On the Dynamic Regret of Following the Regularized Leader: Optimism with History Pruning

We revisit the Follow the Regularized Leader (FTRL) framework for Online Convex Optimization (OCO) over compact sets, focusing on achieving dynamic regret guarantees. Prior work has highlighted the framework's limitations in dynamic environments due to its tendency to produce "lazy" iterates. However, building on insights showing FTRL's ability to produce "agile" iterates, we show that it can indeed recover known dynamic regret bounds through optimistic composition of future costs and careful linearization of past costs, which can lead to pruning some of them. This new analysis of FTRL against dynamic comparators yields a principled way to interpolate between greedy and agile updates and offers several benefits, including refined control over regret terms, optimism without cyclic dependence, and the application of minimal recursive regularization akin to AdaFTRL. More broadly, we show that it is not the lazy projection style of FTRL that hinders (optimistic) dynamic regret, but the decoupling of the algorithm's state (linearized history) from its iterates, allowing the state to grow arbitrarily. Instead, pruning synchronizes these two when necessary.

Optimistic Learning for Communication Networks

AI/ML-based tools are at the forefront of resource management solutions for communication networks. Deep learning, in particular, is highly effective in facilitating fast and high-performing decision-making whenever representative training data is available to build offline accurate models. Conversely, online learning solutions do not require training and enable adaptive decisions based on runtime observations, alas are often overly conservative. This extensive tutorial proposes the use of optimistic learning (OpL) as a decision engine for resource management frameworks in modern communication systems. When properly designed, such solutions can achieve fast and high-performing decisions -- comparable to offline-trained models -- while preserving the robustness and performance guarantees of the respective online learning approaches. We introduce the fundamental concepts, algorithms and results of OpL, discuss the roots of this theory and present different approaches to defining and achieving optimism. We proceed to showcase how OpL can enhance resource management in communication networks for several key problems such as caching, edge computing, network slicing, and workload assignment in decentralized O-RAN platforms. Finally, we discuss the open challenges that must be addressed to unlock the full potential of this new resource management approach.

Smooth Handovers via Smoothed Online Learning

With users demanding seamless connectivity, handovers (HOs) have become a fundamental element of cellular networks. However, optimizing HOs is a challenging problem, further exacerbated by the growing complexity of mobile networks. This paper presents the first countrywide study of HO optimization, through the prism of Smoothed Online Learning (SOL). We first analyze an extensive dataset from a commercial mobile network operator (MNO) in Europe with more than 40M users, to understand and reveal important features and performance impacts on HOs. Our findings highlight a correlation between HO failures/delays, and the characteristics of radio cells and end-user devices, showcasing the impact of heterogeneity in mobile networks nowadays. We subsequently model UE-cell associations as dynamic decisions and propose a realistic system model for smooth and accurate HOs that extends existing approaches by (i) incorporating device and cell features on HO optimization, and (ii) eliminating (prior) strong assumptions about requiring future signal measurements and knowledge of end-user mobility. Our algorithm, aligned with the O-RAN paradigm, provides robust dynamic regret guarantees, even in challenging environments, and shows superior performance in multiple scenarios with real-world and synthetic data.

Optimistic Online Non-stochastic Control via FTRL

This paper brings the concept of "optimism" to the new and promising framework of online Non-stochastic Control (NSC). Namely, we study how can NSC benefit from a prediction oracle of unknown quality responsible for forecasting future costs. The posed problem is first reduced to an optimistic learning with delayed feedback problem, which is handled through the Optimistic Follow the Regularized Leader (OFTRL) algorithmic family. This reduction enables the design of OptFTRL-C, the first Disturbance Action Controller (DAC) with optimistic policy regret bounds. These new bounds are commensurate with the oracle's accuracy, ranging from $\mathcal{O}(1)$ for perfect predictions to the order-optimal $\mathcal{O}(\sqrt{T})$ even when all predictions fail. By addressing the challenge of incorporating untrusted predictions into control systems, our work contributes to the advancement of the NSC framework and paves the way towards effective and robust learning-based controllers.

