Céline Comte

Céline Comte, Matthieu Jonckheere, Jaron Sanders et al.

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.

Abdelkrim Alahyane, Céline Comte, Matthieu Jonckheere et al.

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%.

Céline Comte, Pascal Moyal

In this paper, we introduce a versatile scheme for optimizing the arrival rates of quasi-reversible queueing systems. We first propose an alternative definition of quasi-reversibility that encompasses reversibility and highlights the importance of the definition of customer classes. In a second time, we introduce balanced arrival control policies, which generalize the notion of balanced arrival rates introduced in the context of Whittle networks, to the much broader class of quasi-reversible queueing systems. We prove that supplementing a quasi-reversible queueing system with a balanced arrival-control policy preserves the quasi-reversibility, and we specify the form of the stationary measures. We revisit two canonical examples of quasi-reversible queueing systems, Whittle networks and order-independent queues. Lastly, we focus on the problem of admission control and leverage our results in the frameworks of optimization and reinforcement learning.