arXiv subjects

Luca Ballotta

Publications and source records attributed to Luca Ballotta.

At least 19 recordsLinked to original sources

arXiv2026

Submodular Policy Learning for Distributed Task Allocation in Open Multi-Agent Systems

This paper studies policy learning for distributed task allocation in open multi-agent systems, where agents may join and leave in a time-varying fashion, with submodular stage team utilities. At each time, the active agents select actions from local categorical policies such that the feasible joint agent-action pairs form a partition matroid. Standard continuous relaxations of submodular set functions are based on independent Bernoulli sampling, making them inconsistent with agents' policies.To solve this mismatch, we propose the \emph{partition multilinear extension} (PME), a policy-based relaxation whose continuous support matches feasible actions under categorical policies.We prove that the marginal gains of the stage utility provide an unbiased estimator of the gradient of the PME and that maximizing the PME over action distributions is equivalent to maximizing the stage utilities over agent actions, which are critical to devise principled policy gradient.Building on this, we design \emph{SubMAPL}, a centralized-training decentralized-execution KL-mirror policy-learning method that uses local marginal gains as stochastic PME gradients during training. KL-mirror updates preserve categorical feasibility without Euclidean projection.In the case where agents run tabular-softmax policies, we introduce open policy migration and an open-system KL tracking variation to handle agent arrivals and departures. Using dynamic regret analysis, we establish a lower bound on the cumulative utility which accounts for the openness of the environment and for the gap between optimal stage-wise and global utilities. Simulations on multi-agent coverage demonstrate that SubMAPL outperforms policy-gradient and online-learning baselines.

cs.MA↗

arXiv2026

Pursuing Optimal Stepsize in Adaptive Gradient-Based Quadratic Optimization

In this paper, we address the problem of achieving fast convergence in gradient descent for quadratic functions without relying on a priori knowledge of global function parameters. Inspired by adaptive stepsize algorithms for smooth convex functions, we propose a computationally lightweight strategy based on running estimates of minimal and maximal local curvatures. We prove that our proposed algorithm converges to the optimal constant stepsize which achieves the fastest convergence. Simulations show that the convergence rate achieved by our proposed algorithm is comparable or superior to recent adaptive approaches both in the quadratic case under consideration and in a preliminary test on logistic classification.

math.OC↗

arXiv2026

Adaptive Stepsizes With Certified Convergence in Distributed Gradient Tracking With Quadratic Costs

In this work, we propose an adaptive stepsize rule with guaranteed convergence for Distributed Gradient Tracking applied to scalar quadratic problems with heterogeneous curvatures. Most distributed gradient-based algorithms require a suitable stepsize selection. Available theoretical bounds are often overly conservative, while practical implementations typically rely on empirically tuned heuristics. Online adaptive strategies have only recently emerged for general distributed convex optimization, but their properties and performance remain only partially understood. To gain analytical insight, we focus on the informative setting of scalar quadratic costs, which allows us to explicitly capture the interplay between network topology and curvature heterogeneity. We derive a convergence bound parameterized only by the essential spectral radius of the consensus matrix and the heterogeneity of the local cost curvatures, both computable online without any prior knowledge of the optimization problem. Optimizing this bound yields a computationally tractable surrogate for the convergence rate and the optimal constant stepsize. The resulting stepsize admits an analytical interpretation, guarantees convergence for arbitrary network topologies and curvature heterogeneity, and is provably tight for complete graphs and homogeneous curvatures. Finally, extensive numerical simulations demonstrate that the proposed distributed adaptive strategy significantly outperforms existing offline and online stepsize selection rules in the considered setting.

math.OC↗

arXiv2026

Submodular Multi-Agent Policy Learning for Online Distributed Task Allocation in Open Multi-Agent Systems

This paper studies multi-agent reinforcement learning with submodular team utilities for online distributed task allocation. In this setting, each agent selects one action from a local categorical policy, so feasible joint actions form a partition matroid over agent-action pairs. Classical multilinear extensions use independent Bernoulli sampling and therefore do not match the categorical policies executed by decentralized agents. To address this mismatch, we introduce the Partition Multilinear Extension (PME), a continuous relaxation whose value equals the expected team utility under factorized categorical policies. We prove that submodular difference rewards provide unbiased PME marginal-gradient information and yield a stagewise score-function policy-gradient estimator. Based on this connection, we propose SubMAPG, a centralized-training decentralized-execution policy-gradient framework with masked categorical policies and submodular difference-reward training signals. For the associated PME marginal-space projected stochastic-gradient dynamics, we prove a stagewise 1/2-approximation guarantee and sublinear dynamic regret in slowly varying environments, measured by the path length of the optimal PME marginals. To handle open systems with time-varying agents and targets, we instantiate SubMAPG with graph neural network policies. Experiments on multi-robot coverage and multi-target tracking show that SubMAPG outperforms local greedy and shared-reward baselines and is competitive with centralized myopic greedy strategies.

