arXiv subjects

João Xavier

Publications and source records attributed to João Xavier.

At least 19 recordsLinked to original sources

arXiv2026

Designing trajectories in the Earth--Moon system: a Levenberg--Marquardt approach

Trajectory design in cislunar space under a high-fidelity ephemeris model (HFEM) is pursued through a nonlinear optimization perspective anchored on the transition of solutions from lower fidelity models, namely the Circular Restricted Three-Body Problem (CR3BP). The optimization problem is posed in the likeness of a multiple-shooting approach, aiming for segment-to-segment continuity while tracking proximity to the original CR3BP structures. The analysis of various formulations leads to the selection of an unconstrained least-squares problem for further investigation. The nonlinear optimization problem is convexified and the use of the Levenberg--Marquardt algorithm, as an alternative to the minimum-norm update equation found in most literature, is investigated for its control over the update step and inherent robustness. Additional techniques, such as adaptive weighting, are employed to further consolidate the behavior of the proposed algorithm in challenging scenarios. Numerical trials evaluate the adequacy of the methodology presented and compare it to the minimum-norm baseline over various application cases, including the generation of quasi-periodic trajectories and orbital transfers between them. The proposed technique is found to be a suitable alternative to the minimum-norm scheme, generally retaining better proximity to the original CR3BP trajectories and providing benefits in numerical robustness and stability. Moreover, the ease of including proximity objectives in a relaxed manner is shown to facilitate control over the shape of the final converged solution.

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arXiv2026

Preorder Construct on Simple Undirected Graphs

We construct a novel preorder on the set of nodes of a simple undirected graph. We prove that the preorder (induced by the topology of the graph) is preserved, e.g., by the logistic dynamical system (both in discrete and continuous time). Moreover, the underlying equivalence relation of the preorder corresponds to the coarsest equitable partition (CEP). This will further imply that the logistic dynamical system on a graph preserves its coarsest equitable partition. The results provide a nontrivial invariant set for the logistic and the like dynamical systems, as we show. We note that our construct provides a functional characterization for the CEP as an alternative to the pure set theoretical iterated degree sequences characterization. The construct and results presented might have independent interest for analysis on graphs or qualitative analysis of dynamical systems over networks.

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arXiv2026

A Multi-Token Coordinate Descent Method for Semi-Decentralized Vertical Federated Learning

Most federated learning (FL) methods use a client-server scheme, where clients communicate only with a central server. However, this scheme is prone to bandwidth bottlenecks at the server and has a single point of failure. In contrast, in a (fully) decentralized approach, clients communicate directly with each other, dispensing with the server and mitigating these issues. Yet, as the client network grows larger and sparser, the convergence of decentralized methods slows down, even failing to converge if the network is disconnected. This work addresses this gap between client-server and decentralized schemes, focusing on the vertical FL setup, where clients hold different features of the same samples. We propose multi-token coordinate descent (MTCD), a flexible semi-decentralized method for vertical FL that can exploit both client-server and client-client links. By selecting appropriate hyperparameters, MTCD recovers the client-sever and decentralized schemes as special cases. In fact, its decentralized instance is itself a novel method of independent interest. Yet, by controlling the degree of dependency on client-server links, MTCD can also explore a spectrum of schemes ranging from client-server to decentralized. We prove that, for sufficiently large batch sizes, MTCD converges at an $\mathcal{O}(1/T)$ rate for nonconvex objectives when the tokens roam across disjoint subsets of clients. To capture the aforementioned drawbacks of the client-server scheme succinctly, we model the relative impact of using client-server versus client-client links as the ratio of their "costs", which depends on the application. This allows us to demonstrate, both analytically and empirically, that by tuning the degree of dependency on the server, the semi-decentralized instances of MTCD can outperform both client-server and decentralized approaches across a range of applications.

