Microgrids have emerged as a pivotal solution in the quest for a sustainable and energy-efficient future. While microgrids offer numerous advantages, they are also prone to issues related to reliably forecasting renewable energy demand and production, protecting against cyberattacks, controlling operational costs, optimizing power flow, and regulating the performance of energy management systems (EMS). Tackling these energy management challenges is essential to facilitate microgrid applications and seamlessly incorporate renewable energy resources. Artificial intelligence (AI) has recently demonstrated immense potential for optimizing energy management in microgrids, providing efficient and reliable solutions. This paper highlights the combined benefits of enabling AI-based methodologies in the energy management systems of microgrids by examining the applicability and efficiency of AI-based EMS in achieving specific technical and economic objectives. The paper also points out several future research directions that promise to spearhead AI-driven EMS, namely the development of self-healing microgrids, integration with blockchain technology, use of Internet of things (IoT), and addressing interpretability, data privacy, scalability, and the prospects to generative AI in the context of future AI-based EMS.

We present the first scene-update aerial path planning algorithm specifically designed for detecting and updating change areas in urban environments. While existing methods for large-scale 3D urban scene reconstruction focus on achieving high accuracy and completeness, they are inefficient for scenarios requiring periodic updates, as they often re-explore and reconstruct entire scenes, wasting significant time and resources on unchanged areas. To address this limitation, our method leverages prior reconstructions and change probability statistics to guide UAVs in detecting and focusing on areas likely to have changed. Our approach introduces a novel changeability heuristic to evaluate the likelihood of changes, driving the planning of two flight paths: a prior path informed by static priors and a dynamic real-time path that adapts to newly detected changes. The framework integrates surface sampling and candidate view generation strategies, ensuring efficient coverage of change areas with minimal redundancy. Extensive experiments on real-world urban datasets demonstrate that our method significantly reduces flight time and computational overhead, while maintaining high-quality updates comparable to full-scene re-exploration and reconstruction. These contributions pave the way for efficient, scalable, and adaptive UAV-based scene updates in complex urban environments.

Synthesizability in small molecule generative design remains a bottleneck. Existing works that do consider synthesizability can output predicted synthesis routes for generated molecules. However, there has been minimal attention in addressing the ease of synthesis and enabling flexibility to incorporate desired reaction constraints. In this work, we propose a small molecule generative design framework that enables steerable and granular synthesizability control. Generated molecules satisfy arbitrary multi-parameter optimization objectives with predicted synthesis routes containing pre-defined allowed reactions, while optionally avoiding others. One can also enforce that all reactions belong to a pre-defined set. We show the capability to mix-and-match these reaction constraints across the most common medicinal chemistry transformations. Next, we show how our framework can be used to valorize industrial byproducts towards de novo optimized molecules. Going further, we demonstrate how granular control over synthesizability constraints can loosely mimic virtual screening of ultra-large make-on-demand libraries. Using only a single GPU, we generate and dock 15k molecules to identify promising candidates in Freedom 4.0 constituting 142B make-on-demand molecules (assessing only 0.00001% of the library). Generated molecules satisfying the reaction constraints have > 90% exact match rate. Lastly, we benchmark our framework against recent synthesizability-constrained generative models and demonstrate the highest sample efficiency even when imposing the additional constraint that all molecules must be synthesizable from a single reaction type. The main theme is demonstrating that a pre-trained generalist molecular generative model can be incentivized to generate property-optimized small molecules under challenging synthesizability constraints through reinforcement learning.

Federated Learning (FL) enables distributed machine learning training while preserving privacy, representing a paradigm shift for data-sensitive and decentralized environments. Despite its rapid advancements, FL remains a complex and multifaceted field, requiring a structured understanding of its methodologies, challenges, and applications. In this survey, we introduce a meta-framework perspective, conceptualising FL as a composition of modular components that systematically address core aspects such as communication, optimisation, security, and privacy. We provide a historical contextualisation of FL, tracing its evolution from distributed optimisation to modern distributed learning paradigms. Additionally, we propose a novel taxonomy distinguishing Aggregation from Alignment, introducing the concept of alignment as a fundamental operator alongside aggregation. To bridge theory with practice, we explore available FL frameworks in Python, facilitating real-world implementation. Finally, we systematise key challenges across FL sub-fields, providing insights into open research questions throughout the meta-framework modules. By structuring FL within a meta-framework of modular components and emphasising the dual role of Aggregation and Alignment, this survey provides a holistic and adaptable foundation for understanding and advancing FL research and deployment.

Algorithm selection, aiming to identify the best algorithm for a given problem, plays a pivotal role in continuous black-box optimization. A common approach involves representing optimization functions using a set of features, which are then used to train a machine learning meta-model for selecting suitable algorithms. Various approaches have demonstrated the effectiveness of these algorithm selection meta-models. However, not all evaluation approaches are equally valid for assessing the performance of meta-models. We highlight methodological issues that frequently occur in the community and should be addressed when evaluating algorithm selection approaches. First, we identify flaws with the "leave-instance-out" evaluation technique. We show that non-informative features and meta-models can achieve high accuracy, which should not be the case with a well-designed evaluation framework. Second, we demonstrate that measuring the performance of optimization algorithms with metrics sensitive to the scale of the objective function requires careful consideration of how this impacts the construction of the meta-model, its predictions, and the model's error. Such metrics can falsely present overly optimistic performance assessments of the meta-models. This paper emphasizes the importance of careful evaluation, as loosely defined methodologies can mislead researchers, divert efforts, and introduce noise into the field