eess.SY↗

arXiv2026

Minimal Actuator Selection for Linear Time Invariant Systems

Selecting a few available actuators to ensure the controllability of a linear system is a fundamental problem in control theory. Previous works either focus on optimal performance, simplifying the controllability issue, or make the system controllable under structural assumptions, such as in graphs or when the input matrix is a design parameter. We generalize these approaches to offer a precise characterization of the general minimal actuator selection problem where a set of actuators is given, described by a fixed input matrix, and goal is to choose the fewest actuators that make the system controllable. We show that this problem can be equivalently cast as an integer linear program and, if actuation channels are sufficiently independent, as a set multicover problem under multiplicity constraints. The latter equivalence is always true if the state matrix has all distinct eigenvalues, in which case it simplifies to the set cover problem. Such characterizations hold even when a robust selection that tolerates a given number of faulty actuators is desired. Our established connection legitimates a designer to use algorithms from the rich literature on the set multicover problem to select the smallest subset of actuators, including exact solutions that do not require brute-force search.

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arXiv2025

The role of communication delays in the optimal control of spatially invariant systems

We study optimal proportional feedback controllers for spatially invariant systems when the controller has access to delayed state measurements received from different spatial locations. We analyze how delays affect the spatial locality of the optimal feedback gain leveraging the problem decoupling in the spatial frequency domain. For the cases of expensive control and small delay, we provide exact expressions of the optimal controllers in the limit for infinite control weight and vanishing delay, respectively. In the expensive control regime, the optimal feedback control law decomposes into a delay-aware filtering of the delayed state and the optimal controller in the delay-free setting. Under small delays, the optimal controller is a perturbation of the delay-free one which depends linearly on the delay. We illustrate our analytical findings with a reaction-diffusion process over the real line and a multi-agent system coupled through circulant matrices, showing that delays reduce the effectiveness of optimal feedback control and may require each subsystem within a distributed implementation to communicate with farther-away locations.

math.OC↗

arXiv2025

Confidence Boosts Trust-Based Resilience in Cooperative Multi-Robot Systems

Wireless communication-based multi-robot systems open the door to cyberattacks that can disrupt safety and performance of collaborative robots. The physical channel supporting inter-robot communication offers an attractive opportunity to decouple the detection of malicious robots from task-relevant data exchange between legitimate robots. Yet, trustworthiness indications coming from physical channels are uncertain and must be handled with this in mind. In this paper, we propose a resilient protocol for multi-robot operation wherein a parameter {\lambda}t accounts for how confident a robot is about the legitimacy of nearby robots that the physical channel indicates. Analytical results prove that our protocol achieves resilient coordination with arbitrarily many malicious robots under mild assumptions. Tuning {\lambda}t allows a designer to trade between near-optimal inter-robot coordination and quick task execution; see Fig. 1. This is a fundamental performance tradeoff and must be carefully evaluated based on the task at hand. The effectiveness of our approach is numerically verified with experiments involving platoons of autonomous cars where some vehicles are maliciously spoofed.

eess.SP↗

arXiv2025

Personalized and Resilient Distributed Learning Through Opinion Dynamics

In this paper, we address two practical challenges of distributed learning in multi-agent network systems, namely personalization and resilience. Personalization is the need of heterogeneous agents to learn local models tailored to their own data and tasks, while still generalizing well; on the other hand, the learning process must be resilient to cyberattacks or anomalous training data to avoid disruption. Motivated by a conceptual affinity between these two requirements, we devise a distributed learning algorithm that combines distributed gradient descent and the Friedkin-Johnsen model of opinion dynamics to fulfill both of them. We quantify its convergence speed and the neighborhood that contains the final learned models, which can be easily controlled by tuning the algorithm parameters to enforce a more personalized/resilient behavior. We numerically showcase the effectiveness of our algorithm on synthetic and real-world distributed learning tasks, where it achieves high global accuracy both for personalized models and with malicious agents compared to standard strategies.