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arXiv2026

CLASP: An online learning algorithm for Convex Losses And Squared Penalties

We study Constrained Online Convex Optimization (COCO), where a learner chooses actions iteratively, observes both unanticipated convex loss and convex constraint, and accumulates loss while incurring penalties for constraint violations. We introduce CLASP (Convex Losses And Squared Penalties), an algorithm that minimizes cumulative loss together with squared constraint violations. Our analysis departs from prior work by fully leveraging the firm non-expansiveness of convex projectors, a proof strategy not previously applied in this setting. For convex losses, CLASP achieves regret $O\left(T^{\max\{β,1-β\}}\right)$ and cumulative squared penalty $O\left(T^{1-β}\right)$ for any $β\in (0,1)$. Most importantly, for strongly convex problems, CLASP provides the first logarithmic guarantees on both regret and cumulative squared penalty. In the strongly convex case, the regret is upper bounded by $O( \log T )$ and the cumulative squared penalty is also upper bounded by $O( \log T )$.

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arXiv2025

Communication-efficient Vertical Federated Learning via Compressed Error Feedback

Communication overhead is a known bottleneck in federated learning (FL). To address this, lossy compression is commonly used on the information communicated between the server and clients during training. In horizontal FL, where each client holds a subset of the samples, such communication-compressed training methods have recently seen significant progress. However, in their vertical FL counterparts, where each client holds a subset of the features, our understanding remains limited. To address this, we propose an error feedback compressed vertical federated learning (EF-VFL) method to train split neural networks. In contrast to previous communication-compressed methods for vertical FL, EF-VFL does not require a vanishing compression error for the gradient norm to converge to zero for smooth nonconvex problems. By leveraging error feedback, our method can achieve a $\mathcal{O}(1/T)$ convergence rate for a sufficiently large batch size, improving over the state-of-the-art $\mathcal{O}(1/\sqrt{T})$ rate under $\mathcal{O}(1/\sqrt{T})$ compression error, and matching the rate of uncompressed methods. Further, when the objective function satisfies the Polyak-Łojasiewicz inequality, our method converges linearly. In addition to improving convergence, our method also supports the use of private labels. Numerical experiments show that EF-VFL significantly improves over the prior art, confirming our theoretical results. The code for this work can be found at https://github.com/Valdeira/EF-VFL.

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arXiv2024

Outlier-resilient model fitting via percentile losses: Methods for general and convex residuals

We consider the problem of robustly fitting a model to data that includes outliers by formulating a percentile optimization problem. This problem is non-smooth and non-convex, hence hard to solve. We derive properties that the minimizers of such problems must satisfy. These properties lead to methods that solve the percentile formulation both for general residuals and for convex residuals. The methods fit the model to subsets of the data, and then extract the solution of the percentile formulation from these partial fits. As illustrative simulations show, such methods endure higher outlier percentages, when compared with standard robust estimates. Additionally, the derived properties provide a broader and alternative theoretical validation for existing robust methods, whose validity was previously limited to specific forms of the residuals.

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arXiv2023

Robust Target Localization in 2D: A Value-at-Risk Approach

This paper consider considers the problem of locating a two dimensional target from range-measurements containing outliers. Assuming that the number of outlier is known, we formulate the problem of minimizing inlier losses while ignoring outliers. This leads to a combinatorial, non-convex, non-smooth problem involving the percentile function. Using the framework of risk analysis from Rockafellar et al., we start by interpreting this formulation as a Value-at-risk (VaR) problem from portfolio optimization. To the best of our knowledge, this is the first time that a localization problem was formulated using risk analysis theory. To study the VaR formulation, we start by designing a majorizer set that contains any solution of a general percentile problem. This set is useful because, when applied to a localization scenario in 2D, it allows to majorize the solution set in terms of singletons, circumferences, ellipses and hyperbolas. Using know parametrization of these curves, we propose a grid method for the original non-convex problem. So we reduce the task of optimizing the VaR objective to that of efficiently sampling the proposed majorizer set. We compare our algorithm with four benchmarks in target localization. Numerical simulations show that our method is fast while, on average, improving the accuracy of the best benchmarks by at least 100m in a 1 Km$^2$ area.

