arXiv subjects

Tasmeen Zaman Ornee

Publications and source records attributed to Tasmeen Zaman Ornee.

7 recordsLinked to original sources

arXiv2026

Online Scheduling for Throughput Maximization of Time-varying Markovian Channels with Unknown Statistics

We consider a wireless scheduling problem in downlink wireless networks with unknown channel statistics, where a Base Station (BS) sends data to multiple users. The scheduling performance relies heavily on accurate Channel State Information (CSI), which is often costly to acquire. In this paper, CSI is obtained from ACK/NACK feedback, only after each scheduled transmission. Due to limited wireless channel resources, all users cannot be scheduled for transmission simultaneously. Hence, the most recently observed CSI can be outdated. The traditional approach to solve scheduling problems using outdated CSI is to utilize belief states, which are calculated using the time correlation statistics of channels. However, channel statistics are often unknown; consequently, belief states can be uncountable and this approach becomes infeasible. In this paper, we introduce a new sufficient statistics for the wireless scheduling problem. Towards this effort, we characterize the CSI staleness by the Age of Channel State Information (AoCSI) and show that the latest observed CSI and its AoCSI is a sufficient statistic of the history to make the scheduling decisions. Accordingly, we are able to reduce the state space for online learning. Our goal is to develop an online scheduling algorithm that maximizes the expected sum throughput of all users over a finite time-horizon while satisfying a channel resource constraint. The formulated problem is a Restless Multi-armed Bandit (RMAB). We develop an online Maximum Gain First (Online-MGF) policy, which achieves sub-linear regret on the number of episodes. For a special case of ON/OFF channels, we are able to prove indexability and derive a closed-form expression of the Whittle index. Numerical results demonstrate that the Online-MGF policy converges to MGF and Whittle index policies with known statistics within a very few episodes.

cs.NI↗

arXiv2025

Remote Safety Monitoring: Significance-Aware Status Updating for Situational Awareness

In this study, we consider a problem of remote safety monitoring, where a monitor pulls status updates from multiple sensors monitoring several safety-critical situations. Based on the received updates, multiple estimators determine the current safety-critical situations. Due to transmission errors and limited channel resources, the received status updates may not be fresh, resulting in the possibility of misunderstanding the current safety situation. In particular, if a dangerous situation is misinterpreted as safe, the safety risk is high. We study the joint design of transmission scheduling and estimation for multi-sensor, multi-channel remote safety monitoring, aiming to minimize the loss due to the unawareness of potential danger. We show that the joint design of transmission scheduling and estimation can be reduced to a sequential optimization of estimation and scheduling. The scheduling problem can be formulated as a Restless Multi-armed Bandit (RMAB) , for which it is difficult to establish indexability. We propose a low-complexity Maximum Gain First (MGF) policy and prove it is asymptotically optimal as the numbers of sources and channels scale up proportionally, without requiring the indexability condition. We also provide an information-theoretic interpretation of the transmission scheduling problem. Numerical results show that our estimation and scheduling policies achieves higher performance gain over periodic updating, randomized policy, and Maximum Age First (MAF) policy.

cs.IT↗

arXiv2024

Remote Estimation of Gauss-Markov Processes over Multiple Channels: A Whittle Index Policy

We study a sampling and transmission scheduling problem for multi-source remote estimation, where a scheduler determines when to take samples from multiple continuous-time Gauss-Markov processes and send the samples over multiple channels to remote estimators. The sample transmission times are i.i.d. across samples and channels. The objective of the scheduler is to minimize the weighted sum of the time-average expected estimation errors of these Gauss-Markov sources. This problem is a continuous-time Restless Multi-armed Bandit (RMAB) problem with a continuous state space. We prove that the bandits are indexable and derive an exact expression of the Whittle index. To the extent of our knowledge, this is the first Whittle index policy for multi-source signal-aware remote estimation of Gauss-Markov processes. Our results unite two theoretical frameworks that were used for remote estimation and AoI minimization: threshold-based sampling and Whittle index-based scheduling. In the single-source, single-channel scenario, we demonstrate that the optimal solution to the sampling and scheduling problem can be equivalently expressed as both a threshold-based sampling strategy and a Whittle index-based scheduling policy. Notably, the Whittle index is equal to zero if and only if two conditions are satisfied: (i) the channel is idle, and (ii) the estimation error is precisely equal to the threshold in the threshold-based sampling strategy. Moreover, the methodology employed to derive threshold-based sampling strategies in the single-source, single-channel scenario plays a crucial role in establishing indexability and evaluating the Whittle index in the more intricate multi-source, multi-channel scenario. Our numerical results show that the proposed policy achieves high-performance gain over the existing policies when some of the Gauss-Markov processes are highly unstable.

