Andres Gomez

EUMAS Conference 2025 Demo Paper

Embedding Autonomous Agents in Resource-Constrained Robotic Platforms

• Negar Halakou
• Juan F. Gutiérrez
• Ye Sun
• Han Jiang
• Xueming Wu
• Andres Gomez

JMLR Journal 2025 Journal Article

Rank-one Convexification for Sparse Regression

• Alper Atamturk
• Andres Gomez

Sparse regression models are increasingly prevalent due to their ease of interpretability and superior out-of-sample performance. However, the exact model of sparse regression with an $\ell_0$-constraint restricting the support of the estimators is a challenging (\NP-hard) non-convex optimization problem. In this paper, we derive new strong convex relaxations for sparse regression. These relaxations are based on the convex-hull formulations for rank-one quadratic terms with indicator variables. The new relaxations can be formulated as semidefinite optimization problems in an extended space and are stronger and more general than the state-of-the-art formulations, including the perspective reformulation and formulations with the reverse Huber penalty and the minimax concave penalty functions. Furthermore, the proposed rank-one strengthening can be interpreted as a non-separable, non-convex, unbiased sparsity-inducing regularizer, which dynamically adjusts its penalty according to the shape of the error function without inducing bias for the sparse solutions. In our computational experiments with benchmark datasets, the proposed conic formulations are solved within seconds and result in near-optimal solutions (with 0.4\% optimality gap on average) for non-convex $\ell_0$-problems. Moreover, the resulting estimators also outperform alternative convex approaches, such as lasso and elastic net regression, from a statistical perspective, achieving high prediction accuracy and good interpretability. [abs] [ pdf ][ bib ] &copy JMLR 2025. ( edit, beta )

AAMAS Conference 2021 Conference Paper

Autonomous Agents on the Edge of Things

• Timotheus Kampik
• Andres Gomez
• Andrei Ciortea
• Simon Mayer

This paper describes a demonstration setup that integrates cognitive agents with the latest W3C standardization efforts for the Web of Things (WoT). The conceptual foundations of the implemented system are the integration of cognitive agent abstractions with W3C Web Things, which are generic abstractions of devices and virtual services that provide agents with various interaction affordances (e. g. , actions, events). Together with the W3C WoT Scripting API, which is an ECMAScript-compatible API for W3C WoT environments, these standards allow JavaScript-based agents to be deployed and to operate in heterogeneous WoT environments. The agents can then be effectively distributed across the physical-virtual space in a write once, run anywhere manner: we deploy agents across a heterogeneous information system landscape that includes Web servers, browser-based front-ends, and constrained devices (microcontrollers). The deployment only requires minor platform-specific adjustments to consider resource and performance limitations on constrained devices. As a running example, we demonstrate a semiautonomous assembly scenario with human-in-the-loop support.

NeurIPS Conference 2021 Conference Paper

Scalable Inference of Sparsely-changing Gaussian Markov Random Fields

• Salar Fattahi
• Andres Gomez

We study the problem of inferring time-varying Gaussian Markov random fields, where the underlying graphical model is both sparse and changes {sparsely} over time. Most of the existing methods for the inference of time-varying Markov random fields (MRFs) rely on the \textit{regularized maximum likelihood estimation} (MLE), that typically suffer from weak statistical guarantees and high computational time. Instead, we introduce a new class of constrained optimization problems for the inference of sparsely-changing Gaussian MRFs (GMRFs). The proposed optimization problem is formulated based on the exact $\ell_0$ regularization, and can be solved in near-linear time and memory. Moreover, we show that the proposed estimator enjoys a provably small estimation error. We derive sharp statistical guarantees in the high-dimensional regime, showing that such problems can be learned with as few as one sample per time period. Our proposed method is extremely efficient in practice: it can accurately estimate sparsely-changing GMRFs with more than 500 million variables in less than one hour.

JMLR Journal 2021 Journal Article

Sparse and Smooth Signal Estimation: Convexification of L0-Formulations

• Alper Atamturk
• Andres Gomez
• Shaoning Han

Signal estimation problems with smoothness and sparsity priors can be naturally modeled as quadratic optimization with $\ell_0$-“norm” constraints. Since such problems are non-convex and hard-to-solve, the standard approach is, instead, to tackle their convex surrogates based on $\ell_1$-norm relaxations. In this paper, we propose new iterative (convex) conic quadratic relaxations that exploit not only the $\ell_0$-“norm” terms, but also the fitness and smoothness functions. The iterative convexification approach substantially closes the gap between the $\ell_0$-“norm” and its $\ell_1$ surrogate. These stronger relaxations lead to significantly better estimators than $\ell_1$-norm approaches and also allow one to utilize affine sparsity priors. In addition, the parameters of the model and the resulting estimators are easily interpretable. Experiments with a tailored Lagrangian decomposition method indicate that the proposed iterative convex relaxations yield solutions within 1\% of the exact $\ell_0$-approach, and can tackle instances with up to 100,000 variables under one minute. [abs] [ pdf ][ bib ] &copy JMLR 2021. ( edit, beta )