Invariant risk minimization is an important general machine learning framework that has recently been interpreted as a total variation model (IRM-TV). However, how to improve out-of-distribution (OOD) generalization in the IRM-TV setting remains unsolved. In this paper, we extend IRM-TV to a Lagrangian multiplier model named OOD-TV -IRM. We find that the autonomous TV penalty hyperpa-rameter is exactly the Lagrangian multiplier. Thus OOD-TV -IRM is essentially a primal-dual optimization model, where the primal optimization minimizes the entire invariant risk and the dual optimization strengthens the TV penalty. The objective is to reach a semi-Nash equilibrium where the balance between the training loss and OOD generalization is maintained. We also develop a convergent primal-dual algorithm that facilitates an adversarial learning scheme. Experimental results show that OOD-TV -IRM outperforms IRM-TV in most situations. Traditional risk minimization methods such as Empirical Risk Minimization (ERM) are widely used in machine learning. ERM generally assumes that both training and test data come from the same distribution. Based on this assumption, ERM learns model parameters by minimizing the average loss on the training data.

The hierarchical structure of 3D scene graphs shows a high relevance for representations purposes, as it fits common patterns from man-made environments. But, additionally, the semantic and geometric information in such hierarchical representations could be leveraged to speed up the optimization and management of map elements and robot poses. In this direction, we present our work Situational Graphs 2.0 (S-Graphs 2.0), which leverages the hierarchical structure of indoor scenes for efficient data management and optimization. Our algorithm begins by constructing a situational graph that represents the environment into four layers: Keyframes, Walls, Rooms, and Floors. Our first novelty lies in the front-end, which includes a floor detection module capable of identifying stairways and assigning floor-level semantic relations to the underlying layers. Floor-level semantics allows us to propose a floor-based loop closure strategy, that effectively rejects false positive closures that typically appear due to aliasing between different floors of a building. Our second novelty lies in leveraging our representation hierarchy in the optimization. Our proposal consists of: (1) local optimization over a window of recent keyframes and their connected components across the four representation layers, (2) floor-level global optimization, which focuses only on keyframes and their connections within the current floor during loop closures, and (3) room-level local optimization, marginalizing redundant keyframes that share observations within the room, which reduces the computational footprint. We validate our algorithm extensively in different real multi-floor environments. Our approach shows state-of-art-art accuracy metrics in large-scale multi-floor environments, estimating hierarchical representations up to 10x faster, in average, than competing baselines

Edge inference (EI) is a key solution to address the growing challenges of delayed response times, limited scalability, and privacy concerns in cloud-based Deep Neural Network (DNN) inference. However, deploying DNN models on resource-constrained edge devices faces more severe challenges, such as model storage limitations, dynamic service requests, and privacy risks. This paper proposes a novel framework for privacy-aware joint DNN model deployment and partition optimization to minimize long-term average inference delay under resource and privacy constraints. Specifically, the problem is formulated as a complex optimization problem considering model deployment, user-server association, and model partition strategies. To handle the NP-hardness and future uncertainties, a Lyapunov-based approach is introduced to transform the long-term optimization into a single-time-slot problem, ensuring system performance. Additionally, a coalition formation game model is proposed for edge server association, and a greedy-based algorithm is developed for model deployment within each coalition to efficiently solve the problem. Extensive simulations show that the proposed algorithms effectively reduce inference delay while satisfying privacy constraints, outperforming baseline approaches in various scenarios.

Principal Component Analysis (PCA) is a foundational technique in machine learning for dimensionality reduction of high-dimensional datasets. However, PCA could lead to biased outcomes that disadvantage certain subgroups of the underlying datasets. To address the bias issue, a Fair PCA (FPCA) model was introduced by Samadi et al. (2018) for equalizing the reconstruction loss between subgroups. The semidefinite relaxation (SDR) based approach proposed by Samadi et al. (2018) is computationally expensive even for suboptimal solutions. To improve efficiency, several alternative variants of the FPCA model have been developed. These variants often shift the focus away from equalizing the reconstruction loss. In this paper, we identify a hidden convexity in the FPCA model and introduce an algorithm for convex optimization via eigenvalue optimization. Our approach achieves the desired fairness in reconstruction loss without sacrificing performance. As demonstrated in real-world datasets, the proposed FPCA algorithm runs $8\times$ faster than the SDR-based algorithm, and only at most 85% slower than the standard PCA.

Gradient-based methods are well-suited for derivative-free optimization (DFO), where finite-difference (FD) estimates are commonly used as gradient surrogates. Traditional stochastic approximation methods, such as Kiefer-Wolfowitz (KW) and simultaneous perturbation stochastic approximation (SPSA), typically utilize only two samples per iteration, resulting in imprecise gradient estimates and necessitating diminishing step sizes for convergence. In this paper, we first explore an efficient FD estimate, referred to as correlation-induced FD estimate, which is a batch-based estimate. Then, we propose an adaptive sampling strategy that dynamically determines the batch size at each iteration. By combining these two components, we develop an algorithm designed to enhance DFO in terms of both gradient estimation efficiency and sample efficiency. Furthermore, we establish the consistency of our proposed algorithm and demonstrate that, despite using a batch of samples per iteration, it achieves the same convergence rate as the KW and SPSA methods. Additionally, we propose a novel stochastic line search technique to adaptively tune the step size in practice. Finally, comprehensive numerical experiments confirm the superior empirical performance of the proposed algorithm.

