatorial optimization, with broad applications to industrial decision-making.
Modern machine learning (ML) increasingly relies on complex models whose behavior is difficult to characterize beyond empirical performance metrics. Across a wide range of tasks, including prediction, generation, and decision-making, models with similar empirical performance can exhibit markedly different properties in terms of their transparency, interpretability, robustness, fairness, privacy, and certifiability.
arXiv:2505. 05203v3 Announce Type: replace-cross Abstract: With the increasing penetration of renewable energy and inverter-based resources, traditional physics-based power-system operation faces growing challenges in maintaining economic efficiency, security, and robustness.
arXiv:2505.05261v4 Announce Type: replace-cross Abstract: Two-stage stochastic programming (2SP) offers a basic framework for modelling decision-making under uncertainty, yet scalability remains a ch...