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.

Federated learning (FL) aims to minimize the communication complexity of training a model over heterogeneous data distributed across many clients. A common approach is local methods, where clients take multiple optimization steps over local data before communicating with the server (e.g., FedAvg). Local methods can exploit similarity between clients' data. However, in existing analyses, this comes at the cost of slow convergence in terms of the dependence on the number of communication rounds R. On the other hand, global methods, where clients simply return a gradient vector in each round (e.g., SGD), converge faster in terms of R but fail to exploit the similarity between clients even when clients are homogeneous. We propose FedChain, an algorithmic framework that combines the strengths of local methods and global methods to achieve fast convergence in terms of R while leveraging the similarity between clients. Using FedChain, we instantiate algorithms that improve upon previously known rates in the general convex and PL settings, and are near-optimal (via an algorithm-independent lower bound that we show) for problems that satisfy strong convexity. Empirical results support this theoretical gain over existing methods.

Following the research agenda initiated by Munoz & Vassilvitskii [1] and Lykouris & Vassilvitskii [2] on learning-augmented online algorithms for classical online optimization problems, in this work, we consider the Online Facility Location problem under this framework. In Online Facility Location (OFL), demands arrive one-by-one in a metric space and must be (irrevocably) assigned to an open facility upon arrival, without any knowledge about future demands. We present an online algorithm for OFL that exploits potentially imperfect predictions on the locations of the optimal facilities. We prove that the competitive ratio decreases smoothly from sublogarithmic in the number of demands to constant, as the error, i.e., the total distance of the predicted locations to the optimal facility locations, decreases towards zero. We complement our analysis with a matching lower bound establishing that the dependence of the algorithm's competitive ratio on the error is optimal, up to constant factors. Finally, we evaluate our algorithm on real world data and compare our learning augmented approach with the current best online algorithm for the problem.

In this paper, we introduce $\mathsf{CO}_3$, an algorithm for communication-efficiency federated Deep Neural Network (DNN) training.$\mathsf{CO}_3$ takes its name from three processing applied steps which reduce the communication load when transmitting the local gradients from the remote users to the Parameter Server.Namely:(i) gradient quantization through floating-point conversion, (ii) lossless compression of the quantized gradient, and (iii) quantization error correction.We carefully design each of the steps above so as to minimize the loss in the distributed DNN training when the communication overhead is fixed.In particular, in the design of steps (i) and (ii), we adopt the assumption that DNN gradients are distributed according to a generalized normal distribution.This assumption is validated numerically in the paper. For step (iii), we utilize an error feedback with memory decay mechanism to correct the quantization error introduced in step (i). We argue that this coefficient, similarly to the learning rate, can be optimally tuned to improve convergence. The performance of $\mathsf{CO}_3$ is validated through numerical simulations and is shown having better accuracy and improved stability at a reduced communication payload.

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.

Stochastic optimization algorithms implemented on distributed computing architectures are increasingly used to tackle large-scale machine learning applications. A key bottleneck in such distributed systems is the communication overhead for exchanging information such as stochastic gradients between different workers. Sparse communication with memory and the adaptive aggregation methodology are two successful frameworks among the various techniques proposed to address this issue. In this paper, we exploit the advantages of Sparse communication and Adaptive aggregated Stochastic Gradients to design a communication-efficient distributed algorithm named SASG. Specifically, we determine the workers who need to communicate with the parameter server based on the adaptive aggregation rule and then sparsify the transmitted information. Therefore, our algorithm reduces both the overhead of communication rounds and the number of communication bits in the distributed system. We define an auxiliary sequence and provide convergence results of the algorithm with the help of Lyapunov function analysis. Experiments on training deep neural networks show that our algorithm can significantly reduce the communication overhead compared to the previous methods, with little impact on training and testing accuracy.

