Frugal Machine Learning (FML) refers to the practice of designing Machine Learning (ML) models that are efficient, cost-effective, and mindful of resource constraints. This field aims to achieve acceptable performance while minimizing the use of computational resources, time, energy, and data for both training and inference. FML strategies can be broadly categorized into input frugality, learning process frugality, and model frugality, each focusing on reducing resource consumption at different stages of the ML pipeline. This chapter explores recent advancements, applications, and open challenges in FML, emphasizing its importance for smart environments that incorporate edge computing and IoT devices, which often face strict limitations in bandwidth, energy, or latency. Technological enablers such as model compression, energy-efficient hardware, and data-efficient learning techniques are discussed, along with adaptive methods including parameter regularization, knowledge distillation, and dynamic architecture design that enable incremental model updates without full retraining. Furthermore, it provides a comprehensive taxonomy of frugal methods, discusses case studies across diverse domains, and identifies future research directions to drive innovation in this evolving field.

Signed graphs are equipped with both positive and negative edge weights, encoding pairwise correlations as well as anti-correlations in data. A balanced signed graph is a signed graph with no cycles containing an odd number of negative edges. Laplacian of a balanced signed graph has eigenvectors that map via a simple linear transform to ones in a corresponding positive graph Laplacian, thus enabling reuse of spectral filtering tools designed for positive graphs. We propose an efficient method to learn a balanced signed graph Laplacian directly from data. Specifically, extending a previous linear programming (LP) based sparse inverse covariance estimation method called CLIME, we formulate a new LP problem for each Laplacian column $i$, where the linear constraints restrict weight signs of edges stemming from node $i$, so that nodes of same / different polarities are connected by positive / negative edges. Towards optimal model selection, we derive a suitable CLIME parameter $ρ$ based on a combination of the Hannan-Quinn information criterion and a minimum feasibility criterion. We solve the LP problem efficiently by tailoring a sparse LP method based on ADMM. We theoretically prove local solution convergence of our proposed iterative algorithm. Extensive experimental results on synthetic and real-world datasets show that our balanced graph learning method outperforms competing methods and enables reuse of spectral filters, wavelets, and graph convolutional nets (GCN) constructed for positive graphs.

Federated Unlearning (FU) enables clients to remove the influence of specific data from a collaboratively trained shared global model, addressing regulatory requirements such as GDPR and CCPA. However, this unlearning process introduces a new privacy risk: A malicious server may exploit unlearning updates to reconstruct the data requested for removal, a form of Data Reconstruction Attack (DRA). While DRAs for machine unlearning have been studied extensively in centralized Machine Learning-as-a-Service (MLaaS) settings, their applicability to FU remains unclear due to the decentralized, client-driven nature of FU. This work presents DRAUN, the first attack framework to reconstruct unlearned data in FU systems. DRAUN targets optimization-based unlearning methods, which are widely adopted for their efficiency. We theoretically demonstrate why existing DRAs targeting machine unlearning in MLaaS fail in FU and show how DRAUN overcomes these limitations. We validate our approach through extensive experiments on four datasets and four model architectures, evaluating its performance against five popular unlearning methods, effectively demonstrating that state-of-the-art FU methods remain vulnerable to DRAs.

Reinforcement learning (RL) policies represented in Reproducing Kernel Hilbert Spaces (RKHS) offer powerful representational capabilities. While second-order optimization methods like Newton's method demonstrate faster convergence than first-order approaches, current RKHS-based policy optimization remains constrained to first-order techniques. This limitation stems primarily from the intractability of explicitly computing and inverting the infinite-dimensional Hessian operator in RKHS. We introduce Policy Newton in RKHS, the first second-order optimization framework specifically designed for RL policies represented in RKHS. Our approach circumvents direct computation of the inverse Hessian operator by optimizing a cubic regularized auxiliary objective function. Crucially, we leverage the Representer Theorem to transform this infinite-dimensional optimization into an equivalent, computationally tractable finite-dimensional problem whose dimensionality scales with the trajectory data volume. We establish theoretical guarantees proving convergence to a local optimum with a local quadratic convergence rate. Empirical evaluations on a toy financial asset allocation problem validate these theoretical properties, while experiments on standard RL benchmarks demonstrate that Policy Newton in RKHS achieves superior convergence speed and higher episodic rewards compared to established first-order RKHS approaches and parametric second-order methods. Our work bridges a critical gap between non-parametric policy representations and second-order optimization methods in reinforcement learning.

Developing machine learning (ML) models requires a deep understanding of real-world problems, which are inherently multi-objective. In this paper, we present VirnyFlow, the first design space for responsible model development, designed to assist data scientists in building ML pipelines that are tailored to the specific context of their problem. Unlike conventional AutoML frameworks, VirnyFlow enables users to define customized optimization criteria, perform comprehensive experimentation across pipeline stages, and iteratively refine models in alignment with real-world constraints. Our system integrates evaluation protocol definition, multi-objective Bayesian optimization, cost-aware multi-armed bandits, query optimization, and distributed parallelism into a unified architecture. We show that VirnyFlow significantly outperforms state-of-the-art AutoML systems in both optimization quality and scalability across five real-world benchmarks, offering a flexible, efficient, and responsible alternative to black-box automation in ML development.

