亚洲男人的天堂2018av,欧美草比,久久久久久免费视频精选,国色天香在线看免费,久久久久亚洲av成人片仓井空

We study a new two-time-scale stochastic gradient method for solving optimization problems, where the gradients are computed with the aid of an auxiliary variable under samples generated by time-varying Markov random processes parameterized by the underlying optimization variable. These time-varying samples make gradient directions in our update biased and dependent, which can potentially lead to the divergence of the iterates. In our two-time-scale approach, one scale is to estimate the true gradient from these samples, which is then used to update the estimate of the optimal solution. While these two iterates are implemented simultaneously, the former is updated "faster" (using bigger step sizes) than the latter (using smaller step sizes). Our first contribution is to characterize the finite-time complexity of the proposed two-time-scale stochastic gradient method. In particular, we provide explicit formulas for the convergence rates of this method under different structural assumptions, namely, strong convexity, convexity, the Polyak-Lojasiewicz condition, and general non-convexity. We apply our framework to two problems in control and reinforcement learning. First, we look at the standard online actor-critic algorithm over finite state and action spaces and derive a convergence rate of O(k^(-2/5)), which recovers the best known rate derived specifically for this problem. Second, we study an online actor-critic algorithm for the linear-quadratic regulator and show that a convergence rate of O(k^(-2/3)) is achieved. This is the first time such a result is known in the literature. Finally, we support our theoretical analysis with numerical simulations where the convergence rates are visualized.

This paper investigates a new downlink nonorthogonal multiple access (NOMA) system, where a multiantenna unmanned aerial vehicle (UAV) is powered by wireless power transfer (WPT) and serves as the base station for multiple pairs of ground users (GUs) running NOMA in each pair. An energy efficiency (EE) maximization problem is formulated to jointly optimize the WPT time and the placement for the UAV, and the allocation of the UAV's transmit power between different NOMA user pairs and within each pair. To efficiently solve this nonconvex problem, we decompose the problem into three subproblems using block coordinate descent. For the subproblem of intra-pair power allocation within each NOMA user pair, we construct a supermodular game with confirmed convergence to a Nash equilibrium. Given the intra-pair power allocation, successive convex approximation is applied to convexify and solve the subproblem of WPT time allocation and inter-pair power allocation between the user pairs. Finally, we solve the subproblem of UAV placement by using the Lagrange multiplier method. Simulations show that our approach can substantially outperform its alternatives that do not use NOMA and WPT techniques or that do not optimize the UAV location.

We study a heterogeneous Rayleigh fading wireless sensor network (WSN) in which densely deployed sensor nodes monitor an environment and transmit their sensed information to base stations (BSs) using access points (APs) as relays to facilitate the data transfer. We consider both large-scale and small-scale propagation effects in our system model and formulate the node deployment problem as an optimization problem aimed at minimizing the wireless communication network's power consumption. By imposing a desired outage probability constraint on all communication channels, we derive the necessary conditions for the optimal deployment that not only minimize the power consumption, but also guarantee all wireless links to have an outage probability below the given threshold. In addition, we study the necessary conditions for an optimal deployment given ergodic capacity constraints. We compare our node deployment algorithms with similar algorithms in the literature and demonstrate their efficacy and superiority.

We consider the question of adaptive data analysis within the framework of convex optimization. We ask how many samples are needed in order to compute $\epsilon$-accurate estimates of $O(1/\epsilon^2)$ gradients queried by gradient descent, and we provide two intermediate answers to this question. First, we show that for a general analyst (not necessarily gradient descent) $\Omega(1/\epsilon^3)$ samples are required. This rules out the possibility of a foolproof mechanism. Our construction builds upon a new lower bound (that may be of interest of its own right) for an analyst that may ask several non adaptive questions in a batch of fixed and known $T$ rounds of adaptivity and requires a fraction of true discoveries. We show that for such an analyst $\Omega (\sqrt{T}/\epsilon^2)$ samples are necessary. Second, we show that, under certain assumptions on the oracle, in an interaction with gradient descent $\tilde \Omega(1/\epsilon^{2.5})$ samples are necessary. Our assumptions are that the oracle has only \emph{first order access} and is \emph{post-hoc generalizing}. First order access means that it can only compute the gradients of the sampled function at points queried by the algorithm. Our assumption of \emph{post-hoc generalization} follows from existing lower bounds for statistical queries. More generally then, we provide a generic reduction from the standard setting of statistical queries to the problem of estimating gradients queried by gradient descent. These results are in contrast with classical bounds that show that with $O(1/\epsilon^2)$ samples one can optimize the population risk to accuracy of $O(\epsilon)$ but, as it turns out, with spurious gradients.

