We tackle the anomaly detection problem within a given set of binary processes through a learning-based controlled sensing approach. This problem is particularly pertinent to applications related to the Internet of Things (IoT) that monitor multiple related processes. Each process is defined by a binary random variable indicating its anomalous status. To pinpoint anomalies, a decision-making agent observes a subset of processes at each time point, with each observation incurring an associated cost. We formulate a sequential selection policy that dynamically determines which processes to observe at each moment, aiming to minimize both decision delay and sensing cost. The conventional solution using model-based active hypothesis testing algorithms overlooks the joint statistics of the processes and fails to consider unequal sensing costs or errors in observations. To solve this problem, we, for the first time, pose it as a sequential hypothesis testing problem within the framework of Markov decision processes (MDPs), leveraging both a Bayesian log-likelihood ratio-based reward and an entropy-based reward. We address this problem through two approaches: 1) a deep reinforcement learning-based method involving the design of both deep Q-learning (DQN) and policy gradient actor-critic (AC) algorithms and 2) a deep active inference (AI)-based approach. Our model-based posterior updates to tackle the uncertainties in the observations, combined with the data-driven neural networks to handle the underlying statistical dependence between the processes, strike a balance between the model-based and the data-driven approaches. Our numerical experiments showcase the effectiveness of our algorithms, illustrating their capability to adapt to any unknown statistical dependence among the processes.

We address the problem of sequentially selecting and observing processes from a given set to find the anomalies among them. The decision-maker observes a subset of the processes at any given time instant and obtains a noisy binary indicator of whether or not the corresponding process is anomalous. We develop an anomaly detection algorithm that chooses the processes to be observed at a given time instant, decides when to stop taking observations, and declares the decision on anomalous processes. The objective of the detection algorithm is to identify the anomalies with an accuracy exceeding the desired value while minimizing the delay in decision making. We devise a centralized algorithm where the processes are jointly selected by a common agent as well as a decentralized algorithm where the decision of whether to select a process is made independently for each process. Our algorithms rely on a Markov decision process defined using the marginal probability of each process being normal or anomalous, conditioned on the observations. We implement the detection algorithms using the deep actor-critic reinforcement learning framework. Unlike prior work on this topic that has exponential complexity in the number of processes, our algorithms have computational and memory requirements that are both polynomial in the number of processes. We demonstrate the efficacy of these algorithms using numerical experiments by comparing them with state-of-the-art methods.

We consider a set of data samples such that a fraction of the samples are arbitrary outliers, and the rest are the output samples of a single-layer neural network with rectified linear unit (ReLU) activation. Our goal is to estimate the parameters (weight matrix and bias vector) of the neural network, assuming the bias vector to be non-negative. We estimate the network parameters using the gradient descent algorithm combined with either the median- or trimmed mean-based filters to mitigate the effect of the arbitrary outliers. We then prove that $\tilde{O}( \frac{1}{p^2}+\frac{1}{\epsilon^2p})$ samples and $\tilde{O} ( \frac{d^2}{p^2}+ \frac{d^2}{\epsilon^2p})$ time are sufficient for our algorithm to estimate the neural network parameters within an error of $\epsilon$ when the outlier probability is $1-p$, {where $2/3< p \leq 1$} and the problem dimension is $d$ (with log factors being ignored here). Our theoretical and simulation results provide insights into the training complexity of ReLU neural networks in terms of the probability of outliers and problem dimension.