Consider an edge computing setting in which a user submits queries for the solution of a linear system to an edge processor, which is subject to time-varying computing availability. The edge processor applies a probabilistic linear solver (PLS) so as to be able to respond to the user's query within the allotted time and computing budget. Feedback to the user is in the form of an uncertainty set. Due to model misspecification, the uncertainty set obtained via a direct application of PLS does not come with coverage guarantees with respect to the true solution of the linear system. This work introduces a new method to calibrate the uncertainty sets produced by PLS with the aim of guaranteeing long-term coverage requirements. The proposed method, referred to as online conformal prediction-PLS (OCP-PLS), assumes sporadic feedback from cloud to edge. This enables the online calibration of uncertainty thresholds via online conformal prediction (OCP), an online optimization method previously studied in the context of prediction models. The validity of OCP-PLS is verified via experiments that bring insights into trade-offs between coverage, prediction set size, and cloud usage.

Online conformal prediction enables the runtime calibration of a pre-trained artificial intelligence model using feedback on its performance. Calibration is achieved through set predictions that are updated via online rules so as to ensure long-term coverage guarantees. While recent research has demonstrated the benefits of incorporating prior knowledge into the calibration process, this has come at the cost of replacing coverage guarantees with less tangible regret guarantees based on the quantile loss. This work introduces intermittent mirror online conformal prediction (IM-OCP), a novel runtime calibration framework that integrates prior knowledge, while maintaining long-term coverage and achieving sub-linear regret. IM-OCP features closed-form updates with minimal memory complexity, and is designed to operate under potentially intermittent feedback.

Predictive models are often required to produce reliable predictions under statistical conditions that are not matched to the training data. A common type of training-testing mismatch is covariate shift, where the conditional distribution of the target variable given the input features remains fixed, while the marginal distribution of the inputs changes. Weighted conformal risk control (W-CRC) uses data collected during the training phase to convert point predictions into prediction sets with valid risk guarantees at test time despite the presence of a covariate shift. However, while W-CRC provides statistical reliability, its efficiency -- measured by the size of the prediction sets -- can only be assessed at test time. In this work, we relate the generalization properties of the base predictor to the efficiency of W-CRC under covariate shifts. Specifically, we derive a bound on the inefficiency of the W-CRC predictor that depends on algorithmic hyperparameters and task-specific quantities available at training time. This bound offers insights on relationships between the informativeness of the prediction sets, the extent of the covariate shift, and the size of the calibration and training sets. Experiments on fingerprinting-based localization validate the theoretical results.

In modern wireless network architectures, such as Open Radio Access Network (O-RAN), the operation of the radio access network (RAN) is managed by applications, or apps for short, deployed at intelligent controllers. These apps are selected from a given catalog based on current contextual information. For instance, a scheduling app may be selected on the basis of current traffic and network conditions. Once an app is chosen and run, it is no longer possible to directly test the key performance indicators (KPIs) that would have been obtained with another app. In other words, we can never simultaneously observe both the actual KPI, obtained by the selected app, and the counterfactual KPI, which would have been attained with another app, for the same network condition, making individual-level counterfactual KPIs analysis particularly challenging. This what-if analysis, however, would be valuable to monitor and optimize the network operation, e.g., to identify suboptimal app selection strategies. This paper addresses the problem of estimating the values of KPIs that would have been obtained if a different app had been implemented by the RAN. To this end, we propose a conformal-prediction-based counterfactual analysis method for wireless systems that provides reliable error bars for the estimated KPIs, despite the inherent covariate shift between logged and test data. Experimental results for medium access control-layer apps and for physical-layer apps demonstrate the merits of the proposed method.

Bayesian optimization (BO) is a sequential approach for optimizing black-box objective functions using zeroth-order noisy observations. In BO, Gaussian processes (GPs) are employed as probabilistic surrogate models to estimate the objective function based on past observations, guiding the selection of future queries to maximize utility. However, the performance of BO heavily relies on the quality of these probabilistic estimates, which can deteriorate significantly under model misspecification. To address this issue, we introduce localized online conformal prediction-based Bayesian optimization (LOCBO), a BO algorithm that calibrates the GP model through localized online conformal prediction (CP). LOCBO corrects the GP likelihood based on predictive sets produced by LOCBO, and the corrected GP likelihood is then denoised to obtain a calibrated posterior distribution on the objective function. The likelihood calibration step leverages an input-dependent calibration threshold to tailor coverage guarantees to different regions of the input space. Under minimal noise assumptions, we provide theoretical performance guarantees for LOCBO's iterates that hold for the unobserved objective function. These theoretical findings are validated through experiments on synthetic and real-world optimization tasks, demonstrating that LOCBO consistently outperforms state-of-the-art BO algorithms in the presence of model misspecification.

