arXiv subjects

Alejandro Ribeiro

Publications and source records attributed to Alejandro Ribeiro.

At least 73 records · Page 4Linked to original sources

arXiv2025

Deterministic Policy Gradient Primal-Dual Methods for Continuous-Space Constrained MDPs

We study the problem of computing deterministic optimal policies for constrained Markov decision processes (MDPs) with continuous state and action spaces, which are widely encountered in constrained dynamical systems. Designing deterministic policy gradient methods in continuous state and action spaces is particularly challenging due to the lack of enumerable state-action pairs and the adoption of deterministic policies, hindering the application of existing policy gradient methods. To this end, we develop a deterministic policy gradient primal-dual method to find an optimal deterministic policy with non-asymptotic convergence. Specifically, we leverage regularization of the Lagrangian of the constrained MDP to propose a deterministic policy gradient primal-dual (D-PGPD) algorithm that updates the deterministic policy via a quadratic-regularized gradient ascent step and the dual variable via a quadratic-regularized gradient descent step. We prove that the primal-dual iterates of D-PGPD converge at a sub-linear rate to an optimal regularized primal-dual pair. We instantiate D-PGPD with function approximation and prove that the primal-dual iterates of D-PGPD converge at a sub-linear rate to an optimal regularized primal-dual pair, up to a function approximation error. Furthermore, we demonstrate the effectiveness of our method in two continuous control problems: robot navigation and fluid control. This appears to be the first work that proposes a deterministic policy search method for continuous-space constrained MDPs.

cs.AI↗

arXiv2025

Constrained Learning for Decentralized Multi-Objective Coverage Control

The multi-objective coverage control problem requires a robot swarm to collaboratively provide sensor coverage to multiple heterogeneous importance density fields IDFs simultaneously. We pose this as an optimization problem with constraints and study two different formulations: (1) Fair coverage, where we minimize the maximum coverage cost for any field, promoting equitable resource distribution among all fields; and (2) Constrained coverage, where each field must be covered below a certain cost threshold, ensuring that critical areas receive adequate coverage according to predefined importance levels. We study the decentralized setting where robots have limited communication and local sensing capabilities, making the system more realistic, scalable, and robust. Given the complexity, we propose a novel decentralized constrained learning approach that combines primal-dual optimization with a Learnable Perception-Action-Communication (LPAC) neural network architecture. We show that the Lagrangian of the dual problem can be reformulated as a linear combination of the IDFs, enabling the LPAC policy to serve as a primal solver. We empirically demonstrate that the proposed method (i) significantly outperforms state-of-the-art decentralized controllers by 30% on average in terms of coverage cost, (ii) transfers well to larger environments with more robots, and (iii) scalable in the number of IDFs and robots in the swarm.

eess.SY↗

arXiv2025

Learning Efficient Positional Encodings with Graph Neural Networks

Positional encodings (PEs) are essential for effective graph representation learning because they provide position awareness in inherently position-agnostic transformer architectures and increase the expressive capacity of Graph Neural Networks (GNNs). However, designing powerful and efficient PEs for graphs poses significant challenges due to the absence of canonical node ordering and the scale of the graph. {In this work, we identify four key properties that graph PEs should satisfy}: stability, expressive power, scalability, and genericness. We find that existing eigenvector-based PE methods often fall short of jointly satisfying these criteria. To address this gap, we introduce PEARL, a novel framework of learnable PEs for graphs. Our primary insight is that message-passing GNNs function as nonlinear mappings of eigenvectors, enabling the design of GNN architectures for generating powerful and efficient PEs. A crucial challenge lies in initializing node attributes in a manner that is both expressive and permutation equivariant. We tackle this by initializing GNNs with random node inputs or standard basis vectors, thereby unlocking the expressive power of message-passing operations, while employing statistical pooling functions to maintain permutation equivariance. Our analysis demonstrates that PEARL approximates equivariant functions of eigenvectors with linear complexity, while rigorously establishing its stability and high expressive power. Experimental evaluations show that PEARL outperforms lightweight versions of eigenvector-based PEs and achieves comparable performance to full eigenvector-based PEs, but with one or two orders of magnitude lower complexity. Our code is available at https://github.com/ehejin/Pearl-PE.

