We study Constrained Online Convex Optimization with Memory (COCO-M), where both the loss and the constraints depend on a finite window of past decisions made by the learner. This setting extends the previously studied unconstrained online optimization with memory framework and captures practical problems such as the control of constrained dynamical systems and scheduling with reconfiguration budgets. For this problem, we propose the first algorithms that achieve sublinear regret and sublinear cumulative constraint violation under time-varying constraints, both with and without predictions of future loss and constraint functions. Without predictions, we introduce an adaptive penalty approach that guarantees sublinear regret and constraint violation. When short-horizon and potentially unreliable predictions are available, we reinterpret the problem as online learning with delayed feedback and design an optimistic algorithm whose performance improves as prediction accuracy improves, while remaining robust when predictions are inaccurate. Our results bridge the gap between classical constrained online convex optimization and memory-dependent settings, and provide a versatile learning toolbox with diverse applications.

Applications requiring haptic flows are expected to grow in importance for 6G networks. While the haptic codec has been recently standardized and is based on the Just Noticeable Difference (JND) principle, performance models and associated network control mechanisms are still lacking. We propose in this work a queuing theoretical control framework to minimize the cost of haptic packet delivery, in terms of network resources, while respecting constraints on consecutive packet losses, an essential metric for such applications. The framework switches between different control policies, leveraging resource reservation and/or power control, depending on the network conditions. Each set of policies is parameterized, reflecting a trade-off between system cost and performance of the haptic service. Through this adaptive approach, we derive closed-form solutions that minimize the cost while ensuring adherence to the loss constraints.

We address radio resource allocation for the transport of extreme Ultra Reliable Low Latency and Reliability (URLLC) traffic. One illustrative use case is factory automation using 6G networks. In this context, extreme URLLC has very stringent Quality of Service (QoS) requirements: 0.1 ms for the delay and $10^{-7}$ for the reliability. Reliability can be even higher for other use cases. We model QoS in terms of outage probability, that is the likelihood of failing to serve at least one packet due to insufficient resources, and derive the minimal resource reservation that would meet such requirement. We formulate the problem as chance-constrained optimization and solve it assuming partial knowledge of arriving traffic distribution. We treat the case where traffic is described through its mean and variance, and make use of three approaches to find the optimal solution: distributionally robust using worst-case value at risk approach, distribution-based approximation and bounds from large deviation theory. We also solve the optimization problem using a data driven approach and propose a sliding window mechanism to perform it online. We compare the performance of the aforementioned approaches numerically and show the effectiveness of the data driven approach, accounting for user radio condition heterogeneity and thus different Modulation and Coding Schemes.

We propose a novel resource allocation framework for latency-critical traffic, namely Ultra Reliable Low Latency Communications (URLLC), in mobile networks which meets stringent latency and reliability requirements while minimizing the allocated resources. The Quality of Service (QoS) requirement is formulated in terms of the probability that the latency exceeds a maximal allowed budget. We develop a discrete-time queuing model for the system, in the case where the URLLC reservation is fully-flexible, and when the reservation is made on a slot basis while URLLC packets arrive in mini-slots. We then exploit this model to propose a control scheme that dynamically updates the amount of resources to be allocated per time slot so as to meet the QoS requirement. We formulate an optimization framework that derives the policy which achieves the QoS target while minimizing resource consumption and propose offline algorithms that converge to the quasi optimal reservation policy. In the case when traffic is unknown, we propose online algorithms based on stochastic bandits to achieve this aim. Numerical experiments validate our model and confirm the efficiency of our algorithms in terms of meeting the delay violation target at minimal cost.

We propose a new performance model for transport of time-critical Ultra Reliable Low Latency Communications (URLLC) traffic in 5G networks and Beyond and apply it to dimensioning of such systems. The Quality of Service (QoS) requirement is formulated in terms of an outage probability which is defined as the probability that the latency exceeds a maximal allowed budget, and which should be kept very low. We develop a generic queuing model to compute this outage probability and adapt it to integrate the specificity of the 5G radio interface, taking into account the heterogeneity of users radio conditions and thus their Modulation and Coding Schemes (MCS) as well as retransmissions due to errors on the radio link. We also propose a low complexity method to calculate it using a geometric tail approach to approximate the tail distribution of the queue, for relevant arrival distributions: Poisson and Binomial. We show numerically the performance of our exact model and approximation and that they yield very accurate performance against simulations, and in comparison with other models from the state of the art. We also show the system dimensioning in terms of required resources to satisfy the outage constraint.