In this paper, we analyze the impact of data freshness on remote inference systems, where a pre-trained neural network blue infers a time-varying target (e.g., the locations of vehicles and pedestrians) based on features (e.g., video frames) observed at a sensing node (e.g., a camera). One might expect that the performance of a remote inference system degrades monotonically as the feature becomes stale. Using an information-theoretic analysis, we show that this is true if the feature and target data sequence can be closely approximated as a Markov chain, whereas it is not true if the data sequence is far from being Markovian. Hence, the inference error is a function of Age of Information (AoI), where the function could be non-monotonic. To minimize the inference error in real-time, we propose a new "selection-from-buffer" model for sending the features, which is more general than the "generate-at-will" model used in earlier studies. In addition, we design low-complexity scheduling policies to improve inference performance. For single-source, single-channel systems, we provide an optimal scheduling policy. In multi-source, multi-channel systems, the scheduling problem becomes a multi-action restless multi-armed bandit problem. For this setting, we design a new scheduling policy by integrating Whittle index-based source selection and duality-based feature selection-from-buffer algorithms. This new scheduling policy is proven to be asymptotically optimal. These scheduling results hold for minimizing general AoI functions (monotonic or non-monotonic). Data-driven evaluations demonstrate the significant advantages of our proposed scheduling policies.

We consider a discrete-time system where a resource-constrained source (e.g., a small sensor) transmits its time-sensitive data to a destination over a time-varying wireless channel. Each transmission incurs a fixed transmission cost (e.g., energy cost), and no transmission results in a staleness cost represented by the Age-of-Information. The source must balance the tradeoff between transmission and staleness costs. To address this challenge, we develop a robust online algorithm to minimize the sum of transmission and staleness costs, ensuring a worst-case performance guarantee. While online algorithms are robust, they are usually overly conservative and may have a poor average performance in typical scenarios. In contrast, by leveraging historical data and prediction models, machine learning (ML) algorithms perform well in average cases. However, they typically lack worst-case performance guarantees. To achieve the best of both worlds, we design a learning-augmented online algorithm that exhibits two desired properties: (i) consistency: closely approximating the optimal offline algorithm when the ML prediction is accurate and trusted; (ii) robustness: ensuring worst-case performance guarantee even ML predictions are inaccurate. Finally, we perform extensive simulations to show that our online algorithm performs well empirically and that our learning-augmented algorithm achieves both consistency and robustness.

This paper studies Hoeffding's inequality for Markov chains under the generalized concentrability condition defined via integral probability metric (IPM). The generalized concentrability condition establishes a framework that interpolates and extends the existing hypotheses of Markov chain Hoeffding-type inequalities. The flexibility of our framework allows Hoeffding's inequality to be applied beyond the ergodic Markov chains in the traditional sense. We demonstrate the utility by applying our framework to several non-asymptotic analyses arising from the field of machine learning, including (i) a generalization bound for empirical risk minimization with Markovian samples, (ii) a finite sample guarantee for Ployak-Ruppert averaging of SGD, and (iii) a new regret bound for rested Markovian bandits with general state space. Keywords: Hoeffding's inequality, Markov chains, Dobrushin coefficient, integral probability metric, concentration of measures, ergodicity, empirical risk minimization, stochastic gradient descent, rested bandit