We formalize sequential decision–making with information acquisition as the Probing-augmented User-Centric Selection (PUCS) framework, where a learner first probes a subset of arms to obtain side information on resources and rewards, and then assigns K plays to M arms. PUCS encompasses practical scenarios such as ridesharing, wireless scheduling, and content recommendation, in which both resources and payoffs are initially unknown and probing incurs cost. For the offline setting (known payoff distributions), we present a greedy probing algorithm with a constant-factor approximation guarantee of ζ=(e-1)/(2e-1). For the online setting (unknown payoff distributions), we introduce OLPA, a stochastic combinatorial bandit algorithm that achieves a regret bound of O(√T+ln2T). We also prove an Ω(√T) lower bound, showing that the upper bound is tight up to logarithmic factors. Numerical results using two real-world datasets demonstrate the effectiveness of our solutions.

Stochastic gradient descent is one of the most common iterative algorithms used in machine learning and its convergence analysis is a rich area of research. Understanding its convergence properties can help inform what modifications of it to use in different settings. However, most theoretical results either assume convexity or only provide convergence results in mean. This paper, on the other hand, proves convergence bounds in high probability without assuming convexity. Assuming strong smoothness, we prove high probability convergence bounds in two settings: (1) assuming the Polyak-Łojasiewicz inequality and norm sub-Gaussian gradient noise and (2) assuming norm sub-Weibull gradient noise. In the second setting, as an intermediate step to proving convergence, we prove a sub-Weibull martingale difference sequence self-normalized concentration inequality of independent interest. It extends Freedman-type concentration beyond the sub-exponential threshold to heavier-tailed martingale difference sequences. We also provide a post-processing method that picks a single iterate with a provable convergence guarantee as opposed to the usual bound for the unknown best iterate. Our convergence result for sub-Weibull noise extends the regime where stochastic gradient descent has equal or better convergence guarantees than stochastic gradient descent with modifications such as clipping, momentum, and normalization.

Optimization underpins many of the challenges that science and technology face on a daily basis. Recent years have witnessed a major shift from traditional optimization paradigms grounded on batch algorithms for medium-scale problems to challenging dynamic, time-varying, and even huge-size settings. This is driven by technological transformations that converted infrastructural and social platforms into complex and dynamic networked systems with even pervasive sensing and computing capabilities. This article reviews a broad class of state-of-the-art algorithms for time-varying optimization, with an eye to performing both algorithmic development and performance analysis. It offers a comprehensive overview of available tools and methods and unveils open challenges in application domains of broad range of interest. The real-world examples presented include smart power systems, robotics, machine learning, and data analytics, highlighting domain-specific issues and solutions. The ultimate goal is to exemplify wide engineering relevance of analytical tools and pertinent theoretical foundations.

In this paper, a mathematical relationship between temperature and solar irradiance is established in order to reduce the sample space and provide joint probabilistic forecasts. These forecasts can then be used for the purpose of stochastic optimization in power systems. A Volterra system type of model is derived to characterize the dependence of temperature on solar irradiance. A dataset from NOAA weather station in California is used to validate the fit of the model. Using the model, probabilistic forecasts of both temperature and irradiance are provided and the performance of the forecasting technique highlights the efficacy of the proposed approach. Results are indicative of the fact that the underlying correlation between temperature and irradiance is well captured and will therefore be useful to produce future scenarios of temperature and irradiance while approximating the underlying sample space appropriately.

A cross-layer resource allocation scheme for underlay multi-hop cognitive radio networks is formulated, in the presence of uncertain propagation gains and locations of primary users (PUs). Secondary network design variables are optimized under long-term probability-of-interference constraints, by exploiting channel statistics and maps that pinpoint areas where PU receivers are likely to reside. These maps are tracked using a Bayesian approach, based on 1-bit messages - here refereed to as "interference tweet" - broadcasted by the PU system whenever a communication disruption occurs due to interference. Although nonconvex, the problem has zero duality gap, and it is optimally solved using a Lagrangian dual approach. Numerical experiments demonstrate the ability of the proposed scheme to localize PU receivers, as well as the performance gains enabled by this minimal primary-secondary interplay.