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arXiv2023

Distributed detection of ARMA signals

This paper considers a distributed detection setup where agents in a network want to detect a time-varying signal embedded in temporally correlated noise. The signal of interest is the impulse response of an ARMA (auto-regressive moving average) filter, and the noise is the output of yet another ARMA filter which is fed white Gaussian noise. For this extended problem setup, which can prompt novel behaviour, we propose a comprehensive solution. First, we extend the well-known running consensus detector (RCD) to this correlated setup; then, we design an efficient implementation of the RCD by exploiting the underlying ARMA structures; and, finally, we derive the theoretical asymptotic performance of the RCD in this ARMA setup. It turns out that the error probability at each agent exhibits one of two regimes: either (a) the error probability decays exponentially fast to zero or (b) it converges to a strictly positive error floor. While regime (a) spans staple results in large deviation theory, regime (b) is new in distributed detection and is elicited by the ARMA setup. We fully characterize these two scenarios: we give necessary and sufficient conditions, phrased in terms of the zero and poles of the underlying ARMA models, for the emergence of each regime, and provide closed-form expressions for both the decay rates of regime (a) and the positive error floors of regime (b). Our analysis also shows that the ARMA setup leads to two novel features: (1) the threshold level used in RCD can influence the asymptotics of the error probabilities and (2) some agents might be weakly informative, in the sense that their observations do not improve the asymptotic performance of RCD and, as such, can be safely muted to save sensing resources. Numerical simulations illustrate and confirm the theoretical findings.

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arXiv2022

Robust Localization with Bounded Noise: Creating a Superset of the Possible Target Positions via Linear-Fractional Representations

Locating a target is key in many applications, namely in high-stakes real-world scenarios, like detecting humans or obstacles in vehicular networks. In scenarios where precise statistics of the measurement noise are unavailable, applications require localization methods that assume minimal knowledge on the noise distribution. We present a scalable algorithm delimiting a tight superset of all possible target locations, assuming range measurements to known landmarks, contaminated with bounded noise and unknown distributions. This superset is of primary interest in robust statistics since it is a tight majorizer of the set of Maximum-Likelihood (ML) estimates parametrized by noise densities respecting two main assumptions: (1) the noise distribution is supported on a ellipsoidal uncertainty region and (2) the measurements are non-negative with probability one. We create the superset through convex relaxations that use Linear Fractional Representations (LFRs), a well-known technique in robust control. For low noise regimes the supersets created by our method double the accuracy of a standard semidefinite relaxation. For moderate to high noise regimes our method still improves the benchmark but the benefit tends to be less significant, as both supersets tend to have the same size (area).

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arXiv2022

Distributed Banach-Picard Iteration: Application to Distributed EM and Distributed PCA

In recent work, we proposed a distributed Banach-Picard iteration (DBPI) that allows a set of agents, linked by a communication network, to find a fixed point of a locally contractive (LC) map that is the average of individual maps held by said agents. In this work, we build upon the DBPI and its local linear convergence (LLC) guarantees to make several contributions. We show that Sanger's algorithm for principal component analysis (PCA) corresponds to the iteration of an LC map that can be written as the average of local maps, each map known to each agent holding a subset of the data. Similarly, we show that a variant of the expectation-maximization (EM) algorithm for parameter estimation from noisy and faulty measurements in a sensor network can be written as the iteration of an LC map that is the average of local maps, each available at just one node. Consequently, via the DBPI, we derive two distributed algorithms - distributed EM and distributed PCA - whose LLC guarantees follow from those that we proved for the DBPI. The verification of the LC condition for EM is challenging, as the underlying operator depends on random samples, thus the LC condition is of probabilistic nature.

