Luca Schenato

Alessio Maritan, Subhrakanti Dey, Luca Schenato

Federated learning is a distributed learning framework that allows a set of clients to collaboratively train a model under the orchestration of a central server, without sharing raw data samples. Although in many practical scenarios the derivatives of the objective function are not available, only few works have considered the federated zeroth-order setting, in which functions can only be accessed through a budgeted number of point evaluations. In this work we focus on convex optimization and design the first federated zeroth-order algorithm to estimate the curvature of the global objective, with the purpose of achieving superlinear convergence. We take an incremental Hessian estimator whose error norm converges linearly, and we adapt it to the federated zeroth-order setting, sampling the random search directions from the Stiefel manifold for improved performance. In particular, both the gradient and Hessian estimators are built at the central server in a communication-efficient and privacy-preserving way by leveraging synchronized pseudo-random number generators. We provide a theoretical analysis of our algorithm, named FedZeN, proving local quadratic convergence with high probability and global linear convergence up to zeroth-order precision. Numerical simulations confirm the superlinear convergence rate and show that our algorithm outperforms the federated zeroth-order methods available in the literature.

Luca Ballotta, Nicolò Dal Fabbro, Giovanni Perin et al.

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).

Arman Adibi, Nicolo Dal Fabbro, Luca Schenato et al.

Motivated by applications in large-scale and multi-agent reinforcement learning, we study the non-asymptotic performance of stochastic approximation (SA) schemes with delayed updates under Markovian sampling. While the effect of delays has been extensively studied for optimization, the manner in which they interact with the underlying Markov process to shape the finite-time performance of SA remains poorly understood. In this context, our first main contribution is to show that under time-varying bounded delays, the delayed SA update rule guarantees exponentially fast convergence of the \emph{last iterate} to a ball around the SA operator's fixed point. Notably, our bound is \emph{tight} in its dependence on both the maximum delay $τ_{max}$, and the mixing time $τ_{mix}$. To achieve this tight bound, we develop a novel inductive proof technique that, unlike various existing delayed-optimization analyses, relies on establishing uniform boundedness of the iterates. As such, our proof may be of independent interest. Next, to mitigate the impact of the maximum delay on the convergence rate, we provide the first finite-time analysis of a delay-adaptive SA scheme under Markovian sampling. In particular, we show that the exponent of convergence of this scheme gets scaled down by $τ_{avg}$, as opposed to $τ_{max}$ for the vanilla delayed SA rule; here, $τ_{avg}$ denotes the average delay across all iterations. Moreover, the adaptive scheme requires no prior knowledge of the delay sequence for step-size tuning. Our theoretical findings shed light on the finite-time effects of delays for a broad class of algorithms, including TD learning, Q-learning, and stochastic gradient descent under Markovian sampling.

Alessio Maritan, Luca Schenato

We introduce and address a novel distributed clustering problem where each participant has a private dataset containing only a subset of all available features, and some features are included in multiple datasets. This scenario occurs in many real-world applications, such as in healthcare, where different institutions have complementary data on similar patients. We propose two different algorithms suitable for solving distributed clustering problems that exhibit this type of feature space heterogeneity. The first is a federated algorithm in which participants collaboratively update a set of global centroids. The second is a one-shot algorithm in which participants share a statistical parametrization of their local clusters with the central server, who generates and merges synthetic proxy datasets. In both cases, participants perform local clustering using algorithms of their choice, which provides flexibility and personalized computational costs. Pretending that local datasets result from splitting and masking an initial centralized dataset, we identify some conditions under which the proposed algorithms are expected to converge to the optimal centralized solution. Finally, we test the practical performance of the algorithms on three public datasets.

Nicolò Dal Fabbro, Michele Rossi, Luca Schenato et al.

Edge networks call for communication efficient (low overhead) and robust distributed optimization (DO) algorithms. These are, in fact, desirable qualities for DO frameworks, such as federated edge learning techniques, in the presence of data and system heterogeneity, and in scenarios where internode communication is the main bottleneck. Although computationally demanding, Newton-type (NT) methods have been recently advocated as enablers of robust convergence rates in challenging DO problems where edge devices have sufficient computational power. Along these lines, in this work we propose Q-SHED, an original NT algorithm for DO featuring a novel bit-allocation scheme based on incremental Hessian eigenvectors quantization. The proposed technique is integrated with the recent SHED algorithm, from which it inherits appealing features like the small number of required Hessian computations, while being bandwidth-versatile at a bit-resolution level. Our empirical evaluation against competing approaches shows that Q-SHED can reduce by up to 60% the number of communication rounds required for convergence.

Alessio Maritan, Ganesh Sharma, Luca Schenato et al.

This paper considers the problem of distributed multi-agent learning, where the global aim is to minimize a sum of local objective (empirical loss) functions through local optimization and information exchange between neighbouring nodes. We introduce a Newton-type fully distributed optimization algorithm, Network-GIANT, which is based on GIANT, a Federated learning algorithm that relies on a centralized parameter server. The Network-GIANT algorithm is designed via a combination of gradient-tracking and a Newton-type iterative algorithm at each node with consensus based averaging of local gradient and Newton updates. We prove that our algorithm guarantees semi-global and exponential convergence to the exact solution over the network assuming strongly convex and smooth loss functions. We provide empirical evidence of the superior convergence performance of Network-GIANT over other state-of-art distributed learning algorithms such as Network-DANE and Newton-Raphson Consensus.