Path delays in IP networks are important metrics, required by network operators for assessment, planning, and fault diagnosis. Monitoring delays of all source-destination pairs in a large network are, however, challenging and wasteful of resources. This paper advocates a spatio-temporal Kalman filtering approach to construct network-wide delay maps using measurements on only a few paths. The proposed network cartography framework allows efficient tracking and prediction of delays by relying on both topological as well as historical data. Optimal paths for delay measurement are selected in an online fashion by leveraging the notion of submodularity. The resulting predictor is optimal in the class of linear predictors, and outperforms competing alternatives on real-world data sets.

Conventional spectrum sensing schemes can detect active transmitters but not passive receivers, which have to be nevertheless protected from excessive interference whenever their bands are reused. In this paper, a resource allocation scheme for underlay cognitive radios is formulated, taking into account uncertainty of both propagation gains and locations of incumbent receivers. The performance of orthogonal access by secondary users is maximized under average interference constraints, using channel statistics and maps that pin-point areas where primary receivers are likely to reside. These maps are tracked using a Bayesian approach, based on a 1-bit message sent by the primary system whenever a communication disruption occurs due to interference.

A novel approach to multi-hop routing for cognitive random access is developed under channel gain uncertainty constraints. Motivated by the inherent randomness of the propagation medium, the novel routing strategy leverages pairwise decoding probabilities to randomly route packets to neighboring nodes. The resultant cross-layer optimization framework not only provides optimal routes in a well-defined sense, but also yields transmission probabilities and transmit-powers, thus enabling cognizant adaptation of networking, medium access, and physical layer parameters to the operational environment. The relevant optimization problem is non-convex and hence hard to solve in general. Nevertheless, a successive convex approximation approach is employed to efficiently find a Karush-Kuhn-Tucker solution. Enticingly, the fresh look advocated here permeates benefits also to conventional multi-hop random access networks in the presence of channel uncertainty.

Beamforming for multi-input multi-output (MIMO) cognitive networks is considered in the presence of channel uncertainty induced by errors in estimating cognitive-to-primary channels. A robust beamforming problem is formulated to optimize an appropriate cognitive radio network-wide performance metric, while enforcing protection of the primary system. In spite of the non-convexity of the resultant optimization problem, a block coordinate ascent algorithm is developed with provable convergence to a stationary point. Enticingly, the novel scheme also lends itself naturally to a distributed implementation. Numerical results are reported to corroborate the analytical findings.

To account for the randomness of propagation channels and interference levels in hierarchical spectrum sharing, a novel approach to multihop routing is introduced for cognitive random access networks, whereby packets are randomly routed according to outage probabilities. Leveraging channel and interference level statistics, the resultant cross-layer optimization framework provides optimal routes, transmission probabilities, and transmit-powers, thus enabling cognizant adaptation of routing, medium access, and physical layer parameters to the propagation environment. The associated optimization problem is non-convex, and hence hard to solve in general. Nevertheless, a successive convex approximation approach is adopted to efficiently find a Karush-Kuhn-Tucker solution. Augmented Lagrangian and primal decomposition methods are employed to develop a distributed algorithm, which also lends itself to online implementation. Enticingly, the fresh look advocated here permeates benefits also to conventional multihop wireless networks in the presence of channel uncertainty.

Cognitive radio (CR) networks can re-use the RF spectrum licensed to the primary user (PU) network by carefully controlling the interference to the PUs. However, due to lack of explicit support from the PU system, CR sensing algorithms often face difficulty in acquiring CR-to-PU channels accurately. Moreover, the sensing algorithms cannot detect silent PU receivers, which nevertheless have to be protected. In order to achieve aggressive spectrum re-use even in such challenging scenarios, a CR power control problem with probabilistic interference constraints is formulated. Both log-normal shadowing and small-scale fading uncertainties are taken into account through suitable approximations. In particular, a weighted sum-rate maximization problem is considered, whose Karush-Kuhn-Tucker points are obtained via sequential geometric programming. Numerical tests verify the performance of our novel approach.

