The spectrum cartography (SC) technique constructs multi-domain (e.g., frequency, space, and time) radio frequency (RF) maps from limited measurements, which can be viewed as an ill-posed tensor completion problem. Model-based cartography techniques
often rely on handcrafted priors (e.g., sparsity, smoothness and low-rank structures) for the completion task. Such priors may be inadequate to capture the essence of complex wireless environments -- especially when severe shadowing happens. To circumvent such challenges, offline-trained deep neural models of radio maps were considered for SC, as deep neural networks (DNNs) are able to learn intricate underlying structures from data. However, such deep learning (DL)-based SC approaches encounter serious challenges in both off-line model learning (training) and completion (generalization), possibly because the latent state space for generating the radio maps is prohibitively large. In this work, an emitter radio map disaggregation-based approach is proposed, under which only individual emitters radio maps are modeled by DNNs. This way, the learning and generalization challenges can both be substantially alleviated. Using the learned DNNs, a fast nonnegative matrix factorization-based two-stage SC method and a performance-enhanced iterative optimization algorithm are proposed. Theoretical aspects -- such as recoverability of the radio tensor, sample complexity, and noise robustness -- under the proposed framework are characterized, and such theoretical properties have been elusive in the context of DL-based radio tensor completion. Experiments using synthetic and real-data from indoor and heavily shadowed environments are employed to showcase the effectiveness of the proposed methods.
This paper proposes a new algorithm -- the underline{S}ingle-timescale Dounderline{u}ble-momentum underline{St}ochastic underline{A}pproxunderline{i}matiounderline{n} (SUSTAIN) -- for tackling stochastic unconstrained bilevel optimization problems. W
e focus on bilevel problems where the lower level subproblem is strongly-convex and the upper level objective function is smooth. Unlike prior works which rely on emph{two-timescale} or emph{double loop} techniques, we design a stochastic momentum-assisted gradient estimator for both the upper and lower level updates. The latter allows us to control the error in the stochastic gradient updates due to inaccurate solution to both subproblems. If the upper objective function is smooth but possibly non-convex, we show that {aname}~requires $mathcal{O}(epsilon^{-3/2})$ iterations (each using ${cal O}(1)$ samples) to find an $epsilon$-stationary solution. The $epsilon$-stationary solution is defined as the point whose squared norm of the gradient of the outer function is less than or equal to $epsilon$. The total number of stochastic gradient samples required for the upper and lower level objective functions matches the best-known complexity for single-level stochastic gradient algorithms. We also analyze the case when the upper level objective function is strongly-convex.
Asynchronous and parallel implementation of standard reinforcement learning (RL) algorithms is a key enabler of the tremendous success of modern RL. Among many asynchronous RL algorithms, arguably the most popular and effective one is the asynchronou
s advantage actor-critic (A3C) algorithm. Although A3C is becoming the workhorse of RL, its theoretical properties are still not well-understood, including the non-asymptotic analysis and the performance gain of parallelism (a.k.a. speedup). This paper revisits the A3C algorithm with TD(0) for the critic update, termed A3C-TD(0), with provable convergence guarantees. With linear value function approximation for the TD update, the convergence of A3C-TD(0) is established under both i.i.d. and Markovian sampling. Under i.i.d. sampling, A3C-TD(0) obtains sample complexity of $mathcal{O}(epsilon^{-2.5}/N)$ per worker to achieve $epsilon$ accuracy, where $N$ is the number of workers. Compared to the best-known sample complexity of $mathcal{O}(epsilon^{-2.5})$ for two-timescale AC, A3C-TD(0) achieves emph{linear speedup}, which justifies the advantage of parallelism and asynchrony in AC algorithms theoretically for the first time. Numerical tests on synthetically generated instances and OpenAI Gym environments have been provided to verify our theoretical analysis.
Federated learning (FL) is a recently proposed distributed machine learning paradigm dealing with distributed and private data sets. Based on the data partition pattern, FL is often categorized into horizontal, vertical, and hybrid settings. Despite
the fact that many works have been developed for the first two approaches, the hybrid FL setting (which deals with partially overlapped feature space and sample space) remains less explored, though this setting is extremely important in practice. In this paper, we first set up a new model-matching-based problem formulation for hybrid FL, then propose an efficient algorithm that can collaboratively train the global and local models to deal with full and partial featured data. We conduct numerical experiments on the multi-view ModelNet40 data set to validate the performance of the proposed algorithm. To the best of our knowledge, this is the first formulation and algorithm developed for the hybrid FL.