cs.NI↗

arXiv2023

Context-aware Status Updating: Wireless Scheduling for Maximizing Situational Awareness in Safety-critical Systems

In this study, we investigate a context-aware status updating system consisting of multiple sensor-estimator pairs. A centralized monitor pulls status updates from multiple sensors that are monitoring several safety-critical situations (e.g., carbon monoxide density in forest fire detection, machine safety in industrial automation, and road safety). Based on the received sensor updates, multiple estimators determine the current safety-critical situations. Due to transmission errors and limited communication resources, the sensor updates may not be timely, resulting in the possibility of misunderstanding the current situation. In particular, if a dangerous situation is misinterpreted as safe, the safety risk is high. In this paper, we introduce a novel framework that quantifies the penalty due to the unawareness of a potentially dangerous situation. This situation-unaware penalty function depends on two key factors: the Age of Information (AoI) and the observed signal value. For optimal estimators, we provide an information-theoretic bound of the penalty function that evaluates the fundamental performance limit of the system. To minimize the penalty, we study a pull-based multi-sensor, multi-channel transmission scheduling problem. Our analysis reveals that for optimal estimators, it is always beneficial to keep the channels busy. Due to communication resource constraints, the scheduling problem can be modelled as a Restless Multi-armed Bandit (RMAB) problem. By utilizing relaxation and Lagrangian decomposition of the RMAB, we provide a low-complexity scheduling algorithm which is asymptotically optimal. Our results hold for both reliable and unreliable channels. Numerical evidence shows that our scheduling policy can achieve up to 100 times performance gain over periodic updating and up to 10 times over randomized policy.

cs.IT↗

arXiv2022

Performance Bounds for Sampling and Remote Estimation of Gauss-Markov Processes over a Noisy Channel with Random Delay

In this study, we generalize a problem of sampling a scalar Gauss Markov Process, namely, the Ornstein-Uhlenbeck (OU) process, where the samples are sent to a remote estimator and the estimator makes a causal estimate of the observed realtime signal. In recent years, the problem is solved for stable OU processes. We present solutions for the optimal sampling policy that exhibits a smaller estimation error for both stable and unstable cases of the OU process along with a special case when the OU process turns to a Wiener process. The obtained optimal sampling policy is a threshold policy. However, the thresholds are different for all three cases. Later, we consider additional noise with the sample when the sampling decision is made beforehand. The estimator utilizes noisy samples to make an estimate of the current signal value. The mean-square error (mse) is changed from previous due to noise and the additional term in the mse is solved which provides performance upper bound and room for a pursuing further investigation on this problem to find an optimal sampling strategy that minimizes the estimation error when the observed samples are noisy. Numerical results show performance degradation caused by the additive noise.

cs.IT↗

arXiv2022

A Local Geometric Interpretation of Feature Extraction in Deep Feedforward Neural Networks

In this paper, we present a local geometric analysis to interpret how deep feedforward neural networks extract low-dimensional features from high-dimensional data. Our study shows that, in a local geometric region, the optimal weight in one layer of the neural network and the optimal feature generated by the previous layer comprise a low-rank approximation of a matrix that is determined by the Bayes action of this layer. This result holds (i) for analyzing both the output layer and the hidden layers of the neural network, and (ii) for neuron activation functions with non-vanishing gradients. We use two supervised learning problems to illustrate our results: neural network based maximum likelihood classification (i.e., softmax regression) and neural network based minimum mean square estimation. Experimental validation of these theoretical results will be conducted in our future work.

cs.LG↗

arXiv2021

Sampling and Remote Estimation for the Ornstein-Uhlenbeck Process through Queues: Age of Information and Beyond

The age of information, as a metric for evaluating information freshness, has received a lot of attention. Recently, an interesting connection between the age of information and remote estimation error was found in a sampling problem of Wiener processes: If the sampler has no knowledge of the signal being sampled, the optimal sampling strategy is to minimize the age of information; however, by exploiting causal knowledge of the signal values, it is possible to achieve a smaller estimation error. In this paper, we extend a previous study by investigating a problem of sampling a stationary Gauss-Markov process, namely the Ornstein-Uhlenbeck (OU) process. The optimal sampling problem is formulated as a constrained continuous-time Markov decision process (MDP) with an uncountable state space. We provide an exact solution to this MDP: The optimal sampling policy is a threshold policy on instantaneous estimation error and the threshold is found. Further, if the sampler has no knowledge of the OU process, the optimal sampling problem reduces to an MDP for minimizing a nonlinear age of information metric. The age-optimal sampling policy is a threshold policy on expected estimation error and the threshold is found. These results hold for (i) general service time distributions of the queueing server and (ii) sampling problems both with and without a sampling rate constraint. Numerical results are provided to compare different sampling policies.

cs.IT↗