In this paper, we study a system in which a sensor forwards status updates to a receiver through an error-prone channel, while the receiver sends the transmission results back to the sensor via a reliable channel. Both channels are subject to random delays. To evaluate the timeliness of the status information at the receiver, we use the Age of Information (AoI) metric. The objective is to design a sampling policy that minimizes the expected time-average AoI, even when the channel statistics (e.g., delay distributions) are unknown. We first review the threshold structure of the optimal offline policy under known channel statistics and then reformulate the design of the online algorithm as a stochastic approximation problem. We propose a Robbins-Monro algorithm to solve this problem and demonstrate that the optimal threshold can be approximated almost surely. Moreover, we prove that the cumulative AoI regret of the online algorithm increases with rate$\mathcal {O}(\ln K)$, where$K$is the number of successful transmissions. In addition, our algorithm is shown to be minimax order optimal, in the sense that for any online learning algorithm, the cumulative AoI regret up to the$K$-th successful transmissions grows with the rate at least$\Omega (\ln K)$in the worst case delay distribution. Finally, we improve the stability of the proposed online learning algorithm through a momentum-based stochastic gradient descent algorithm. Simulation results validate the performance of our proposed algorithm.

Solving image inverse problems (e.g., super-resolution and inpainting) requires generating a high fidelity image that matches the given input (the low-resolution image or the masked image). By using the input image as guidance, we can leverage a pretrained diffusion generative model to solve a wide range of image inverse tasks without task specific model fine-tuning. To precisely estimate the guidance score function of the input image, we propose Diffusion Policy Gradient (DPG), a tractable computation method by viewing the intermediate noisy images as policies and the target image as the states selected by the policy. Experiments show that our method is robust to both Gaussian and Poisson noise degradation on multiple linear and non-linear inverse tasks, resulting into a higher image restoration quality on FFHQ, ImageNet and LSUN datasets.

In this paper, we study an online sampling problem of the Wiener process. The goal is to minimize the mean squared error (MSE) of the remote estimator under a sampling frequency constraint when the transmission delay distribution is unknown. The sampling problem is reformulated into an optional stopping problem, and we propose an online sampling algorithm that can adaptively learn the optimal stopping threshold through stochastic approximation. We prove that the cumulative MSE regret grows with rate$\mathcal{O}(\ln k)$, where$k$is the number of samples. Through Le Cam’s two point method, we show that the worst-case cumulative MSE regret of any online sampling algorithm is lower bounded by$\Omega(\ln k)$. Hence, the proposed online sampling algorithm is minimax order-optimal. Finally, we validate the performance of the proposed algorithm via numerical simulations.

In this work, we study a system with a sensor forwarding status update to the receiver through an error-prone channel, and the receiver sends the transmission results to the sensor via a reliable link. We assume both transmission links suffer from random delays. We use Age of Information (AoI) to measure the freshness of the status information at the receiver. Our goal is to design a sampling policy that minimizes the expected time average AoI when the channel statistics are unknown. The problem is reformulated into a renewal-reward process optimization, and an online algorithm based on the Robbins-Monro algorithm is proposed. We prove that when the forward and backward transmission delays are bounded, the AoI difference between the online algorithm and the optimal policy decays with rate$\mathcal{O}(\ln K/K)$, where$K$is the number of successful transmissions. Simulation results validate the performance of our proposed algorithm.

This paper revisits the problem of sampling and transmitting status updates through a channel with random delay under a sampling frequency constraint. We use the Age of Information (AoI) to characterize the status information freshness at the receiver. The goal is to design a sampling policy that can minimize the average AoI when the statistics of delay is unknown. We reformulate the problem as the optimization of a renewal-reward process, and propose an online sampling strategy based on the Robbins-Monro algorithm. We prove that the proposed algorithm satisfies the sampling frequency constraint. Moreover, when the transmission delay is bounded and its distribution is absolutely continuous, the average AoI obtained by the proposed algorithm converges to the minimum AoI when the number of samples$K$goes to infinity with probability 1. We show that the optimality gap decays with rate$\mathcal {O}\left ({\ln K/K}\right)$, and the proposed algorithm is minimax rate optimal. Simulation results validate the performance of our proposed algorithm.