--Data imputation is a critical step in data pre-processing, particularly for datasets with missing or unreliable values. This study introduces a novel quantum-inspired imputation framework evaluated on the UCI Diabetes dataset, which contains biologically implausible missing values across several clinical features. The method integrates Principal Component Analysis (PCA) with quantum-assisted rotations, optimized through gradient-free classical optimizers--COBYLA, Simulated Annealing, and Differential Evolution--to reconstruct missing values while preserving statistical fidelity. Reconstructed values are constrained within 2 standard deviations of original feature distributions, avoiding unrealistic clustering around central tendencies. This approach achieves a substantial and statistically significant improvement, including an average reduction of over 85% in Wasserstein distance and Kolmogorov-Smirnov test p-values between 0.18 and 0.22, compared to p-values > 0.99 in classical methods such as Mean, KNN, and MICE. The method also eliminates zero-value artifacts and enhances the realism and variability of imputed data. By combining quantum-inspired transformations with a scalable classical framework, this methodology provides a robust solution for imputation tasks in domains such as healthcare and AI pipelines, where data quality and integrity are crucial. I NTRODUCTION Data imputation is a statistical technique for addressing missing or partial data values within a dataset. Missing data may arise from various sources, including sensor faults, human errors, system failures, or privacy constraints [1]. The imputation process replaces missing values with estimates derived from the available data while preserving the dataset's integrity and minimizing bias [2]. Imputation plays a vital role in numerous sectors and scenarios where data completeness is essential for analysis and decision-making.

With the success that the field of bilevel optimization has seen in recent years, similar methodologies have started being applied to solving more difficult applications that arise in trilevel optimization. At the helm of these applications are new machine learning formulations that have been proposed in the trilevel context and, as a result, efficient and theoretically sound stochastic methods are required. In this work, we propose the first-ever stochastic gradient descent method for solving unconstrained trilevel optimization problems and provide a convergence theory that covers all forms of inexactness of the trilevel adjoint gradient, such as the inexact solutions of the middle-level and lower-level problems, inexact computation of the trilevel adjoint formula, and noisy estimates of the gradients, Hessians, Jacobians, and tensors of third-order derivatives involved. We also demonstrate the promise of our approach by providing numerical results on both synthetic trilevel problems and trilevel formulations for hyperparameter adversarial tuning.

We consider a class of stochastic programming problems where the implicitly decision-dependent random variable follows a nonparametric regression model with heteroscedastic error. The Clarke subdifferential and surrogate functions are not readily obtainable due to the latent decision dependency. To deal with such a computational difficulty, we develop an adaptive learning-based surrogate method that integrates the simulation scheme and statistical estimates to construct estimation-based surrogate functions in a way that the simulation process is adaptively guided by the algorithmic procedure. We establish the non-asymptotic convergence rate analysis in terms of $(ν, δ)$-near stationarity in expectation under variable proximal parameters and batch sizes, which exhibits the superior convergence performance and enhanced stability in both theory and practice. We provide numerical results with both synthetic and real data which illustrate the benefits of the proposed algorithm in terms of algorithmic stability and efficiency.

Optimal Transport is a foundational mathematical theory that connects optimization, partial differential equations, and probability. It offers a powerful framework for comparing probability distributions and has recently become an important tool in machine learning, especially for designing and evaluating generative models. These course notes cover the fundamental mathematical aspects of OT, including the Monge and Kantorovich formulations, Brenier's theorem, the dual and dynamic formulations, the Bures metric on Gaussian distributions, and gradient flows. It also introduces numerical methods such as linear programming, semi-discrete solvers, and entropic regularization. Applications in machine learning include topics like training neural networks via gradient flows, token dynamics in transformers, and the structure of GANs and diffusion models. These notes focus primarily on mathematical content rather than deep learning techniques.

Estimating parameters from samples of an optimal probability distribution is essential in applications ranging from socio-economic modeling to biological system analysis. In these settings, the probability distribution arises as the solution to an optimization problem that captures either static interactions among agents or the dynamic evolution of a system over time. Our approach relies on minimizing a new class of loss functions, called sharpened Fenchel-Young losses, which measure the sub-optimality gap of the optimization problem over the space of measures. We study the stability of this estimation method when only a finite number of sample is available. The parameters to be estimated typically correspond to a cost function in static problems and to a potential function in dynamic problems. To analyze stability, we introduce a general methodology that leverages the strong convexity of the loss function together with the sample complexity of the forward optimization problem. Our analysis emphasizes two specific settings in the context of optimal transport, where our method provides explicit stability guarantees: The first is inverse unbalanced optimal transport (iUOT) with entropic regularization, where the parameters to estimate are cost functions that govern transport computations; this method has applications such as link prediction in machine learning. The second is inverse gradient flow (iJKO), where the objective is to recover a potential function that drives the evolution of a probability distribution via the Jordan-Kinderlehrer-Otto (JKO) time-discretization scheme; this is particularly relevant for understanding cell population dynamics in single-cell genomics. Finally, we validate our approach through numerical experiments on Gaussian distributions, where closed-form solutions are available, to demonstrate the practical performance of our methods