We study the decentralized consensus and stochastic optimization problems with compressed communications over static directed graphs. We propose an iterative gradient-based algorithm that compresses messages according to a desired compression ratio. The proposed method provably reduces the communication overhead on the network at every communication round. Contrary to existing literature, we allow for arbitrary compression ratios in the communicated messages. We show a linear convergence rate for the proposed method on the consensus problem. Moreover, we provide explicit convergence rates for decentralized stochastic optimization problems on smooth functions that are either (i) strongly convex, (ii) convex, or (iii) non-convex. Finally, we provide numerical experiments to illustrate convergence under arbitrary compression ratios and the communication efficiency of our algorithm.

We introduce a restriction of the classical 2-party deterministic communication protocol where Alice and Bob are restricted to using only comparison functions. We show that the complexity of a function in the model is, up to a constant factor, determined by a complexity measure analogous to Yao's tiling number, which we call the geometric tiling number which can be computed in polynomial time. As a warm-up, we consider an analogous restricted decision tree model and observe a 1-dimensional analog of the above results.

In large scale dynamic wireless networks, the amount of overhead caused by channel estimation (CE) is becoming one of the main performance bottlenecks. This is due to the large number users whose channels should be estimated, the user mobility, and the rapid channel change caused by the usage of the high-frequency spectrum (e.g. millimeter wave). In this work, we propose a new hybrid channel estimation/prediction (CEP) scheme to reduce overhead in time-division duplex (TDD) wireless cell-free massive multiple-input-multiple-output (mMIMO) systems. The scheme proposes sending a pilot signal from each user only once in a given number (window) of coherence intervals (CIs). Then minimum mean-square error (MMSE) estimation is used to estimate the channel of this CI, while a deep neural network (DNN) is used to predict the channels of the remaining CIs in the window. The DNN exploits the temporal correlation between the consecutive CIs and the received pilot signals to improve the channel prediction accuracy. By doing so, CE overhead is reduced by at least 50 percent at the expense of negligible CE error for practical user mobility settings. Consequently, the proposed CEP scheme improves the spectral efficiency compared to the conventional MMSE CE approach, especially when the number of users is large, which is demonstrated numerically.

Multihop relaying is a potential technique to mitigate channel impairments in optical wireless communications (OWC). In this paper, multiple fixed-gain amplify-and-forward (AF) relays are employed to enhance the OWC performance under the combined effect of atmospheric turbulence, pointing errors, and fog. We consider a long-range OWC link by modeling the atmospheric turbulence by the Fisher-Snedecor ${\cal{F}}$ distribution, pointing errors by the generalized non-zero boresight model, and random path loss due to fog. We also consider a short-range OWC system by ignoring the impact of atmospheric turbulence. We derive novel upper bounds on the probability density function (PDF) and cumulative distribution function (CDF) of the end-to-end signal-to-noise ratio (SNR) for both short and long-range multihop OWC systems by developing exact statistical results for a single-hop OWC system under the combined effect of ${\cal{F}}$-turbulence channels, non-zero boresight pointing errors, and fog-induced fading. Based on these expressions, we present analytical expressions of outage probability (OP) and average bit-error-rate (ABER) performance for the considered OWC systems involving single-variate Fox's H and Meijer's G functions. Moreover, asymptotic expressions of the outage probability in high SNR region are developed using simpler Gamma functions to provide insights on the effect of channel and system parameters. The derived analytical expressions are validated through Monte-Carlo simulations, and the scaling of the OWC performance with the number of relay nodes is demonstrated with a comparison to the single-hop transmission.

The stochastic gradient Langevin Dynamics is one of the most fundamental algorithms to solve sampling problems and non-convex optimization appearing in several machine learning applications. Especially, its variance reduced versions have nowadays gained particular attention. In this paper, we study two variants of this kind, namely, the Stochastic Variance Reduced Gradient Langevin Dynamics and the Stochastic Recursive Gradient Langevin Dynamics. We prove their convergence to the objective distribution in terms of KL-divergence under the sole assumptions of smoothness and Log-Sobolev inequality which are weaker conditions than those used in prior works for these algorithms. With the batch size and the inner loop length set to $\sqrt{n}$, the gradient complexity to achieve an $\epsilon$-precision is $\tilde{O}((n+dn^{1/2}\epsilon^{-1})\gamma^2 L^2\alpha^{-2})$, which is an improvement from any previous analyses. We also show some essential applications of our result to non-convex optimization.

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.