We present a distributed quasi-Newton (DQN) method, which enables a group of agents to compute an optimal solution of a separable multi-agent optimization problem locally using an approximation of the curvature of the aggregate objective function. Each agent computes a descent direction from its local estimate of the aggregate Hessian, obtained from quasi-Newton approximation schemes using the gradient of its local objective function. Moreover, we introduce a distributed quasi-Newton method for equality-constrained optimization (EC-DQN), where each agent takes Karush-Kuhn-Tucker-like update steps to compute an optimal solution. In our algorithms, each agent communicates with its one-hop neighbors over a peer-to-peer communication network to compute a common solution. We prove convergence of our algorithms to a stationary point of the optimization problem. In addition, we demonstrate the competitive empirical convergence of our algorithm in both well-conditioned and ill-conditioned optimization problems, in terms of the computation time and communication cost incurred by each agent for convergence, compared to existing distributed first-order and second-order methods. Particularly, in ill-conditioned problems, our algorithms achieve a faster computation time for convergence, while requiring a lower communication cost, across a range of communication networks with different degrees of connectedness, by leveraging information on the curvature of the problem.
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Efficient implementation of massive multiple-input-multiple-output (MIMO) transceivers is essential for the next-generation wireless networks. To reduce the high computational complexity of the massive MIMO transceiver, in this paper, we propose a new massive MIMO architecture using finite-precision arithmetic. First, we conduct the rounding error analysis and derive the lower bound of the achievable rate for single-input-multiple-output (SIMO) using maximal ratio combining (MRC) and multiple-input-single-output (MISO) systems using maximal ratio transmission (MRT) with finite-precision arithmetic. Then, considering the multi-user scenario, the rounding error analysis of zero-forcing (ZF) detection and precoding is derived by using the normal equations (NE) method. The corresponding lower bounds of the achievable sum rate are also derived and asymptotic analyses are presented. Built upon insights from these analyses and lower bounds, we propose a mixed-precision architecture for massive MIMO systems to offset performance gaps due to finite-precision arithmetic. The corresponding analysis of rounding errors and computational costs is obtained. Simulation results validate the derived bounds and underscore the superiority of the proposed mixed-precision architecture to the conventional structure.
For doubly-selective channels, delay-Doppler (DD) modulation, mostly known as orthogonal time frequency space (OTFS) modulation, enables simultaneous compensation of delay and Doppler shifts. However, OTFS modulated signal has high peak-to-average power ratio (PAPR) because of its precoding operation performed over the DD domain. In order to deal with this problem, we propose a single-carrier transmission with delay-Doppler domain equalization (SC-DDE). In this system, the discretized time-domain SC signal is converted to the DD domain by discrete Zak transform (DZT) at the receiver side, followed by delay-Doppler domain equalization (DDE). Since equalization is performed in the DD domain, the SC-DDE receiver should acquire the channel delay-Doppler response. To this end, we introduce an embedded pilot-aided channel estimation scheme designed for SC-DDE, which does not affect the peak power property of transmitted signals. Through computer simulation, distribution of PAPR and bit error rate (BER) performance of the proposed system are compared with those of the conventional OTFS and SC with frequency-domain equalization (SC-FDE). As a result, our proposed SC-DDE significantly outperforms SC-FDE in terms of BER at the expense of additional computational complexity at the receiver. Furthermore, SC-DDE shows much lower PAPR than OTFS even though they achieve comparable coded BER performance.
Movable antenna (MA) is a promising technology to improve wireless communication performance by varying the antenna position in a given finite area at the transceivers to create more favorable channel conditions. In this paper, we investigate the MA-enhanced multiple-access channel (MAC) for the uplink transmission from multiple users each equipped with a single MA to a base station (BS) with a fixed-position antenna (FPA) array. A field-response based channel model is used to characterize the multi-path channel between the antenna array of the BS and each user's MA with a flexible position. To evaluate the MAC performance gain provided by MAs, we formulate an optimization problem for minimizing the total transmit power of users, subject to a minimum-achievable-rate requirement for each user, where the positions of MAs and the transmit powers of users, as well as the receive combining matrix of the BS are jointly optimized. To solve this non-convex optimization problem involving intricately coupled variables, we develop two algorithms based on zero-forcing (ZF) and minimum mean square error (MMSE) combining methods, respectively. Specifically, for each algorithm, the combining matrix of the BS and the total transmit power of users are expressed as a function of the MAs' position vectors, which are then optimized by using the proposed multi-directional descent (MDD) framework. It is shown that the proposed ZF-based and MMSE-based MDD algorithms can converge to high-quality suboptimal solutions with low computational complexities. Simulation results demonstrate that the proposed solutions for MA-enhanced multiple access systems can significantly decrease the total transmit power of users as compared to conventional FPA systems employing antenna selection under both perfect and imperfect field-response information.