The diversity-multiplexing tradeoff (DMT) provides a fundamental performance metric for different multiple-input multiple-output (MIMO) schemes in wireless communications. In this paper, we explore the block fading optical wireless communication (OWC) channels and characterize the DMT in the presence of both optical peak- and average-power constraints. Three different fading distributions are considered, which reflect different channel conditions. In each channel condition, we obtain the optimal DMT when the block length is sufficiently large, and we also derive the lower and upper bounds of the DMT curve when the block length is small. These results are dramatically different from the existing DMT results in radio-frequency (RF) channels. These differences may be due to the fact that the optical input signal is real and bounded, while its RF counterpart is usually complex and unbounded.

In this work, we study a status update system with a source node sending timely information to the destination through a channel with random delay. We measure the timeliness of the information stored at the receiver via the Age of Information (AoI), the time elapsed since the freshest sample stored at the receiver is generated. The goal is to design a sampling strategy that minimizes the total cost of the expected time average AoI and sampling cost in the absence of transmission delay statistics. We reformulate the total cost minimization problem as the optimization of a renewal-reward process, and propose an online sampling strategy based on the Robbins-Monro algorithm. Denote K to be the number of samples we have taken. We show that, when the transmission delay is bounded, the expected time average total cost obtained by the proposed online algorithm converges to the minimum cost when K goes to infinity, and the optimality gap decays with rate ${\mathcal{O}}$(ln K/K). Simulation results validate the performance of our proposed algorithm.

In this paper, we study an online sampling problem of the Wiener process. The goal is to minimize the mean squared error (MSE) of the remote estimator under a sampling frequency constraint when the transmission delay distribution is unknown. The sampling problem is reformulated into a renewal reward optimization problem, and we propose an online sampling algorithm that can adaptively learn the optimal sampling policy through stochastic approximation. We show that the cumulative MSE regret grows with rate O(ln k), where k is the number of samples. Through Le Cam's two point method, we show that the worst-case cumulative MSE regret of any online sampling algorithm is lower bounded by Ω (ln k). Hence, the proposed online sampling algorithm is minimax order-optimal. Finally, we validate the performance of the proposed algorithm via numerical simulations.

In this work, we consider the problem of transmission rate selection for a discrete time point-to-point block fading wire-less communication link. The wireless channel remains constant within the channel coherence time but can change rapidly across blocks. The goal is to design a link rate selection strategy that can identify the best transmission rate quickly and adaptively in quasi-static channels. This problem can be cast into the stochastic bandit framework, and the unawareness of time-stamps where channel changes necessitates running change-point detection simultaneously with stochastic bandit algorithms to improve adaptivity. We present a joint channel change-point detection and link rate selection algorithm based on Thompson Sampling (CD-TS) and show it can achieve a sublinear regret with respect to the number of time steps$T$when the channel coherence time is larger than a threshold. We then improve the CD-TS algorithm by considering the fact that higher transmission rate has higher packet-loss probability. Finally, we validate the performance of the proposed algorithms through numerical simulations.

Conventional supervised learning methods, especially deep ones, are found to be sensitive to out-of-distribution (OOD) examples, largely because the learned representation mixes the semantic factor with the variation factor due to their domain-specific correlation, while only the semantic factor causes the output. To address the problem, we propose a Causal Semantic Generative model (CSG) based on a causal reasoning so that the two factors are modeled separately, and develop methods for OOD prediction from a single training domain, which is common and challenging. The methods are based on the causal invariance principle, with a novel design in variational Bayes for both efficient learning and easy prediction. Theoretically, we prove that under certain conditions, CSG can identify the semantic factor by fitting training data, and this semantic-identification guarantees the boundedness of OOD generalization error and the success of adaptation. Empirical study shows improved OOD performance over prevailing baselines.

We study whether and how can we model a joint distribution $p(x,z)$ using two conditional models $p(x|z)$ and $q(z|x)$ that form a cycle. This is motivated by the observation that deep generative models, in addition to a likelihood model $p(x|z)$, often also use an inference model $q(z|x)$ for extracting representation, but they rely on a usually uninformative prior distribution $p(z)$ to define a joint distribution, which may render problems like posterior collapse and manifold mismatch. To explore the possibility to model a joint distribution using only $p(x|z)$ and $q(z|x)$, we study their compatibility and determinacy, corresponding to the existence and uniqueness of a joint distribution whose conditional distributions coincide with them. We develop a general theory for operable equivalence criteria for compatibility, and sufficient conditions for determinacy. Based on the theory, we propose a novel generative modeling framework CyGen that only uses the two cyclic conditional models. We develop methods to achieve compatibility and determinacy, and to use the conditional models to fit and generate data. With the prior constraint removed, CyGen better fits data and captures more representative features, supported by both synthetic and real-world experiments.