In the storied Colonel Blotto game, two colonels allocate $a$ and $b$ troops, respectively, to $k$ distinct battlefields. A colonel wins a battle if they assign more troops to that particular battle, and each colonel seeks to maximize their total number of victories. Despite the problem's formulation in 1921, the first polynomial-time algorithm to compute Nash equilibrium (NE) strategies for this game was discovered only quite recently. In 2016, \citep{ahmadinejad_dehghani_hajiaghayi_lucier_mahini_seddighin_2019} formulated a breakthrough algorithm to compute NE strategies for the Colonel Blotto game\footnote{To the best of our knowledge, the algorithm from \citep{ahmadinejad_dehghani_hajiaghayi_lucier_mahini_seddighin_2019} has computational complexity $O(k^{14}\max\{a,b\}^{13})$}, receiving substantial media coverage (e.g. \citep{Insider}, \citep{NSF}, \citep{ScienceDaily}). In this work, we present the first known $\epsilon$-approximation algorithm to compute NE strategies in the two-player Colonel Blotto game in runtime $\widetilde{O}(\epsilon^{-4} k^8 \max\{a,b\}^2)$ for arbitrary settings of these parameters. Moreover, this algorithm computes approximate coarse correlated equilibrium strategies in the multiplayer (continuous and discrete) Colonel Blotto game (when there are $\ell > 2$ colonels) with runtime $\widetilde{O}(\ell \epsilon^{-4} k^8 n^2 + \ell^2 \epsilon^{-2} k^3 n (n+k))$, where $n$ is the maximum troop count. Before this work, no polynomial-time algorithm was known to compute exact or approximate equilibrium (in any sense) strategies for multiplayer Colonel Blotto with arbitrary parameters. Our algorithm computes these approximate equilibria by a novel (to the author's knowledge) sampling technique with which we implicitly perform multiplicative weights update over the exponentially many strategies available to each player.

Federated Learning has promised a new approach to resolve the challenges in machine learning by bringing computation to the data. The popularity of the approach has led to rapid progress in the algorithmic aspects and the emergence of systems capable of simulating Federated Learning. State of art systems in Federated Learning support a single node aggregator that is insufficient to train a large corpus of devices or train larger-sized models. As the model size or the number of devices increase the single node aggregator incurs memory and computation burden while performing fusion tasks. It also faces communication bottlenecks when a large number of model updates are sent to a single node. We classify the workload for the aggregator into categories and propose a new aggregation service for handling each load. Our aggregation service is based on a holistic approach that chooses the best solution depending on the model update size and the number of clients. Our system provides a fault-tolerant, robust and efficient aggregation solution utilizing existing parallel and distributed frameworks. Through evaluation, we show the shortcomings of the state of art approaches and how a single solution is not suitable for all aggregation requirements. We also provide a comparison of current frameworks with our system through extensive experiments.

We demonstrate that merely analog transmissions and match filtering can realize the function of an edge server in federated learning (FL). Therefore, a network with massively distributed user equipments (UEs) can achieve large-scale FL without an edge server. We also develop a training algorithm that allows UEs to continuously perform local computing without being interrupted by the global parameter uploading, which exploits the full potential of UEs' processing power. We derive convergence rates for the proposed schemes to quantify their training efficiency. The analyses reveal that when the interference obeys a Gaussian distribution, the proposed algorithm retrieves the convergence rate of a server-based FL. But if the interference distribution is heavy-tailed, then the heavier the tail, the slower the algorithm converges. Nonetheless, the system run time can be largely reduced by enabling computation in parallel with communication, whereas the gain is particularly pronounced when communication latency is high. These findings are corroborated via excessive simulations.

The aim of this work is to develop a fully-distributed algorithmic framework for training graph convolutional networks (GCNs). The proposed method is able to exploit the meaningful relational structure of the input data, which are collected by a set of agents that communicate over a sparse network topology. After formulating the centralized GCN training problem, we first show how to make inference in a distributed scenario where the underlying data graph is split among different agents. Then, we propose a distributed gradient descent procedure to solve the GCN training problem. The resulting model distributes computation along three lines: during inference, during back-propagation, and during optimization. Convergence to stationary solutions of the GCN training problem is also established under mild conditions. Finally, we propose an optimization criterion to design the communication topology between agents in order to match with the graph describing data relationships. A wide set of numerical results validate our proposal. To the best of our knowledge, this is the first work combining graph convolutional neural networks with distributed optimization.