We introduce PLUME search, a data-driven framework that enhances search efficiency in combinatorial optimization through unsupervised learning. Unlike supervised or reinforcement learning, PLUME search learns directly from problem instances using a permutation-based loss with a non-autoregressive approach. We evaluate its performance on the quadratic assignment problem, a fundamental NP-hard problem that encompasses various combinatorial optimization problems. Experimental results demonstrate that PLUME search consistently improves solution quality. Furthermore, we study the generalization behavior and show that the learned model generalizes across different densities and sizes.

Artificial intelligence has gained widespread popularity and adoption across diverse industries due to its ability of automatic decision-making processes. In numerous contexts where artificial intelligence permeates various aspects of our lives, from business operations to societal dynamics and policy formulation, ensuring fairness is of greatest importance to meeting environmental, social, and governance standards. While for nearly any problem in the field of artificial intelligence, there can exist multiple measures of individual fairness as well as multiple measures of subgroup fairness. Often, Subgroup fairness involves multiple protected attributes (e.g., race, sex), creating numerous combinations of subgroups and corresponding subgroup fairness measures, all of which deserve consideration. Hence, it becomes essential to take into account the trade-offs among optimising for multiple fairness measures.

Multi-robot navigation and path planning in continuous state and action spaces with uncertain environments remains an open challenge. Deep Reinforcement Learning (RL) is one of the most popular paradigms for solving this task, but its real-world application has been limited due to sample inefficiency and long training periods. Moreover, the existing works using RL for multi-robot navigation lack formal guarantees while designing the environment. In this paper, we introduce an efficient and highly customizable environment for continuous-control multi-robot navigation, where the robots must visit a set of regions of interest (ROIs) by following the shortest paths. The task is formally modeled as a Markov Decision Process (MDP). We describe the multi-robot navigation task as an optimization problem and relate it to finding an optimal policy for the MDP. We crafted several variations of the environment and measured the performance using both gradient and non-gradient based RL methods: A2C, PPO, TRPO, TQC, CrossQ and ARS. To show real-world applicability, we deployed our environment to a 3-D agricultural field with uncertainties using the CoppeliaSim robot simulator and measured the robustness by running inference on the learned models. We believe our work will guide the researchers on how to develop MDP-based environments that are applicable to real-world systems and solve them using the existing state-of-the-art RL methods with limited resources and within reasonable time periods.

Predict+Optimize, a novel extension catering to applications where unknown parameters are instead revealed in sequential stages, with optimization decisions made in between. We further develop three training algorithms for neural networks (NNs) for our framework as proof of concept, all of which can handle mixed integer linear programs.

Inverse optimization has been increasingly used to estimate unknown parameters in an optimization model based on decision data.

This paper presents Dual Lagrangian Learning (DLL), a principled learning methodology for dual conic optimization proxies.

This allows us to derive an explicit expression of the Wasserstein distance between graph signal distributions in terms of the graph Laplacian matrices.

Recent work [Ma et al., 2019] shows that in the non-convex case, sampling