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arXiv2022

Decentralized EM to Learn Gaussian Mixtures from Datasets Distributed by Features

Expectation Maximization (EM) is the standard method to learn Gaussian mixtures. Yet its classic, centralized form is often infeasible, due to privacy concerns and computational and communication bottlenecks. Prior work dealt with data distributed by examples, horizontal partitioning, but we lack a counterpart for data scattered by features, an increasingly common scheme (e.g. user profiling with data from multiple entities). To fill this gap, we provide an EM-based algorithm to fit Gaussian mixtures to Vertically Partitioned data (VP-EM). In federated learning setups, our algorithm matches the centralized EM fitting of Gaussian mixtures constrained to a subspace. In arbitrary communication graphs, consensus averaging allows VP-EM to run on large peer-to-peer networks as an EM approximation. This mismatch comes from consensus error only, which vanishes exponentially fast with the number of consensus rounds. We demonstrate VP-EM on various topologies for both synthetic and real data, evaluating its approximation of centralized EM and seeing that it outperforms the available benchmark.

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arXiv2021

Distributed Banach-Picard Iteration for Locally Contractive Maps

The Banach-Picard iteration is widely used to find fixed points of locally contractive (LC) maps. This paper extends the Banach-Picard iteration to distributed settings; specifically, we assume the map of which the fixed point is sought to be the average of individual (not necessarily LC) maps held by a set of agents linked by a communication network. An additional difficulty is that the LC map is not assumed to come from an underlying optimization problem, which prevents exploiting strong global properties such as convexity or Lipschitzianity. Yet, we propose a distributed algorithm and prove its convergence, in fact showing that it maintains the linear rate of the standard Banach-Picard iteration for the average LC map. As another contribution, our proof imports tools from perturbation theory of linear operators, which, to the best of our knowledge, had not been used before in the theory of distributed computation.

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arXiv2021

StochaLM: a Stochastic alternate Linearization Method for distributed optimization

We present the Stochastic alternate Linearization Method (StochaLM), a token-based method for distributed optimization. This algorithm finds the solution of a consensus optimization problem by solving a sequence of subproblems where some components of the cost are linearized around specific anchor points. StochaLM can be interpreted as a dual block coordinate ascent method whose block components are selected using the state of an ergodic Markov chain. This sampling process is neither essentially cyclic nor independent over time, preventing us from using proofs of convergence of dual block coordinate ascent methods done in previous works. The proof of convergence of our method is, therefore, also novel. We show that, if the cost is strongly convex and the network is fully connected, then, with probability one, the primal sequence generated by StochaLM converges to the solution. Our method is application-friendly, as it has no global hyperparameters to tune; any hyperparameters can be tuned locally by the agents, using information regarding their private cost and neighbourhood. Our method is, therefore, decentralized in the truest sense. Numerical experiments evidence that our method converges to the solution faster than other token-based methods, even when these methods' hyperparameters are tuned for optimal performance.

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arXiv2021

COCO Denoiser: Using Co-Coercivity for Variance Reduction in Stochastic Convex Optimization

First-order methods for stochastic optimization have undeniable relevance, in part due to their pivotal role in machine learning. Variance reduction for these algorithms has become an important research topic. In contrast to common approaches, which rarely leverage global models of the objective function, we exploit convexity and L-smoothness to improve the noisy estimates outputted by the stochastic gradient oracle. Our method, named COCO denoiser, is the joint maximum likelihood estimator of multiple function gradients from their noisy observations, subject to co-coercivity constraints between them. The resulting estimate is the solution of a convex Quadratically Constrained Quadratic Problem. Although this problem is expensive to solve by interior point methods, we exploit its structure to apply an accelerated first-order algorithm, the Fast Dual Proximal Gradient method. Besides analytically characterizing the proposed estimator, we show empirically that increasing the number and proximity of the queried points leads to better gradient estimates. We also apply COCO in stochastic settings by plugging it in existing algorithms, such as SGD, Adam or STRSAGA, outperforming their vanilla versions, even in scenarios where our modelling assumptions are mismatched.