We propose a data-driven control method for systems with aleatoric uncertainty, for example, robot fleets with variations between agents. Our method leverages shared trajectory data to increase the robustness of the designed controller and thus facilitate transfer to new variations without the need for prior parameter and uncertainty estimations. In contrast to existing work on experience transfer for performance, our approach focuses on robustness and uses data collected from multiple realizations to guarantee generalization to unseen ones. Our method is based on scenario optimization combined with recent formulations for direct data-driven control. We derive lower bounds on the amount of data required to achieve quadratic stability for probabilistic systems with aleatoric uncertainty and demonstrate the benefits of our data-driven method through a numerical example. We find that the learned controllers generalize well to high variations in the dynamics even when based on only a few short open-loop trajectories. Robust experience transfer enables the design of safe and robust controllers that work out of the box without any additional learning during deployment.
Eigenvector continuation is a computational method for parametric eigenvalue problems that uses subspace projection with a basis derived from eigenvector snapshots from different parameter sets. It is part of a broader class of subspace-projection techniques called reduced-basis methods. In this colloquium article, we present the development, theory, and applications of eigenvector continuation and projection-based emulators. We introduce the basic concepts, discuss the underlying theory and convergence properties, and present recent applications for quantum systems and future prospects.
We present a new framework to address the non-convex robust hypothesis testing problem, wherein the goal is to seek the optimal detector that minimizes the maximum of worst-case type-I and type-II risk functions. The distributional uncertainty sets are constructed to center around the empirical distribution derived from samples based on Sinkhorn discrepancy. Given that the objective involves non-convex, non-smooth probabilistic functions that are often intractable to optimize, existing methods resort to approximations rather than exact solutions. To tackle the challenge, we introduce an exact mixed-integer exponential conic reformulation of the problem, which can be solved into a global optimum with a moderate amount of input data. Subsequently, we propose a convex approximation, demonstrating its superiority over current state-of-the-art methodologies in literature. Furthermore, we establish connections between robust hypothesis testing and regularized formulations of non-robust risk functions, offering insightful interpretations. Our numerical study highlights the satisfactory testing performance and computational efficiency of the proposed framework.
We study differentially private (DP) algorithms for recovering clusters in well-clustered graphs, which are graphs whose vertex set can be partitioned into a small number of sets, each inducing a subgraph of high inner conductance and small outer conductance. Such graphs have widespread application as a benchmark in the theoretical analysis of spectral clustering. We provide an efficient ($\epsilon$,$\delta$)-DP algorithm tailored specifically for such graphs. Our algorithm draws inspiration from the recent work of Chen et al., who developed DP algorithms for recovery of stochastic block models in cases where the graph comprises exactly two nearly-balanced clusters. Our algorithm works for well-clustered graphs with $k$ nearly-balanced clusters, and the misclassification ratio almost matches the one of the best-known non-private algorithms. We conduct experimental evaluations on datasets with known ground truth clusters to substantiate the prowess of our algorithm. We also show that any (pure) $\epsilon$-DP algorithm would result in substantial error.
The development of autonomous agents which can interact with other agents to accomplish a given task is a core area of research in artificial intelligence and machine learning. Towards this goal, the Autonomous Agents Research Group develops novel machine learning algorithms for autonomous systems control, with a specific focus on deep reinforcement learning and multi-agent reinforcement learning. Research problems include scalable learning of coordinated agent policies and inter-agent communication; reasoning about the behaviours, goals, and composition of other agents from limited observations; and sample-efficient learning based on intrinsic motivation, curriculum learning, causal inference, and representation learning. This article provides a broad overview of the ongoing research portfolio of the group and discusses open problems for future directions.
Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.
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