cs.MA↗

arXiv2024

Friedkin-Johnsen Model with Diminishing Competition

This letter studies the Friedkin-Johnsen (FJ) model with diminishing competition, or stubbornness. The original FJ model assumes that each agent assigns a constant competition weight to its initial opinion. In contrast, we investigate the effect of diminishing competition on the convergence point and speed of the FJ dynamics. We prove that, if the competition is uniform across agents and vanishes asymptotically, the convergence point coincides with the nominal consensus reached with no competition. However, the diminishing competition slows down convergence according to its own rate of decay. We study this phenomenon analytically and provide upper and lower bounds on the convergence rate. Further, if competition is not uniform across agents, we show that the convergence point may not coincide with the nominal consensus point. Finally, we evaluate our analytical insights numerically.

eess.SY↗

arXiv2024

Pointwise-Sparse Actuator Scheduling for Linear Systems with Controllability Guarantee

This paper considers the design of sparse actuator schedules for linear time-invariant systems. An actuator schedule selects, for each time instant, which control inputs act on the system in that instant. We address the optimal scheduling of control inputs under a hard constraint on the number of inputs that can be used at each time. For a sparsely controllable system, we characterize sparse actuator schedules that make the system controllable, and then devise a greedy selection algorithm that guarantees controllability while heuristically providing low control effort. We further show how to enhance our greedy algorithm via Markov chain Monte Carlo-based randomized optimization

math.OC↗

arXiv2024

The Role of Confidence for Trust-based Resilient Consensus (Extended Version)

We consider a multi-agent system where agents aim to achieve a consensus despite interactions with malicious agents that communicate misleading information. Physical channels supporting communication in cyberphysical systems offer attractive opportunities to detect malicious agents, nevertheless, trustworthiness indications coming from the channel are subject to uncertainty and need to be treated with this in mind. We propose a resilient consensus protocol that incorporates trust observations from the channel and weighs them with a parameter that accounts for how confident an agent is regarding its understanding of the legitimacy of other agents in the network, with no need for the initial observation window $T_0$ that has been utilized in previous works. Analytical and numerical results show that (i) our protocol achieves a resilient consensus in the presence of malicious agents and (ii) the steady-state deviation from nominal consensus can be minimized by a suitable choice of the confidence parameter that depends on the statistics of trust observations.

cs.MA↗

arXiv2024

Safe Distributed Control of Multi-Robot Systems with Communication Delays

Safe operation of multi-robot systems is critical, especially in communication-degraded environments such as underwater for seabed mapping, underground caves for navigation, and in extraterrestrial missions for assembly and construction. We address safety of networked autonomous systems where the information exchanged between robots incurs communication delays. We formalize a notion of distributed control barrier function for multi-robot systems, a safety certificate amenable to a distributed implementation, which provides formal ground to using graph neural networks to learn safe distributed controllers. Further, we observe that learning a distributed controller ignoring delays can severely degrade safety. We finally propose a predictor-based framework to train a safe distributed controller under communication delays, where the current state of nearby robots is predicted from received data and age-of-information. Numerical experiments on multi-robot collision avoidance show that our predictor-based approach can significantly improve the safety of a learned distributed controller under communication delays. A video abstract is available at https://youtu.be/Hcu1Ri32Spk.

cs.RO↗

arXiv2023

VREM-FL: Mobility-Aware Computation-Scheduling Co-Design for Vehicular Federated Learning

Assisted and autonomous driving are rapidly gaining momentum and will soon become a reality. Artificial intelligence and machine learning are regarded as key enablers thanks to the massive amount of data that smart vehicles will collect from onboard sensors. Federated learning is one of the most promising techniques for training global machine learning models while preserving data privacy of vehicles and optimizing communications resource usage. In this article, we propose vehicular radio environment map federated learning (VREM-FL), a computation-scheduling co-design for vehicular federated learning that combines mobility of vehicles with 5G radio environment maps. VREM-FL jointly optimizes learning performance of the global model and wisely allocates communication and computation resources. This is achieved by orchestrating local computations at the vehicles in conjunction with transmission of their local models in an adaptive and predictive fashion, by exploiting radio channel maps. The proposed algorithm can be tuned to trade training time for radio resource usage. Experimental results demonstrate that VREM-FL outperforms literature benchmarks for both a linear regression model (learning time reduced by 28%) and a deep neural network for semantic image segmentation (doubling the number of model updates within the same time window).