We consider updating strategies for a local cache which downloads time-sensitive files from a remote server through a bandwidth-constrained link. The files are requested randomly from the cache by local users according to a popularity distribution which varies over time according to a Markov chain structure. We measure the freshness of the requested time-sensitive files through their Age of Information (AoI). The goal is then to minimize the average AoI of all requested files by appropriately designing the local cache’s downloading strategy. To achieve this goal, the original problem is relaxed and cast into a Constrained Markov Decision Problem (CMDP), which we solve using a Lagrangian approach and Linear Programming. Inspired by this solution for the relaxed problem, we propose a practical cache updating strategy that meets all the constraints of the original problem. Under certain assumptions, the practical updating strategy is shown to be optimal for the original problem in the asymptotic regime of a large number of files. For a finite number of files, we show the gain of our practical updating strategy over the traditional square-root-law strategy (which is optimal for fixed non time-varying file popularities) through numerical simulations.

This work is motivated by the need of collecting fresh data from power-constrained sensors in the industrial Internet of Things (IIoT) network. A recently proposed metric, the Age of Information (AoI) is adopted to measure data freshness from the perspective of the central controller in the IIoT network. We wonder what is the minimum average AoI the network can achieve and how to design scheduling algorithms to approach it. To answer these questions when the channel states of the network are time-varying and scheduling decisions are restricted to both bandwidth and power consumption constraint, we first decouple the multi-sensor scheduling problem into a single-sensor constrained Markov decision process (CMDP) by relaxing the hard bandwidth constraint. Next we exploit the threshold structure of the optimal policy for the decoupled single sensor CMDP and obtain the optimum solution through linear programming (LP). Finally, an asymptotically optimal truncated policy that can satisfy the hard bandwidth constraint is built upon the optimal solution to each of the decoupled single-sensor. Our investigation shows that to obtain a small average AoI over the network: (1) The scheduler exploits good channels to schedule sensors supported by limited power; (2) Sensors equipped with enough transmission power are updated in a timely manner such that the bandwidth constraint can be satisfied.

In this work, a wireless broadcast network with a base station (BS) sending random time-sensitive information updates to multiple users under bandwidth constraint is considered. To measure the effect of data desynchronization when the updates appear randomly because of external environment, the metric Age of Synchronization (AoS) is adopted in this work. It shows the amount of the time elapsed since freshest information at the receiver becomes desynchronized. The AoS minimization scheduling problem is formulated into a discrete time Markov decision process and the optimal solution is approximated through structural finite state policy iteration. An index based heuristic scheduling policy based on restless multi-arm bandit (RMAB) is provided to further reduce the computational complexity. Simulation results show that the proposed index policy achieves compatible performance with the MDP and is close to the AoS lower bound. Our work indicates that, to obtain a small AoS over the entire network, users with larger transmission success probability and smaller random update probability are more likely to be scheduled at smaller AoS.

In this work, a wireless broadcast network with a base station (BS) sending random time-sensitive information updates to multiple users with interference constraints is considered. The Age of Synchronization (AoS), namely the amount of time elapsed since the information stored at the network user becomes desynchronized, is adopted to measure data freshness from the perspective of network users. Compared with the more widely used metric-the Age of Information (AoI), AoS accounts for the freshness of the randomly changing content. We formulate the scheduling problem into a discrete time Markov decision process and approximate the optimal solution through finite state policy iteration. An index based heuristic scheduling policy based on restless multi-arm bandit (RMAB) is provided to reduce computational complexity. Numerical results are presented to demonstrate the performance of the proposed policies.

To increase the performance of a brain-computer interface and brain-machine interface system, we propose some methods and algorithms for electroencephalograph (EEG) signal analysis. The recorded EEG signal is transmitted to the computer and the upper limb robotic arm interface via a bluetooth. To obtain effective commands from brain, the recorded EEG signal is processed by a front filter, denoise filter, feature extraction, and classification, while the personal computer software and upper limb arm are driven by EEG-based commands. Through the encoders and gyroscopes on the upper limb arm, we can acquire some feedback signals in real time, such as joint angle, arm accelerated speed, and angular speed. The theory of wavelet denoising method, common spatial pattern algorithm and linear discriminant analysis algorithm are investigated in this paper. The simulations and experiments demonstrate the effectiveness and accuracy of these algorithms on EEG signal denoising, feature extraction, and classification.