Differentially Private Stochastic Gradient Descent (DPSGD) is widely used to protect sensitive data during the training of machine learning models, but its privacy guarantees often come at the cost of model performance, largely due to the inherent challenge of accurately quantifying privacy loss. While recent efforts have strengthened privacy guarantees by focusing solely on the final output and bounded domain cases, they still impose restrictive assumptions, such as convexity and other parameter limitations, and often lack a thorough analysis of utility. In this paper, we provide rigorous privacy and utility characterization for DPSGD for smooth loss functions in both bounded and unbounded domains. We track the privacy loss over multiple iterations by exploiting the noisy smooth-reduction property and establish the utility analysis by leveraging the projection's non-expansiveness and clipped SGD properties. In particular, we show that for DPSGD with a bounded domain, (i) the privacy loss can still converge without the convexity assumption, and (ii) a smaller bounded diameter can improve both privacy and utility simultaneously under certain conditions. Numerical results validate our results.

Variational inequalities (VIs) encompass many fundamental problems in diverse areas ranging from engineering to economics and machine learning. However, their considerable expressivity comes at the cost of computational intractability. In this paper, we introduce and analyze a natural relaxation -- which we refer to as expected variational inequalities (EVIs) -- where the goal is to find a distribution that satisfies the VI constraint in expectation. By adapting recent techniques from game theory, we show that, unlike VIs, EVIs can be solved in polynomial time under general (nonmonotone) operators. EVIs capture the seminal notion of correlated equilibria, but enjoy a greater reach beyond games. We also employ our framework to capture and generalize several existing disparate results, including from settings such as smooth games, and games with coupled constraints or nonconcave utilities.

Risk-sensitive planning aims to identify policies maximizing some tail-focused metrics in Markov Decision Processes (MDPs). Such an optimization task can be very costly for the most widely used and interpretable metrics such as threshold probabilities or (Conditional) Values at Risk. Indeed, previous work showed that only Entropic Risk Measures (EntRM) can be efficiently optimized through dynamic programming, leaving a hard-to-interpret parameter to choose. We show that the computation of the full set of optimal policies for EntRM across parameter values leads to tight approximations for the metrics of interest. We prove that this optimality front can be computed effectively thanks to a novel structural analysis and smoothness properties of entropic risks. Empirical results demonstrate that our approach achieves strong performance in a variety of decision-making scenarios.

The transition from 5G to 6G mobile networks necessitates network automation to meet the escalating demands for high data rates, ultra-low latency, and integrated technology. Recently, Zero-Touch Networks (ZTNs), driven by Artificial Intelligence (AI) and Machine Learning (ML), are designed to automate the entire lifecycle of network operations with minimal human intervention, presenting a promising solution for enhancing automation in 5G/6G networks. However, the implementation of ZTNs brings forth the need for autonomous and robust cybersecurity solutions, as ZTNs rely heavily on automation. AI/ML algorithms are widely used to develop cybersecurity mechanisms, but require substantial specialized expertise and encounter model drift issues, posing significant challenges in developing autonomous cybersecurity measures. Therefore, this paper proposes an automated security framework targeting Physical Layer Authentication (PLA) and Cross-Layer Intrusion Detection Systems (CLIDS) to address security concerns at multiple Internet protocol layers. The proposed framework employs drift-adaptive online learning techniques and a novel enhanced Successive Halving (SH)-based Automated ML (AutoML) method to automatically generate optimized ML models for dynamic networking environments. Experimental results illustrate that the proposed framework achieves high performance on the public Radio Frequency (RF) fingerprinting and the Canadian Institute for CICIDS2017 datasets, showcasing its effectiveness in addressing PLA and CLIDS tasks within dynamic and complex networking environments. Furthermore, the paper explores open challenges and research directions in the 5G/6G cybersecurity domain. This framework represents a significant advancement towards fully autonomous and secure 6G networks, paving the way for future innovations in network automation and cybersecurity.

Achieving realistic simulations of humans interacting with a wide range of objects has long been a fundamental goal. Extending physics-based motion imitation to complex human-object interactions (HOIs) is challenging due to intricate human-object coupling, variability in object geometries, and artifacts in motion capture data, such as inaccurate contacts and limited hand detail. We introduce InterMimic, a framework that enables a single policy to robustly learn from hours of imperfect MoCap data covering diverse full-body interactions with dynamic and varied objects. Our key insight is to employ a curriculum strategy -- perfect first, then scale up. We first train subject-specific teacher policies to mimic, retarget, and refine motion capture data. Next, we distill these teachers into a student policy, with the teachers acting as online experts providing direct supervision, as well as high-quality references. Notably, we incorporate RL fine-tuning on the student policy to surpass mere demonstration replication and achieve higher-quality solutions. Our experiments demonstrate that InterMimic produces realistic and diverse interactions across multiple HOI datasets. The learned policy generalizes in a zero-shot manner and seamlessly integrates with kinematic generators, elevating the framework from mere imitation to generative modeling of complex human-object interactions.