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Recent years have witnessed the emergence of mobile edge computing (MEC), on the premise of a costeffective enhancement in the computational ability of hardwareconstrained wireless devices (WDs) comprising the Internet of Things (IoT). In a general multi-server multi-user MEC system, each WD has a computational task to execute and has to select binary (off)loading decisions, along with the analog-amplitude resource allocation variables in an online manner, with the goal of minimizing the overall energy-delay cost (EDC) with dynamic system states. While past works typically rely on the explicit expression of the EDC function, the present contribution considers a practical setting, where in lieu of system state information, the EDC function is not available in analytical form, and instead only the function values at queried points are revealed. Towards tackling such a challenging online combinatorial problem with only bandit information, novel Bayesian optimization (BO) based approaches are put forth by leveraging the multi-armed bandit (MAB) framework. Per time slot, the discrete offloading decisions are first obtained via the MAB method, and the analog resource allocation variables are subsequently optimized using the BO selection rule. By exploiting both temporal and contextual information, two novel BO approaches, termed time-varying BO and contextual time-varying BO, are developed. Numerical tests validate the merits of the proposed BO approaches compared with contemporary benchmarks under different MEC network sizes. 

Partial correlations (PCs) and the related inverse covariance matrix adopted by graphical lasso, are widely applicable tools for learning graph connectivity given nodal observations. The resultant estimators however, can be sensitive to outliers. Robust approaches developed so far to cope with outliers do not (explicitly) account for nonlinear interactions possibly present among nodal processes. This can hurt the identification of graph connectivity, merely due to model mismatch. To overcome this limitation, a novel formulation of robust PC is introduced based on nonlinear kernel functions. The proposed scheme leverages robust ridge regression techniques, spectral Fourier feature based kernel approximants, and robust association measures. Numerical tests on synthetic and real data illustrate the potential of the novel approach. 

Graph-guided learning has well-documented impact in a gamut of network science applications. A prototypical graph-guided learning task deals with semi-supervised learning over graphs, where the goal is to predict the nodal values or labels of unobserved nodes, by leveraging a few nodal observations along with the underlying graph structure. This is particularly challenging under privacy constraints or generally when acquiring nodal observations incurs high cost. In this context, the present work puts forth a Bayesian graph-driven self-supervised learning (Self-SL) approach that: (i) learns powerful nodal embeddings emanating from easier to solve auxiliary tasks that map local to global connectivity information; and, (ii) adopts an ensemble of Gaussian processes (EGPs) with adaptive weights as nodal embeddings are processed online. Unlike most existing deterministic approaches, the novel approach offers accurate estimates of the unobserved nodal values along with uncertainty quantification that is important especially in safety critical applications. Numerical tests on synthetic and real graph datasets showcase merits of the novel EGP-based Self-SL method.