Synchronous federated learning (FL) scales poorly with the number of clients due to the straggler effect. Algorithms like FedAsync and GeneralizedFedAsync address this limitation by enabling asynchronous communication between clients and the central server. In this work, we rely on stochastic modeling and analysis to better understand the impact of design choices in asynchronous FL algorithms, such as the concurrency level and routing probabilities, and we leverage this knowledge to optimize loss. Compared to most existing studies, we account for the joint impact of heterogeneous and variable service speeds and heterogeneous datasets at the clients. We characterize in particular a fundamental trade-off for optimizing asynchronous FL: minimizing gradient estimation errors by avoiding model parameter staleness, while also speeding up the system by increasing the throughput of model updates. Our two main contributions can be summarized as follows. First, we prove a discrete variant of Little’s law to derive a closed-form expression for relative delay, a metric that quantifies staleness. This allows us to efficiently minimize the average loss per model update, which has been the gold standard in literature to date, using the upper-bound of Leconte et al. as a proxy. Second, we observe that naively optimizing this metric drastically slows down the system by overemphasizing staleness at the expense of throughput. This motivates us to introduce an alternative metric that also accounts for speed, for which we derive a tractable upper-bound that can be minimized numerically. Extensive numerical results show these optimizations enhance accuracy by 10% to 30%.

In this paper, we introduce a policy-gradient method for model-based reinforcement learning (RL) that exploits a type of stationary distributions commonly obtained from Markov decision processes (MDPs) in stochastic networks, queueing systems, and statistical mechanics. Specifically, when the stationary distribution of the MDP belongs to an exponential family that is parametrized by policy parameters, we can improve existing policy gradient methods for average-reward RL. Our key identification is a family of gradient estimators, called score-aware gradient estimators (SAGEs), that enable policy gradient estimation without relying on value-function estimation in the aforementioned setting. We show that SAGE-based policy-gradient locally converges, and we obtain its regret. This includes cases when the state space of the MDP is countable and unstable policies can exist. Under appropriate assumptions such as starting sufficiently close to a maximizer and the existence of a local Lyapunov function, the policy under SAGE-based stochastic gradient ascent has an overwhelming probability of converging to the associated optimal policy. Furthermore, we conduct a numerical comparison between a SAGE-based policy-gradient method and an actor-critic method on several examples inspired from stochastic networks, queueing systems, and models derived from statistical physics. Our results demonstrate that a SAGE-based method finds close-to-optimal policies faster than an actor-critic method.

A classical result in queuing theory states that in a parallel-queue single-server model, the maximum stability region is unaffected by scheduling decision epochs, and in particular is the same for preemptive and non-preemptive systems. We examine a scenario where queues are randomly connected to the server and show that, unlike the classical case, the maximum stability region strongly depends on the scheduling decision epochs. We compare three settings: decisions can be made anytime (unconstrained), decisions are made only at departures (non-preemptive), and decisions occur when a$\gamma $-rate exponential clock rings. We observe a significant reduction in the stability region in the non-preemptive setting compared to the unconstrained one, showing that a non-preemptive scheduler cannot take opportunistically advantage of the random varying connectivity. Also, in the$\gamma $-rate clock setting, one can be arbitrarily close to the maximum stability region in the unconstrained setting if we choose$\gamma $large enough. In all the settings, we show that the Longest Connected Queue (LCQ) policy achieves maximum stability. From a methodological viewpoint, we introduce a new theoretical tool called “test for fluid limits” (TFL), which offers a method to determine stability on the basis of a simple formal test.

We study asynchronous federated learning mechanisms with nodes having potentially different computational speeds. In such an environment, each node is allowed to work on models with potential delays and contribute to updates to the central server at its own pace. Existing analyses of such algorithms typically depend on intractable quantities such as the maximum node delay and do not consider the underlying queuing dynamics of the system. In this paper, we propose a non-uniform sampling scheme for the central server that allows for lower delays with better complexity, taking into account the closed Jackson network structure of the associated computational graph. Our experiments clearly show a significant improvement of our method over current state-of-the-art asynchronous algorithms on image classification problems.

Though very popular, it is well known that the Expectation-Maximisation (EM) algorithm for the Gaussian mixture model performs poorly for non-Gaussian distributions or in the presence of outliers or noise. In this paper, we propose a Flexible EM-like Clustering Algorithm (FEMCA): a new clustering algorithm following an EM procedure is designed. It is based on both estimations of cluster centers and covariances. In addition, using a semi-parametric paradigm, the method estimates an unknown scale parameter per data point. This allows the algorithm to accommodate heavier tail distributions, noise, and outliers without significantly losing efficiency in various classical scenarios. We first present the general underlying model for independent, but not necessarily identically distributed, samples of elliptical distributions. We then derive and analyze the proposed algorithm in this context, showing in particular important distribution-free properties of the underlying data distributions. The algorithm convergence and accuracy properties are analyzed by considering the first synthetic data. Finally, we show that FEMCA outperforms other classical unsupervised methods of the literature, such as k-means, EM for Gaussian mixture models, and its recent modifications or spectral clustering when applied to real data sets as MNIST, NORB, and 20newsgroups.