Nicolò Dal Fabbro, Subhrakanti Dey, Michele Rossi et al.

There is a growing interest in the distributed optimization framework that goes under the name of Federated Learning (FL). In particular, much attention is being turned to FL scenarios where the network is strongly heterogeneous in terms of communication resources (e.g., bandwidth) and data distribution. In these cases, communication between local machines (agents) and the central server (Master) is a main consideration. In this work, we present SHED, an original communication-constrained Newton-type (NT) algorithm designed to accelerate FL in such heterogeneous scenarios. SHED is by design robust to non i.i.d. data distributions, handles heterogeneity of agents' communication resources (CRs), only requires sporadic Hessian computations, and achieves super-linear convergence. This is possible thanks to an incremental strategy, based on eigendecomposition of the local Hessian matrices, which exploits (possibly) outdated second-order information. The proposed solution is thoroughly validated on real datasets by assessing (i) the number of communication rounds required for convergence, (ii) the overall amount of data transmitted and (iii) the number of local Hessian computations. For all these metrics, the proposed approach shows superior performance against state-of-the art techniques like GIANT and FedNL.

Enrica Rossi, Marco Tognon, Ruggero Carli et al.

In this work we consider the problem of mobile robots that need to manipulate/transport an object via cables or robotic arms. We consider the scenario where the number of manipulating robots is redundant, i.e. a desired object configuration can be obtained by different configurations of the robots. The objective of this work is to show that communication can be used to implement cooperative local feedback controllers in the robots to improve disturbance rejection and reduce structural stress in the object. In particular we consider the realistic scenario where measurements are sampled and transmitted over wireless, and the sampling period is comparable with the system dynamics time constants. We first propose a kinematic model which is consistent with the overall systems dynamics under high-gain control and then we provide sufficient conditions for the exponential stability and monotonic decrease of the configuration error under different norms. Finally, we test the proposed controllers on the full dynamical systems showing the benefit of local communication.

Enrica Rossi, Marco Tognon, Luca Ballotta et al.

In this paper, we propose an inverse-kinematics controller for a class of multi-robot systems in the scenario of sampled communication. The goal is to make a group of robots perform trajectory tracking in a coordinated way when the sampling time of communications is much larger than the sampling time of low-level controllers, disrupting theoretical convergence guarantees of standard control design in continuous time. Given a desired trajectory in configuration space which is precomputed offline, the proposed controller receives configuration measurements, possibly via wireless, to re-compute velocity references for the robots, which are tracked by a low-level controller. We propose joint design of a sampled proportional feedback plus a novel continuous-time feedforward that linearizes the dynamics around the reference trajectory: this method is amenable to distributed communication implementation where only one broadcast transmission is needed per sample. Also, we provide closed-form expressions for instability and stability regions and convergence rate in terms of proportional gain $k$ and sampling period $T$. We test the proposed control strategy via numerical simulations in the scenario of cooperative aerial manipulation of a cable-suspended load using a realistic simulator (Fly-Crane). Finally, we compare our proposed controller with centralized approaches that adapt the feedback gain online through smart heuristics, and show that it achieves comparable performance.

Marco Todescato, Andrea Carron, Ruggero Carli et al.

In this work we study the non-parametric reconstruction of spatio-temporal dynamical Gaussian processes (GPs) via GP regression from sparse and noisy data. GPs have been mainly applied to spatial regression where they represent one of the most powerful estimation approaches also thanks to their universal representing properties. Their extension to dynamical processes has been instead elusive so far since classical implementations lead to unscalable algorithms. We then propose a novel procedure to address this problem by coupling GP regression and Kalman filtering. In particular, assuming space/time separability of the covariance (kernel) of the process and rational time spectrum, we build a finite-dimensional discrete-time state-space process representation amenable of Kalman filtering. With sampling over a finite set of fixed spatial locations, our major finding is that the Kalman filter state at instant $t_k$ represents a sufficient statistic to compute the minimum variance estimate of the process at any $t \geq t_k$ over the entire spatial domain. This result can be interpreted as a novel Kalman representer theorem for dynamical GPs. We then extend the study to situations where the set of spatial input locations can vary over time. The proposed algorithms are finally tested on both synthetic and real field data, also providing comparisons with standard GP and truncated GP regression techniques.

Andrea Carron, Marco Todescato, Ruggero Carli et al.

We consider a scenario where the aim of a group of agents is to perform the optimal coverage of a region according to a sensory function. In particular, centroidal Voronoi partitions have to be computed. The difficulty of the task is that the sensory function is unknown and has to be reconstructed on line from noisy measurements. Hence, estimation and coverage needs to be performed at the same time. We cast the problem in a Bayesian regression framework, where the sensory function is seen as a Gaussian random field. Then, we design a set of control inputs which try to well balance coverage and estimation, also discussing convergence properties of the algorithm. Numerical experiments show the effectivness of the new approach.