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arXiv2018

FADE: Fast and Asymptotically efficient Distributed Estimator for dynamic networks

Consider a set of agents that wish to estimate a vector of parameters of their mutual interest. For this estimation goal, agents can sense and communicate. When sensing, an agent measures (in additive gaussian noise) linear combinations of the unknown vector of parameters. When communicating, an agent can broadcast information to a few other agents, by using the channels that happen to be randomly at its disposal at the time. To coordinate the agents towards their estimation goal, we propose a novel algorithm called FADE (Fast and Asymptotically efficient Distributed Estimator), in which agents collaborate at discrete time-steps; at each time-step, agents sense and communicate just once, while also updating their own estimate of the unknown vector of parameters. FADE enjoys five attractive features: first, it is an intuitive estimator, simple to derive; second, it withstands dynamic networks, that is, networks whose communication channels change randomly over time; third, it is strongly consistent in that, as time-steps play out, each agent's local estimate converges (almost surely) to the true vector of parameters; fourth, it is both asymptotically unbiased and efficient, which means that, across time, each agent's estimate becomes unbiased and the mean-square error (MSE) of each agent's estimate vanishes to zero at the same rate of the MSE of the optimal estimator at an almighty central node; fifth, and most importantly, when compared with a state-of-art consensus+innovation (CI) algorithm, it yields estimates with outstandingly lower mean-square errors, for the same number of communications -- for example, in a sparsely connected network model with 50 agents, we find through numerical simulations that the reduction can be dramatic, reaching several orders of magnitude.

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arXiv2018

DJAM: distributed Jacobi asynchronous method for learning personal models

Processing data collected by a network of agents often boils down to solving an optimization problem. The distributed nature of these problems calls for methods that are, themselves, distributed. While most collaborative learning problems require agents to reach a common (or consensus) model, there are situations in which the consensus solution may not be optimal. For instance, agents may want to reach a compromise between agreeing with their neighbors and minimizing a personal loss function. We present DJAM, a Jacobi-like distributed algorithm for learning personalized models. This method is implementation-friendly: it has no hyperparameters that need tuning, it is asynchronous, and its updates only require single-neighbor interactions. We prove that DJAM converges with probability one to the solution, provided that the personal loss functions are strongly convex and have Lipschitz gradient. We then give evidence that DJAM is on par with state-of-the-art methods: our method reaches a solution with error similar to the error of a carefully tuned ADMM in about the same number of single-neighbor interactions.

cs.LG↗

arXiv2018

Distributed Estimation Via a Roaming Token

We present an algorithm for the problem of linear distributed estimation of a parameter in a network where a set of agents are successively taking measurements. The approach considers a roaming token in a network that carries the estimate, and jumps from one agent to another in its vicinity according to the probabilities of a Markov chain. When the token is at an agent it records the agent's local information. We analyze the proposed algorithm and show that it is consistent and asymptotically optimal, in the sense that its mean-square-error (MSE) rate of decay approaches the centralized one as the number of iterations increases. We show these results for a scenario where the network changes over time, and we consider two different set of assumptions on the network instantiations: they are i.i.d. and connected on the average, or they are deterministic and strongly connected for every finite time window of a fixed size. Simulations show our algorithm is competitive with consensus+innovations type algorithms, achieving a smaller MSE at each iteration in all considered scenarios.

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arXiv2017

Thermodynamic Limit of Interacting Particle Systems over Time-varying Sparse Random Networks

We establish a functional weak law of large numbers for observable macroscopic state variables of interacting particle systems (e.g., voter and contact processes) over fast time-varying sparse random networks of interactions. We show that, as the number of agents $N$ grows large, the proportion of agents $\left(\overline{Y}_{k}^{N}(t)\right)$ at a certain state $k$ converges in distribution -- or, more precisely, weakly with respect to the uniform topology on the space of \emph{càdlàg} sample paths -- to the solution of an ordinary differential equation over any compact interval $\left[0,T\right]$. Although the limiting process is Markov, the prelimit processes, i.e., the normalized macrostate vector processes $\left(\mathbf{\overline{Y}}^{N}(t)\right)=\left(\overline{Y}_{1}^{N}(t),\ldots,\overline{Y}_{K}^{N}(t)\right)$, are non-Markov as they are tied to the \emph{high-dimensional} microscopic state of the system, which precludes the direct application of standard arguments for establishing weak convergence. The techniques developed in the paper for establishing weak convergence might be of independent interest.

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