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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.

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.

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.

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.

In this paper, a new communication-efficient federated learning (FL) framework is proposed, inspired by vector quantized compressed sensing. The basic strategy of the proposed framework is to compress the local model update at each device by applying dimensionality reduction followed by vector quantization. Subsequently, the global model update is reconstructed at a parameter server (PS) by applying a sparse signal recovery algorithm to the aggregation of the compressed local model updates. By harnessing the benefits of both dimensionality reduction and vector quantization, the proposed framework effectively reduces the communication overhead of local update transmissions. Both the design of the vector quantizer and the key parameters for the compression are optimized so as to minimize the reconstruction error of the global model update under the constraint of wireless link capacity. By considering the reconstruction error, the convergence rate of the proposed framework is also analyzed for a smooth loss function. Simulation results on the MNIST and CIFAR-10 datasets demonstrate that the proposed framework provides more than a 2.5% increase in classification accuracy compared to state-of-art FL frameworks when the communication overhead of the local model update transmission is less than 0.1 bit per local model entry.

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 adaptive processing of structured data is a long-standing research topic in machine learning that investigates how to automatically learn a mapping from a structured input to outputs of various nature. Recently, there has been an increasing interest in the adaptive processing of graphs, which led to the development of different neural network-based methodologies. In this thesis, we take a different route and develop a Bayesian Deep Learning framework for graph learning. The dissertation begins with a review of the principles over which most of the methods in the field are built, followed by a study on graph classification reproducibility issues. We then proceed to bridge the basic ideas of deep learning for graphs with the Bayesian world, by building our deep architectures in an incremental fashion. This framework allows us to consider graphs with discrete and continuous edge features, producing unsupervised embeddings rich enough to reach the state of the art on several classification tasks. Our approach is also amenable to a Bayesian nonparametric extension that automatizes the choice of almost all model's hyper-parameters. Two real-world applications demonstrate the efficacy of deep learning for graphs. The first concerns the prediction of information-theoretic quantities for molecular simulations with supervised neural models. After that, we exploit our Bayesian models to solve a malware-classification task while being robust to intra-procedural code obfuscation techniques. We conclude the dissertation with an attempt to blend the best of the neural and Bayesian worlds together. The resulting hybrid model is able to predict multimodal distributions conditioned on input graphs, with the consequent ability to model stochasticity and uncertainty better than most works. Overall, we aim to provide a Bayesian perspective into the articulated research field of deep learning for graphs.

This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.

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.