In this paper, a consensus-based clock synchronization algorithm is presented and its resilience to frequency displacement estimation errors as well as communication noise is analyzed. The synchronization-enforcing control that is to be applied to clock periods is derived upon re-casting the consensus problem into a convex optimization problem and solving it in a distributed fashion via alternating direction method of multipliers. Conversely, plain consensus is used for reaching agreement on clock values. The proposed algorithm achieves higher convergence rates and equivalent noise resilience with respect to algorithmic solutions based on the only plain average consensus. The superior clock synchronization performance is corroborated via numerical tests.

Cognitive radio (CR) networks can re-use the RF spectrum licensed to a primary user (PU) network, provided that the interference inflicted to the PUs is carefully controlled. However, due to lack of explicit cooperation between CR and PU systems, it is often difficult for CRs to acquire CR-to-PU channels accurately. In fact, if the PU receivers are off, the sensing algorithms cannot obtain the channels for the PU receivers, although they have to be protected nevertheless. In order to achieve aggressive spectrum re-use even in such challenging scenarios, power control algorithms that take channel uncertainty into account are developed. Both log-normal shadowing and small-scale fading effects are considered through suitable approximations. Accounting for the latter, centralized network utility maximization (NUM) problems are formulated, and their Karush-Kuhn-Tucker points are obtained via sequential geometric programming. For the case where CR-to-CR channels are also uncertain, a novel outage probability-based NUM formulation is proposed, and its solution method developed in a unified fashion. Numerical tests verify the performance merits of the novel design.

The robustness of the linear minimum mean square error (LMMSE) channel estimator is studied with respect to the reliability of the estimated channel correlation matrix used for its implementation. The analysis is of interest in practical applications of multiple-input multiple-output (MIMO) systems, where a perfect estimate of the channel correlation matrix is not available. The channel estimation mean square error (MSE) is analytically analyzed assuming a general structure for the estimated channel correlation matrix used to implement the LMMSE channel estimator. The obtained results are successively detailed to the case of channel correlation matrices derived by sample correlation estimation methods. It is observed that the use of a coarse estimate of the channel correlation matrix can lead to a severe degradation on the LMMSE channel estimator performance, whereas the simpler least-square (LS) channel estimator may provide comparatively better results. Nevertheless, it is shown that a robust approach, although suboptimal, relies on implementing the LMMSE channel estimator by assuming transmissions over uncorrelated channels, since, with such an assumption, the resulting estimation MSE is certainly smaller than for the LS channel estimator.

In this paper, we investigate the effects of imperfect knowledge of the channel covariance matrix on the performance of a linear minimum mean-square-error (MMSE) estimator for multiple-input multiple-output (MIMO) channels. The estimation mean-square-error (MSE) is analytically analyzed by providing both a very tight lower bound and an upper bound. The proposed analysis is useful for the understanding of how estimation accuracy of the channel covariance matrix impacts on system performance, depending on the average signal-to-noise ratio (SNR) and specific propagation conditions. Conclusions are fully supported by numerical results.

This paper deals with the impact of channel estimation errors on the capacity of correlated fading MIMO channels. In literature the effect of channel uncertainty at the receiver is often investigated with the assumption that channel estimation errors are identically distributed and independent of both SNR and channel correlation values. In this paper we extend the analysis by considering correlation among the channel estimation errors as typically happen when the MIMO channel to be estimated is spatially correlated. We propose and study upper and lower bounds on the MIMO channel capacity giving emphasis to the impact of the resulting channel estimation error, through its covariance matrix. The role played by the effective SNR and spatial correlation is studied by detailing the results to MIMO systems employing linear MMSE channel estimators.