cs.LG↗

arXiv2025

LoRTA: Low Rank Tensor Adaptation of Large Language Models

Low Rank Adaptation (LoRA) is a popular Parameter Efficient Fine Tuning (PEFT) method that effectively adapts large pre-trained models for downstream tasks. LoRA parameterizes model updates using low-rank matrices at each layer, significantly reducing the number of trainable parameters and, consequently, resource requirements during fine-tuning. However, the lower bound on the number of trainable parameters remains high due to the use of the low-rank matrix model. Recent works have addressed this limitation by proposing low rank tensor parameterizations for model updates. However, they only exploit redundancy across layers, or tensorize individual matrices using ad-hoc schemes that introduce additional hyperparameters. In this work, we propose a higher-order Candecomp/Parafac (CP) decomposition, enabling a more compact and flexible representation compared to existing matrix and tensor based PEFT methods. Our experiments on Natural Language Understanding, Instruction Tuning, Preference Optimization and Protein Folding benchmarks demonstrate that our method can achieve a reduction in the number of parameters while maintaining comparable performance.

cs.CL↗

arXiv2025

Learning to Slice Wi-Fi Networks: A State-Augmented Primal-Dual Approach

Network slicing is a key feature in 5G/NG cellular networks that creates customized slices for different service types with various quality-of-service (QoS) requirements, which can achieve service differentiation and guarantee service-level agreement (SLA) for each service type. In Wi-Fi networks, there is limited prior work on slicing, and a potential solution is based on a multi-tenant architecture on a single access point (AP) that dedicates different channels to different slices. In this paper, we define a flexible, constrained learning framework to enable slicing in Wi-Fi networks subject to QoS requirements. We specifically propose an unsupervised learning-based network slicing method that leverages a state-augmented primal-dual algorithm, where a neural network policy is trained offline to optimize a Lagrangian function and the dual variable dynamics are updated online in the execution phase. We show that state augmentation is crucial for generating slicing decisions that meet the ergodic QoS requirements.

eess.SP↗

arXiv2025

Feasible Learning

We introduce Feasible Learning (FL), a sample-centric learning paradigm where models are trained by solving a feasibility problem that bounds the loss for each training sample. In contrast to the ubiquitous Empirical Risk Minimization (ERM) framework, which optimizes for average performance, FL demands satisfactory performance on every individual data point. Since any model that meets the prescribed performance threshold is a valid FL solution, the choice of optimization algorithm and its dynamics play a crucial role in shaping the properties of the resulting solutions. In particular, we study a primal-dual approach which dynamically re-weights the importance of each sample during training. To address the challenge of setting a meaningful threshold in practice, we introduce a relaxation of FL that incorporates slack variables of minimal norm. Our empirical analysis, spanning image classification, age regression, and preference optimization in large language models, demonstrates that models trained via FL can learn from data while displaying improved tail behavior compared to ERM, with only a marginal impact on average performance.

cs.LG↗

arXiv2025

Explainable Brain Age Gap Prediction in Neurodegenerative Conditions using coVariance Neural Networks

Brain age is the estimate of biological age derived from neuroimaging datasets using machine learning algorithms. Increasing \textit{brain age gap} characterized by an elevated brain age relative to the chronological age can reflect increased vulnerability to neurodegeneration and cognitive decline. Hence, brain age gap is a promising biomarker for monitoring brain health. However, black-box machine learning approaches to brain age gap prediction have limited practical utility. Recent studies on coVariance neural networks (VNN) have proposed a relatively transparent deep learning pipeline for neuroimaging data analyses, which possesses two key features: (i) inherent \textit{anatomically interpretablity} of derived biomarkers; and (ii) a methodologically interpretable perspective based on \textit{linkage with eigenvectors of anatomic covariance matrix}. In this paper, we apply the VNN-based approach to study brain age gap using cortical thickness features for various prevalent neurodegenerative conditions. Our results reveal distinct anatomic patterns for brain age gap in Alzheimer's disease, frontotemporal dementia, and atypical Parkinsonian disorders. Furthermore, we demonstrate that the distinct anatomic patterns of brain age gap are linked with the differences in how VNN leverages the eigenspectrum of the anatomic covariance matrix, thus lending explainability to the reported results.