eess.SY↗

arXiv2023

Faster Consensus via a Sparser Controller

In this paper, we investigate the architecture of an optimal controller that maximizes the convergence speed of a consensus protocol with single-integrator dynamics. Under the assumption that communication delays increase with the number of hops from which information is allowed to reach each agent, we address the optimal control design under delayed feedback and show that the optimal controller features, in general, a sparsely connected architecture.

math.OC↗

arXiv2022

D-Lite: Navigation-Oriented Compression of 3D Scene Graphs for Multi-Robot Collaboration

For a multi-robot team that collaboratively explores an unknown environment, it is of vital importance that collected information is efficiently shared among robots in order to support exploration and navigation tasks. Practical constraints of wireless channels, such as limited bandwidth, urge robots to carefully select information to be transmitted. In this paper, we consider the case where environmental information is modeled using a 3D Scene Graph, a hierarchical map representation that describes both geometric and semantic aspects of the environment. Then, we leverage graph-theoretic tools, namely graph spanners, to design greedy algorithms that efficiently compress 3D Scene Graphs with the aim of enabling communication between robots under bandwidth constraints. Our compression algorithms are navigation-oriented in that they are designed to approximately preserve shortest paths between locations of interest, while meeting a user-specified communication budget constraint. The effectiveness of the proposed algorithms is demonstrated in synthetic robot navigation experiments in a realistic simulator. A video abstract is available at https://youtu.be/nKYXU5VC6A8.

cs.RO↗

arXiv2022

To Compute or not to Compute? Adaptive Smart Sensing in Resource-Constrained Edge Computing

We consider a network of smart sensors for an edge computing application that sample a time-varying signal and send updates to a base station for remote global monitoring. Sensors are equipped with sensing and compute, and can either send raw data or process them on-board before transmission. Limited hardware resources at the edge generate a fundamental latency-accuracy trade-off: raw measurements are inaccurate but timely, whereas accurate processed updates are available after processing delay. Hence, one needs to decide when sensors should transmit raw measurements or rely on local processing to maximize network monitoring performance. To tackle this sensing design problem, we model an estimation-theoretic optimization framework that embeds both computation and communication latency, and propose a Reinforcement Learning-based approach that dynamically allocates computational resources at each sensor. Effectiveness of our proposed approach is validated through numerical experiments motivated by smart sensing for the Internet of Drones and self-driving vehicles. In particular, we show that, under constrained computation at the base station, monitoring performance can be further improved by an online sensor selection.

cs.DC↗

arXiv2022

Can Competition Outperform Collaboration? The Role of Misbehaving Agents

We investigate a novel approach to resilient distributed optimization with quadratic costs in a multi-agent system prone to unexpected events that make some agents misbehave. In contrast to commonly adopted filtering strategies, we draw inspiration from phenomena modeled through the Friedkin-Johnsen dynamics and argue that adding competition to the mix can improve resilience in the presence of misbehaving agents. Our intuition is corroborated by analytical and numerical results showing that (i) there exists a nontrivial trade-off between full collaboration and full competition and (ii) our competition-based approach can outperform state-of-the-art algorithms based on Weighted Mean Subsequence Reduced. We also study impact of communication topology and connectivity on resilience, pointing out insights to robust network design.

eess.SY↗

arXiv2022

A Reinforcement Learning Approach to Sensing Design in Resource-Constrained Wireless Networked Control Systems

In this paper, we consider a wireless network of smart sensors (agents) that monitor a dynamical process and send measurements to a base station that performs global monitoring and decision-making. Smart sensors are equipped with both sensing and computation, and can either send raw measurements or process them prior to transmission. Constrained agent resources raise a fundamental latency-accuracy trade-off. On the one hand, raw measurements are inaccurate but fast to produce. On the other hand, data processing on resource-constrained platforms generates accurate measurements at the cost of non-negligible computation latency. Further, if processed data are also compressed, latency caused by wireless communication might be higher for raw measurements. Hence, it is challenging to decide when and where sensors in the network should transmit raw measurements or leverage time-consuming local processing. To tackle this design problem, we propose a Reinforcement Learning approach to learn an efficient policy that dynamically decides when measurements are to be processed at each sensor. Effectiveness of our proposed approach is validated through a numerical simulation with case study on smart sensing motivated by the Internet of Drones.

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