Fair Resource Allocation in Virtualized O-RAN Platforms

O-RAN systems and their deployment in virtualized general-purpose computing platforms (O-Cloud) constitute a paradigm shift expected to bring unprecedented performance gains. However, these architectures raise new implementation challenges and threaten to worsen the already-high energy consumption of mobile networks. This paper presents first a series of experiments which assess the O-Cloud's energy costs and their dependency on the servers' hardware, capacity and data traffic properties which, typically, change over time. Next, it proposes a compute policy for assigning the base station data loads to O-Cloud servers in an energy-efficient fashion; and a radio policy that determines at near-real-time the minimum transmission block size for each user so as to avoid unnecessary energy costs. The policies balance energy savings with performance, and ensure that both of them are dispersed fairly across the servers and users, respectively. To cater for the unknown and time-varying parameters affecting the policies, we develop a novel online learning framework with fairness guarantees that apply to the entire operation horizon of the system (long-term fairness). The policies are evaluated using trace-driven simulations and are fully implemented in an O-RAN compatible system where we measure the energy costs and throughput in realistic scenarios.

Adaptive Online Non-stochastic Control

We tackle the problem of Non-stochastic Control with the aim of obtaining algorithms that adapt to the controlled environment. Namely, we tailor the FTRL framework to dynamical systems where the existence of a state, or equivalently a memory, couples the effect of the online decisions. By designing novel regularization techniques that take the system's memory into consideration, we obtain controllers with new sub-linear data adaptive policy regret bounds. Furthermore, we append these regularizers with untrusted predictions of future costs, which enables the design of the first Optimistic FTRL-based controller whose regret bound is adaptive to the accuracy of the predictions, shrinking when they are accurate while staying sub-linear even when they all fail.

Adaptive Resource Allocation for Virtualized Base Stations in O-RAN with Online Learning

Open Radio Access Network systems, with their virtualized base stations (vBSs), offer operators the benefits of increased flexibility, reduced costs, vendor diversity, and interoperability. Optimizing the allocation of resources in a vBS is challenging since it requires knowledge of the environment, (i.e., "external'' information), such as traffic demands and channel quality, which is difficult to acquire precisely over short intervals of a few seconds. To tackle this problem, we propose an online learning algorithm that balances the effective throughput and vBS energy consumption, even under unforeseeable and "challenging'' environments; for instance, non-stationary or adversarial traffic demands. We also develop a meta-learning scheme, which leverages the power of other algorithmic approaches, tailored for more "easy'' environments, and dynamically chooses the best performing one, thus enhancing the overall system's versatility and effectiveness. We prove the proposed solutions achieve sub-linear regret, providing zero average optimality gap even in challenging environments. The performance of the algorithms is evaluated with real-world data and various trace-driven evaluations, indicating savings of up to 64.5% in the power consumption of a vBS compared with state-of-the-art benchmarks.

Solving Recurrent MIPs with Semi-supervised Graph Neural Networks

We propose an ML-based model that automates and expedites the solution of MIPs by predicting the values of variables. Our approach is motivated by the observation that many problem instances share salient features and solution structures since they differ only in few (time-varying) parameters. Examples include transportation and routing problems where decisions need to be re-optimized whenever commodity volumes or link costs change. Our method is the first to exploit the sequential nature of the instances being solved periodically, and can be trained with ``unlabeled'' instances, when exact solutions are unavailable, in a semi-supervised setting. Also, we provide a principled way of transforming the probabilistic predictions into integral solutions. Using a battery of experiments with representative binary MIPs, we show the gains of our model over other ML-based optimization approaches.

Bandit Convex Optimisation Revisited: FTRL Achieves $\tilde{O}(t^{1/2})$ Regret

We show that a kernel estimator using multiple function evaluations can be easily converted into a sampling-based bandit estimator with expectation equal to the original kernel estimate. Plugging such a bandit estimator into the standard FTRL algorithm yields a bandit convex optimisation algorithm that achieves $\tilde{O}(t^{1/2})$ regret against adversarial time-varying convex loss functions.

Energy-aware Scheduling of Virtualized Base Stations in O-RAN with Online Learning

The design of Open Radio Access Network (O-RAN) compliant systems for configuring the virtualized Base Stations (vBSs) is of paramount importance for network operators. This task is challenging since optimizing the vBS scheduling procedure requires knowledge of parameters, which are erratic and demanding to obtain in advance. In this paper, we propose an online learning algorithm for balancing the performance and energy consumption of a vBS. This algorithm provides performance guarantees under unforeseeable conditions, such as non-stationary traffic and network state, and is oblivious to the vBS operation profile. We study the problem in its most general form and we prove that the proposed technique achieves sub-linear regret (i.e., zero average optimality gap) even in a fast-changing environment. By using real-world data and various trace-driven evaluations, our findings indicate savings of up to 74.3% in the power consumption of a vBS in comparison with state-of-the-art benchmarks.