--This paper introduces an innovative error feedback framework designed to mitigate quantization noise in distributed graph filtering, where communications are constrained to quantized messages. It comes from error spectrum shaping techniques from state-space digital filters, and therefore establishes connections between quantized filtering processes over different domains. In contrast to existing error compensation methods, our framework quantitatively feeds back the quantization noise for exact compensation. We examine the framework under three key scenarios: (i) deterministic graph filtering, (ii) graph filtering over random graphs, and (iii) graph filtering with random node-asynchronous updates. Rigorous theoretical analysis demonstrates that the proposed framework significantly reduces the effect of quantization noise, and we provide closed-form solutions for the optimal error feedback coefficients. Moreover, this quantitative error feedback mechanism can be seamlessly integrated into communication-efficient decentralized optimization frameworks, enabling lower error floors. Numerical experiments validate the theoretical results, consistently showing that our method outperforms conventional quantization strategies in terms of both accuracy and robustness. Index T erms --Graph signal processing, distributed graph filtering, quantization, error feedback, stochastic linear system, decentralized optimization. HE theory of graph filtering has seen substantial progress in recent years [1]-[4], emerging as a cornerstone of modern signal processing and machine learning on networked data.

Structured data-quality issues, such as missing values correlated with demographics, culturally biased labels, or systemic selection biases, routinely degrade the reliability of machine-learning pipelines. Regulators now increasingly demand evidence that high-stakes systems can withstand these realistic, interdependent errors, yet current robustness evaluations typically use random or overly simplistic corruptions, leaving worst-case scenarios unexplored. We introduce SAVAGE, a causally inspired framework that (i) formally models realistic data-quality issues through dependency graphs and flexible corruption templates, and (ii) systematically discovers corruption patterns that maximally degrade a target performance metric. SAVAGE employs a bi-level optimization approach to efficiently identify vulnerable data subpopulations and fine-tune corruption severity, treating the full ML pipeline, including preprocessing and potentially non-differentiable models, as a black box. Extensive experiments across multiple datasets and ML tasks (data cleaning, fairness-aware learning, uncertainty quantification) demonstrate that even a small fraction (around 5 %) of structured corruptions identified by SAVAGE severely impacts model performance, far exceeding random or manually crafted errors, and invalidating core assumptions of existing techniques. Thus, SAVAGE provides a practical tool for rigorous pipeline stress-testing, a benchmark for evaluating robustness methods, and actionable guidance for designing more resilient data workflows.

Recently, 3D Gaussian splatting-based RGB-D SLAM displays remarkable performance of high-fidelity 3D reconstruction. However, the lack of depth rendering consistency and efficient loop closure limits the quality of its geometric reconstructions and its ability to perform globally consistent mapping online. In this paper, we present 2DGS-SLAM, an RGB-D SLAM system using 2D Gaussian splatting as the map representation. By leveraging the depth-consistent rendering property of the 2D variant, we propose an accurate camera pose optimization method and achieve geometrically accurate 3D reconstruction. In addition, we implement efficient loop detection and camera relocalization by leveraging MASt3R, a 3D foundation model, and achieve efficient map updates by maintaining a local active map. Experiments show that our 2DGS-SLAM approach achieves superior tracking accuracy, higher surface reconstruction quality, and more consistent global map reconstruction compared to existing rendering-based SLAM methods, while maintaining high-fidelity image rendering and improved computational efficiency.

Marketing optimization, commonly formulated as an online budget allocation problem, has emerged as a pivotal factor in driving user growth. Most existing research addresses this problem by following the principle of 'first predict then optimize' for each individual, which presents challenges related to large-scale counterfactual prediction and solving complexity trade-offs. Note that the practical data quality is uncontrollable, and the solving scale tends to be tens of millions. Therefore, the existing approaches make the robust budget allocation non-trivial, especially in industrial scenarios with considerable data noise. To this end, this paper proposes a novel approach that solves the problem from the cluster perspective. Specifically, we propose a multi-task representation network to learn the inherent attributes of individuals and project the original features into high-dimension hidden representations through the first two layers of the trained network. Then, we divide these hidden representations into $K$ groups through partitioning-based clustering, thus reformulating the problem as an integer stochastic programming problem under different total budgets. Finally, we distill the representation module and clustering model into a multi-category model to facilitate online deployment. Offline experiments validate the effectiveness and superiority of our approach compared to six state-of-the-art marketing optimization algorithms. Online A/B tests on the Meituan platform indicate that the approach outperforms the online algorithm by 0.53% and 0.65%, considering order volume (OV) and gross merchandise volume (GMV), respectively.

We propose a novel discriminative model for sequence labeling called Bregman conditional random fields (BCRF). Contrary to standard linear-chain conditional random fields, BCRF allows fast parallelizable inference algorithms based on iterative Bregman projections. We show how such models can be learned using Fenchel-Young losses, including extension for learning from partial labels. Experimentally, our approach delivers comparable results to CRF while being faster, and achieves better results in highly constrained settings compared to mean field, another parallelizable alternative.