cs.LG↗

arXiv2024

Learning State-Augmented Policies for Information Routing in Communication Networks

This paper examines the problem of information routing in a large-scale communication network, which can be formulated as a constrained statistical learning problem having access to only local information. We delineate a novel State Augmentation (SA) strategy to maximize the aggregate information at source nodes using graph neural network (GNN) architectures, by deploying graph convolutions over the topological links of the communication network. The proposed technique leverages only the local information available at each node and efficiently routes desired information to the destination nodes. We leverage an unsupervised learning procedure to convert the output of the GNN architecture to optimal information routing strategies. In the experiments, we perform the evaluation on real-time network topologies to validate our algorithms. Numerical simulations depict the improved performance of the proposed method in training a GNN parameterization as compared to baseline algorithms.

cs.NI↗

arXiv2024

Robust Stochastically-Descending Unrolled Networks

Deep unrolling, or unfolding, is an emerging learning-to-optimize method that unrolls a truncated iterative algorithm in the layers of a trainable neural network. However, the convergence guarantees and generalizability of the unrolled networks are still open theoretical problems. To tackle these problems, we provide deep unrolled architectures with a stochastic descent nature by imposing descending constraints during training. The descending constraints are forced layer by layer to ensure that each unrolled layer takes, on average, a descent step toward the optimum during training. We theoretically prove that the sequence constructed by the outputs of the unrolled layers is then guaranteed to converge for unseen problems, assuming no distribution shift between training and test problems. We also show that standard unrolling is brittle to perturbations, and our imposed constraints provide the unrolled networks with robustness to additive noise and perturbations. We numerically assess unrolled architectures trained under the proposed constraints in two different applications, including the sparse coding using learnable iterative shrinkage and thresholding algorithm (LISTA) and image inpainting using proximal generative flow (GLOW-Prox), and demonstrate the performance and robustness benefits of the proposed method.

cs.LG↗

arXiv2024

Constrained Diffusion Models via Dual Training

Diffusion models have attained prominence for their ability to synthesize a probability distribution for a given dataset via a diffusion process, enabling the generation of new data points with high fidelity. However, diffusion processes are prone to generating samples that reflect biases in a training dataset. To address this issue, we develop constrained diffusion models by imposing diffusion constraints based on desired distributions that are informed by requirements. Specifically, we cast the training of diffusion models under requirements as a constrained distribution optimization problem that aims to reduce the distribution difference between original and generated data while obeying constraints on the distribution of generated data. We show that our constrained diffusion models generate new data from a mixture data distribution that achieves the optimal trade-off among objective and constraints. To train constrained diffusion models, we develop a dual training algorithm and characterize the optimality of the trained constrained diffusion model. We empirically demonstrate the effectiveness of our constrained models in two constrained generation tasks: (i) we consider a dataset with one or more underrepresented classes where we train the model with constraints to ensure fairly sampling from all classes during inference; (ii) we fine-tune a pre-trained diffusion model to sample from a new dataset while avoiding overfitting.

cs.LG↗

arXiv2024

T-GAE: Transferable Graph Autoencoder for Network Alignment

Network alignment is the task of establishing one-to-one correspondences between the nodes of different graphs. Although finding a plethora of applications in high-impact domains, this task is known to be NP-hard in its general form. Existing optimization algorithms do not scale up as the size of the graphs increases. While being able to reduce the matching complexity, current GNN approaches fit a deep neural network on each graph and requires re-train on unseen samples, which is time and memory inefficient. To tackle both challenges we propose T-GAE, a transferable graph autoencoder framework that leverages transferability and stability of GNNs to achieve efficient network alignment on out-of-distribution graphs without retraining. We prove that GNN-generated embeddings can achieve more accurate alignment compared to classical spectral methods. Our experiments on real-world benchmarks demonstrate that T-GAE outperforms the state-of-the-art optimization method and the best GNN approach by up to 38.7% and 50.8%, respectively, while being able to reduce 90% of the training time when matching out-of-distribution large scale networks. We conduct ablation studies to highlight the effectiveness of the proposed encoder architecture and training objective in enhancing the expressiveness of GNNs to match perturbed graphs. T-GAE is also proved to be flexible to utilize matching algorithms of different complexities. Our code is available at https://github.com/Jason-Tree/T-GAE.

