Non-Asymptotic Bounds for Closed-Loop Identification of Unstable Nonlinear Stochastic Systems

We consider the problem of least squares parameter estimation from single-trajectory data for discrete-time, unstable, closed-loop nonlinear stochastic systems, with linearly parameterised uncertainty. Assuming a region of the state space produces informative data, and the system is sub-exponentially unstable, we establish non-asymptotic guarantees on the estimation error at times where the state trajectory evolves in this region. If the whole state space is informative, high probability guarantees on the error hold for all times. Examples are provided where our results are useful for analysis, but existing results are not.

GNN-Based Joint Channel and Power Allocation in Heterogeneous Wireless Networks

The optimal allocation of channels and power resources plays a crucial role in ensuring minimal interference, maximal data rates, and efficient energy utilisation. As a successful approach for tackling resource management problems in wireless networks, Graph Neural Networks (GNNs) have attracted a lot of attention. This article proposes a GNN-based algorithm to address the joint resource allocation problem in heterogeneous wireless networks. Concretely, we model the heterogeneous wireless network as a heterogeneous graph and then propose a graph neural network structure intending to allocate the available channels and transmit power to maximise the network throughput. Our proposed joint channel and power allocation graph neural network (JCPGNN) comprises a shared message computation layer and two task-specific layers, with a dedicated focus on channel and power allocation tasks, respectively. Comprehensive experiments demonstrate that the proposed algorithm achieves satisfactory performance but with higher computational efficiency compared to traditional optimisation algorithms.

Accelerating Graph Neural Networks via Edge Pruning for Power Allocation in Wireless Networks

Neural Networks (GNNs) have recently emerged as a promising approach to tackling power allocation problems in wireless networks. Since unpaired transmitters and receivers are often spatially distant, the distanced-based threshold is proposed to reduce the computation time by excluding or including the channel state information in GNNs. In this paper, we are the first to introduce a neighbour-based threshold approach to GNNs to reduce the time complexity. Furthermore, we conduct a comprehensive analysis of both distance-based and neighbour-based thresholds and provide recommendations for selecting the appropriate value in different communication channel scenarios. We design the corresponding distance-based and neighbour-based Graph Neural Networks with the aim of allocating transmit powers to maximise the network throughput. Our results show that our proposed GNNs offer significant advantages in terms of reducing time complexity while preserving strong performance. Besides, we show that by choosing a suitable threshold, the time complexity is reduced from O(|V|^2) to O(|V|), where |V| is the total number of transceiver pairs.

Stability Bounds for Learning-Based Adaptive Control of Discrete-Time Multi-Dimensional Stochastic Linear Systems with Input Constraints

We consider the problem of adaptive stabilization for discrete-time, multi-dimensional linear systems with bounded control input constraints and unbounded stochastic disturbances, where the parameters of the true system are unknown. To address this challenge, we propose a certainty-equivalent control scheme which combines online parameter estimation with saturated linear control. We establish the existence of a high probability stability bound on the closed-loop system, under additional assumptions on the system and noise processes. Finally, numerical examples are presented to illustrate our results.

Graph Neural Networks for Power Allocation in Wireless Networks with Full Duplex Nodes

Due to mutual interference between users, power allocation problems in wireless networks are often non-convex and computationally challenging. Graph neural networks (GNNs) have recently emerged as a promising approach to tackling these problems and an approach that exploits the underlying topology of wireless networks. In this paper, we propose a novel graph representation method for wireless networks that include full-duplex (FD) nodes. We then design a corresponding FD Graph Neural Network (F-GNN) with the aim of allocating transmit powers to maximise the network throughput. Our results show that our F-GNN achieves state-of-art performance with significantly less computation time. Besides, F-GNN offers an excellent trade-off between performance and complexity compared to classical approaches. We further refine this trade-off by introducing a distance-based threshold for inclusion or exclusion of edges in the network. We show that an appropriately chosen threshold reduces required training time by roughly 20% with a relatively minor loss in performance.