Unmanned aerial vehicle (UAV) swarm has emerged as a promising novel paradigm to achieve better coverage and higher capacity for future wireless network by exploiting the more favorable line-of-sight (LoS) propagation. To reap the potential gains of
UAV swarm, the remote control signal sent by ground control unit (GCU) is essential, whereas the control signal quality are susceptible in practice due to the effect of the adjacent channel interference (ACI) and the external interference (EI) from radiation sources distributed across the region. To tackle these challenges, this paper considers priority-aware resource coordination in a multi-UAV communication system, where multiple UAVs are controlled by a GCU to perform certain tasks with a pre-defined trajectory. Specifically, we maximize the minimum signal-to-interference-plus-noise ratio (SINR) among all the UAVs by jointly optimizing channel assignment and power allocation strategy under stringent resource availability constraints. According to the intensity of ACI, we consider the corresponding problem in two scenarios, i.e., Null-ACI and ACI systems. By virtue of the particular problem structure in Null-ACI case, we first recast the formulation into an equivalent yet more tractable form and obtain the global optimal solution via Hungarian algorithm. For general ACI systems, we develop an efficient iterative algorithm for its solution based on the smooth approximation and alternating optimization methods. Extensive simulation results demonstrate that the proposed algorithms can significantly enhance the minimum SINR among all the UAVs and adapt the allocation of communication resources to diverse mission priority.
This paper studies the generalization bounds for the empirical saddle point (ESP) solution to stochastic saddle point (SSP) problems. For SSP with Lipschitz continuous and strongly convex-strongly concave objective functions, we establish an $mathcal
{O}(1/n)$ generalization bound by using a uniform stability argument. We also provide generalization bounds under a variety of assumptions, including the cases without strong convexity and without bounded domains. We illustrate our results in two examples: batch policy learning in Markov decision process, and mixed strategy Nash equilibrium estimation for stochastic games. In each of these examples, we show that a regularized ESP solution enjoys a near-optimal sample complexity. To the best of our knowledge, this is the first set of results on the generalization theory of ESP.
Motivated by a growing list of nontraditional statistical estimation problems of the piecewise kind, this paper provides a survey of known results supplemented with new results for the class of piecewise linear-quadratic programs. These are linearly
constrained optimization problems with piecewise linear-quadratic (PLQ) objective functions. Starting from a study of the representation of such a function in terms of a family of elementary functions consisting of squared affine functions, squared plus-composite-affine functions, and affine functions themselves, we summarize some local properties of a PLQ function in terms of their first and second-order directional derivatives. We extend some well-known necessary and sufficient second-order conditions for local optimality of a quadratic program to a PLQ program and provide a dozen such equivalent conditions for strong, strict, and isolated local optimality, showing in particular that a PLQ program has the same characterizations for local minimality as a standard quadratic program. As a consequence of one such condition, we show that the number of strong, strict, or isolated local minima of a PLQ program is finite; this result supplements a recent result about the finite number of directional stationary objective values. Interestingly, these finiteness results can be uncovered by invoking a very powerful property of subanalytic functions; our proof is fairly elementary, however. We discuss applications of PLQ programs in some modern statistical estimation problems. These problems lead to a special class of unconstrained composite programs involving the non-differentiable $ell_1$-function, for which we show that the task of verifying the second-order stationary condition can be converted to the problem of checking the copositivity of certain Schur complement on the nonnegative orthant.
This article presents a powerful algorithmic framework for big data optimization, called the Block Successive Upper bound Minimization (BSUM). The BSUM includes as special cases many well-known methods for analyzing massive data sets, such as the Blo
ck Coordinate Descent (BCD), the Convex-Concave Procedure (CCCP), the Block Coordinate Proximal Gradient (BCPG) method, the Nonnegative Matrix Factorization (NMF), the Expectation Maximization (EM) method and so on. In this article, various features and properties of the BSUM are discussed from the viewpoint of design flexibility, computational efficiency, parallel/distributed implementation and the required communication overhead. Illustrative examples from networking, signal processing and machine learning are presented to demonstrate the practical performance of the BSUM framework