We introduce adaptive learn-then-test (aLTT), an efficient hyperparameter selection procedure that provides finite-sample statistical guarantees on the population risk of AI models. Unlike the existing learn-then-test (LTT) technique, which relies on conventional p-value-based multiple hypothesis testing (MHT), aLTT implements sequential data-dependent MHT with early termination by leveraging e-processes. As a result, aLTT can reduce the number of testing rounds, making it particularly well-suited for scenarios in which testing is costly or presents safety risks. Apart from maintaining statistical validity, in applications such as online policy selection for offline reinforcement learning and hyperparameter tuning for engineering systems, aLTT is shown to achieve the same performance as LTT while requiring only a fraction of the testing rounds.

In modern wireless network architectures, such as O-RAN, artificial intelligence (AI)-based applications are deployed at intelligent controllers to carry out functionalities like scheduling or power control. The AI "apps" are selected on the basis of contextual information such as network conditions, topology, traffic statistics, and design goals. The mapping between context and AI model parameters is ideally done in a zero-shot fashion via an automatic model selection (AMS) mapping that leverages only contextual information without requiring any current data. This paper introduces a general methodology for the online optimization of AMS mappings. Optimizing an AMS mapping is challenging, as it requires exposure to data collected from many different contexts. Therefore, if carried out online, this initial optimization phase would be extremely time consuming. A possible solution is to leverage a digital twin of the physical system to generate synthetic data from multiple simulated contexts. However, given that the simulator at the digital twin is imperfect, a direct use of simulated data for the optimization of the AMS mapping would yield poor performance when tested in the real system. This paper proposes a novel method for the online optimization of AMS mapping that corrects for the bias of the simulator by means of limited real data collected from the physical system. Experimental results for a graph neural network-based power control app demonstrate the significant advantages of the proposed approach.

Adaptive Risk Control (ARC) is an online calibration strategy based on set prediction that offers worst-case deterministic long-term risk control, as well as statistical marginal coverage guarantees. ARC adjusts the size of the prediction set by varying a single scalar threshold based on feedback from past decisions. In this work, we introduce Localized Adaptive Risk Control (L-ARC), an online calibration scheme that targets statistical localized risk guarantees ranging from conditional risk to marginal risk, while preserving the worst-case performance of ARC. L-ARC updates a threshold function within a reproducing kernel Hilbert space (RKHS), with the kernel determining the level of localization of the statistical risk guarantee. The theoretical results highlight a trade-off between localization of the statistical risk and convergence speed to the long-term risk target. Thanks to localization, L-ARC is demonstrated via experiments to produce prediction sets with risk guarantees across different data subpopulations, significantly improving the fairness of the calibrated model for tasks such as image segmentation and beam selection in wireless networks.

Large pre-trained sequence models, such as transformers, excel as few-shot learners capable of in-context learning (ICL). In ICL, a model is trained to adapt its operation to a new task based on limited contextual information, typically in the form of a few training examples for the given task. Previous work has explored the use of ICL for channel equalization in single-user multi-input and multiple-output (MIMO) systems. In this work, we demonstrate that ICL can be also used to tackle the problem of multi-user equalization in cell-free MIMO systems with limited fronthaul capacity. In this scenario, a task is defined by channel statistics, signal-to-noise ratio, and modulation schemes. The context encompasses the users' pilot sequences, the corresponding quantized received signals, and the current received data signal. Different prompt design strategies are proposed and evaluated that encompass also large-scale fading and modulation information. Experiments demonstrate that ICL-based equalization provides estimates with lower mean squared error as compared to the linear minimum mean squared error equalizer, especially in the presence of limited fronthaul capacity and pilot contamination.

Large pre-trained sequence models, such as transformer-based architectures, have been recently shown to have the capacity to carry out in-context learning (ICL). In ICL, a decision on a new input is made via a direct mapping of the input and of a few examples from the given task, serving as the task's context, to the output variable. No explicit updates of the model parameters are needed to tailor the decision to a new task. Pre-training, which amounts to a form of meta-learning, is based on the observation of examples from several related tasks. Prior work has shown ICL capabilities for linear regression. In this study, we leverage ICL to address the inverse problem of multiple-input and multiple-output (MIMO) equalization based on a context given by pilot symbols. A task is defined by the unknown fading channel and by the signal-to-noise ratio (SNR) level, which may be known. To highlight the practical potential of the approach, we allow the presence of quantization of the received signals. We demonstrate via numerical results that transformer-based ICL has a threshold behavior, whereby, as the number of pre-training tasks grows, the performance switches from that of a minimum mean squared error (MMSE) equalizer with a prior determined by the pre-trained tasks to that of an MMSE equalizer with the true data-generating prior.