On the tightness of information-theoretic bounds on generalization error of learning algorithms

A recent line of works, initiated by Russo and Xu, has shown that the generalization error of a learning algorithm can be upper bounded by information measures. In most of the relevant works, the convergence rate of the expected generalization error is in the form of $O(\sqrt{\lambda/n})$ where $\lambda$ is some information-theoretic quantities such as the mutual information or conditional mutual information between the data and the learned hypothesis. However, such a learning rate is typically considered to be ``slow", compared to a ``fast rate" of $O(\lambda/n)$ in many learning scenarios. In this work, we first show that the square root does not necessarily imply a slow rate, and a fast rate result can still be obtained using this bound under appropriate assumptions. Furthermore, we identify the critical conditions needed for the fast rate generalization error, which we call the $(\eta,c)$-central condition. Under this condition, we give information-theoretic bounds on the generalization error and excess risk, with a fast convergence rate for specific learning algorithms such as empirical risk minimization and its regularized version. Finally, several analytical examples are given to show the effectiveness of the bounds.

On the Value of Stochastic Side Information in Online Learning

We study the effectiveness of stochastic side information in deterministic online learning scenarios. We propose a forecaster to predict a deterministic sequence where its performance is evaluated against an expert class. We assume that certain stochastic side information is available to the forecaster but not the experts. We define the minimax expected regret for evaluating the forecasters performance, for which we obtain both upper and lower bounds. Consequently, our results characterize the improvement in the regret due to the stochastic side information. Compared with the classical online learning problem with regret scales with O(\sqrt(n)), the regret can be negative when the stochastic side information is more powerful than the experts. To illustrate, we apply the proposed bounds to two concrete examples of different types of side information.

Committed Private Information Retrieval

A private information retrieval (PIR) scheme allows a client to retrieve a data item $x_i$ among $n$ items $x_1,x_2,...,x_n$ from $k$ servers, without revealing what $i$ is even when $t < k$ servers collude and try to learn $i$. Such a PIR scheme is said to be $t$-private. A PIR scheme is $v$-verifiable if the client can verify the correctness of the retrieved $x_i$ even when $v \leq k$ servers collude and try to fool the client by sending manipulated data. Most of the previous works in the literature on PIR assumed that $v < k$, leaving the case of all-colluding servers open. We propose a generic construction that combines a linear map commitment (LMC) and an arbitrary linear PIR scheme to produce a $k$-verifiable PIR scheme, termed a committed PIR scheme. Such a scheme guarantees that even in the worst scenario, when all servers are under the control of an attacker, although the privacy is unavoidably lost, the client won't be fooled into accepting an incorrect $x_i$. We demonstrate the practicality of our proposal by implementing the committed PIR schemes based on the Lai-Malavolta LMC and three well-known PIR schemes using the GMP library and \texttt{blst}, the current fastest C library for elliptic curve pairings.

Learning-Based Adaptive Control for Stochastic Linear Systems with Input Constraints

We propose a certainty-equivalence scheme for adaptive control of scalar linear systems subject to additive, i.i.d. Gaussian disturbances and bounded control input constraints, without requiring prior knowledge of the bounds of the system parameters, nor the control direction. Assuming that the system is at-worst marginally stable, mean square boundedness of the closed-loop system states is proven. Lastly, numerical examples are presented to illustrate our results.

Design and Analysis of Hardware-limited Non-uniform Task-based Quantizers

Hardware-limited task-based quantization is a new design paradigm for data acquisition systems equipped with serial scalar analog-to-digital converters using a small number of bits. By taking into account the underlying system task, task-based quantizers can efficiently recover the desired parameters from the low-bit quantized observation. Current design and analysis frameworks for hardware-limited task-based quantization are only applicable to inputs with bounded support and uniform quantizers with non-subtractive dithering. Here, we propose a new framework based on generalized Bussgang decomposition that enables the design and analysis of hardware-limited task-based quantizers that are equipped with non-uniform scalar quantizers or that have inputs with unbounded support. We first consider the scenario in which the task is linear. Under this scenario, we derive new pre-quantization and post-quantization linear mappings for task-based quantizers with mean squared error (MSE) that closely matches the theoretical MSE. Next, we extend the proposed analysis framework to quadratic tasks. We demonstrate that our derived analytical expression for the MSE accurately predicts the performance of task-based quantizers with quadratic tasks.