cs.LG↗

arXiv2024

Generalizability of Graph Neural Networks for Decentralized Unlabeled Motion Planning

Unlabeled motion planning involves assigning a set of robots to target locations while ensuring collision avoidance, aiming to minimize the total distance traveled. The problem forms an essential building block for multi-robot systems in applications such as exploration, surveillance, and transportation. We address this problem in a decentralized setting where each robot knows only the positions of its $k$-nearest robots and $k$-nearest targets. This scenario combines elements of combinatorial assignment and continuous-space motion planning, posing significant scalability challenges for traditional centralized approaches. To overcome these challenges, we propose a decentralized policy learned via a Graph Neural Network (GNN). The GNN enables robots to determine (1) what information to communicate to neighbors and (2) how to integrate received information with local observations for decision-making. We train the GNN using imitation learning with the centralized Hungarian algorithm as the expert policy, and further fine-tune it using reinforcement learning to avoid collisions and enhance performance. Extensive empirical evaluations demonstrate the scalability and effectiveness of our approach. The GNN policy trained on 100 robots generalizes to scenarios with up to 500 robots, outperforming state-of-the-art solutions by 8.6\% on average and significantly surpassing greedy decentralized methods. This work lays the foundation for solving multi-robot coordination problems in settings where scalability is important.

cs.RO↗

arXiv2024

A Networked Multi-Agent System for Mobile Wireless Infrastructure on Demand

Despite the prevalence of wireless connectivity in urban areas around the globe, there remain numerous and diverse situations where connectivity is insufficient or unavailable. To address this, we introduce mobile wireless infrastructure on demand, a system of UAVs that can be rapidly deployed to establish an ad-hoc wireless network. This network has the capability of reconfiguring itself dynamically to satisfy and maintain the required quality of communication. The system optimizes the positions of the UAVs and the routing of data flows throughout the network to achieve this quality of service (QoS). By these means, task agents using the network simply request a desired QoS, and the system adapts accordingly while allowing them to move freely. We have validated this system both in simulation and in real-world experiments. The results demonstrate that our system effectively offers mobile wireless infrastructure on demand, extending the operational range of task agents and supporting complex mobility patterns, all while ensuring connectivity and being resilient to agent failures.

cs.RO↗

arXiv2024

Generalization of Graph Neural Networks is Robust to Model Mismatch

Graph neural networks (GNNs) have demonstrated their effectiveness in various tasks supported by their generalization capabilities. However, the current analysis of GNN generalization relies on the assumption that training and testing data are independent and identically distributed (i.i.d). This imposes limitations on the cases where a model mismatch exists when generating testing data. In this paper, we examine GNNs that operate on geometric graphs generated from manifold models, explicitly focusing on scenarios where there is a mismatch between manifold models generating training and testing data. Our analysis reveals the robustness of the GNN generalization in the presence of such model mismatch. This indicates that GNNs trained on graphs generated from a manifold can still generalize well to unseen nodes and graphs generated from a mismatched manifold. We attribute this mismatch to both node feature perturbations and edge perturbations within the generated graph. Our findings indicate that the generalization gap decreases as the number of nodes grows in the training graph while increasing with larger manifold dimension as well as larger mismatch. Importantly, we observe a trade-off between the generalization of GNNs and the capability to discriminate high-frequency components when facing a model mismatch. The most important practical consequence of this analysis is to shed light on the filter design of generalizable GNNs robust to model mismatch. We verify our theoretical findings with experiments on multiple real-world datasets.