Linear and Quadratic Discriminant Analysis are well-known classical methods but can heavily suffer from non-Gaussian distributions and/or contaminated datasets, mainly because of the underlying Gaussian assumption that is not robust. To fill this gap, this paper presents a new robust discriminant analysis where each data point is drawn by its own arbitrary Elliptically Symmetrical (ES) distribution and its own arbitrary scale parameter. Such a model allows for possibly very heterogeneous, independent but non-identically distributed samples. After deriving a new decision rule, it is shown that maximum-likelihood parameter estimation and classification are very simple, fast and robust compared to state-of-the-art methods.

Load balancing with various types of load information has become a key component of modern communication and information systems. In many systems, characterizing precisely the blocking probability allows to establish a performance trade-off between delay and losses. We address here the problem of giving robust performance bounds based on the study of the asymptotic behavior of the insensitive load balancing schemes when the number of servers and the load scales jointly. These schemes have the desirable property that the stationary distribution of the resulting stochastic network depends on the distribution of job sizes only through its mean. It was shown that they give good estimates of performance indicators for systems with finite buffers, generalizing henceforth Erlang's formula whereas optimal policies are already theoretically and computationally out of reach for networks of moderate size.

We investigate the scheduling of a common resource between several concurrent users when the feasible transmission rate of each user varies randomly over time. Time is slotted, and users arrive and depart upon service completion. This may model, for example, the flow-level behavior of end-users in a narrowband HDR wireless channel (CDMA 1xEV-DO). As performance criteria, we consider the stability of the system and the mean delay experienced by the users. Given the complexity of the problem, we investigate the fluid-scaled system, which allows to obtain important results and insights for the original system: 1) We characterize for a large class of scheduling policies the stability conditions and identify a set of maximum stable policies, giving in each time-slot preference to users being in their best possible channel condition. We find in particular that many opportunistic scheduling policies like Score-Based, Proportionally Best, or Potential Improvement are stable under the maximum stability conditions, whereas the opportunistic scheduler Relative-Best or thecμ-rule are not. 2) We show that choosing the right tie-breaking rule is crucial for the performance (e.g., average delay) as perceived by a user. We prove that a policy is asymptotically optimal if it is maximum stable and the tie-breaking rule gives priority to the user with the highest departure probability. We will refer to such tie-breaking rule as myopic. 3) We derive the growth rates of the number of users in the system in overload settings under various policies, which give additional insights on the performance. 4) We conclude that simple priority-index policies with the myopic tie-breaking rule are stable and asymptotically optimal. All our findings are validated with extensive numerical experiments.

Channel-aware scheduling strategies provide an effective mechanism for improving the throughput performance in wireless data networks by exploiting channel fluctuations. The performance of channel-aware scheduling algorithms has mainly been examined at the packet level for a static user population, often assuming infinite backlogs. Recently, some studies have also explored the flow-level performance in a scenario with user dynamics governed by the arrival and completion of random service demands over time. Although in certain cases the performance may be evaluated by means of a Processor-Sharing model, in general the flow-level behavior has remained largely intractable, even basic stability properties. In the present paper we derive simple necessary stability conditions, and show that these are also sufficient for a wide class of utility-based scheduling policies. This contrasts with the fact that the latter class of strategies generally fail to provide maximum-throughput guarantees at the packet level.

Many communication systems can be efficiently modelled using queueing networks with a stationary distribution that is insensitive to detailed traffic characteristics and depends on arrival rates and mean service requirements only. This robustness enables simple engineering rules and is thus of considerable practical interest. In this paper we extend previous results by relaxing the usual assumption of static routing and balanced service rates to account for both dynamic capacity allocation and dynamic load balancing. This relaxation is necessary to model systems like grid computing, for instance. Our results identify joint dynamic allocation and routing policies for single input reversible networks that are optimal for a wide range of performance metrics. A simple two-pass algorithm is presented for finding the optimal policy. The derived analytical results are applied in a number of simple numerical examples that illustrate their modelling potential.

A large variety of communication systems, including telephone and data networks, can be represented by so-called Whittle networks. The stationary distribution of these networks is insensitive, depending on the service requirements at each node through their mean only. These models are of considerable practical interest as derived engineering rules are robust to the evolution of traffic characteristics. In this paper we relax the usual assumption of static routing and address the issue of dynamic load balancing. Specifically, we identify the class of load balancing policies which preserve insensitivity and characterize optimal strategies in some specific cases. Analytical results are illustrated numerically on a number of toy network examples.