cs.LG↗

arXiv2024

Loss Shaping Constraints for Long-Term Time Series Forecasting

Several applications in time series forecasting require predicting multiple steps ahead. Despite the vast amount of literature in the topic, both classical and recent deep learning based approaches have mostly focused on minimising performance averaged over the predicted window. We observe that this can lead to disparate distributions of errors across forecasting steps, especially for recent transformer architectures trained on popular forecasting benchmarks. That is, optimising performance on average can lead to undesirably large errors at specific time-steps. In this work, we present a Constrained Learning approach for long-term time series forecasting that aims to find the best model in terms of average performance that respects a user-defined upper bound on the loss at each time-step. We call our approach loss shaping constraints because it imposes constraints on the loss at each time step, and leverage recent duality results to show that despite its non-convexity, the resulting problem has a bounded duality gap. We propose a practical Primal-Dual algorithm to tackle it, and demonstrate that the proposed approach exhibits competitive average performance in time series forecasting benchmarks, while shaping the distribution of errors across the predicted window.

cs.LG↗

arXiv2024

Distributed Training of Large Graph Neural Networks with Variable Communication Rates

Training Graph Neural Networks (GNNs) on large graphs presents unique challenges due to the large memory and computing requirements. Distributed GNN training, where the graph is partitioned across multiple machines, is a common approach to training GNNs on large graphs. However, as the graph cannot generally be decomposed into small non-interacting components, data communication between the training machines quickly limits training speeds. Compressing the communicated node activations by a fixed amount improves the training speeds, but lowers the accuracy of the trained GNN. In this paper, we introduce a variable compression scheme for reducing the communication volume in distributed GNN training without compromising the accuracy of the learned model. Based on our theoretical analysis, we derive a variable compression method that converges to a solution equivalent to the full communication case, for all graph partitioning schemes. Our empirical results show that our method attains a comparable performance to the one obtained with full communication. We outperform full communication at any fixed compression ratio for any communication budget.

cs.LG↗

arXiv2024

Primal Dual Continual Learning: Balancing Stability and Plasticity through Adaptive Memory Allocation

Continual learning is inherently a constrained learning problem. The goal is to learn a predictor under a no-forgetting requirement. Although several prior studies formulate it as such, they do not solve the constrained problem explicitly. In this work, we show that it is both possible and beneficial to undertake the constrained optimization problem directly. To do this, we leverage recent results in constrained learning through Lagrangian duality. We focus on memory-based methods, where a small subset of samples from previous tasks can be stored in a replay buffer. In this setting, we analyze two versions of the continual learning problem: a coarse approach with constraints at the task level and a fine approach with constraints at the sample level. We show that dual variables indicate the sensitivity of the optimal value of the continual learning problem with respect to constraint perturbations. We then leverage this result to partition the buffer in the coarse approach, allocating more resources to harder tasks, and to populate the buffer in the fine approach, including only impactful samples. We derive a deviation bound on dual variables as sensitivity indicators, and empirically corroborate this result in diverse continual learning benchmarks. We also discuss the limitations of these methods with respect to the amount of memory available and the expressiveness of the parametrization.

cs.LG↗

arXiv2024

Near-Optimal Solutions of Constrained Learning Problems

With the widespread adoption of machine learning systems, the need to curtail their behavior has become increasingly apparent. This is evidenced by recent advancements towards developing models that satisfy robustness, safety, and fairness requirements. These requirements can be imposed (with generalization guarantees) by formulating constrained learning problems that can then be tackled by dual ascent algorithms. Yet, though these algorithms converge in objective value, even in non-convex settings, they cannot guarantee that their outcome is feasible. Doing so requires randomizing over all iterates, which is impractical in virtually any modern applications. Still, final iterates have been observed to perform well in practice. In this work, we address this gap between theory and practice by characterizing the constraint violation of Lagrangian minimizers associated with optimal dual variables, despite lack of convexity. To do this, we leverage the fact that non-convex, finite-dimensional constrained learning problems can be seen as parametrizations of convex, functional problems. Our results show that rich parametrizations effectively mitigate the issue of feasibility in dual methods, shedding light on prior empirical successes of dual learning. We illustrate our findings in fair learning tasks.

cs.LG↗