XGBoost is one of the most widely used machine learning models in the industry due to its superior learning accuracy and efficiency. Targeting at data isolation issues in the big data problems, it is crucial to deploy a secure and efficient federated XGBoost (FedXGB) model. Existing FedXGB models either have data leakage issues or are only applicable to the two-party setting with heavy communication and computation overheads. In this paper, a lossless multi-party federated XGB learning framework is proposed with a security guarantee, which reshapes the XGBoost's split criterion calculation process under a secret sharing setting and solves the leaf weight calculation problem by leveraging distributed optimization. Remarkably, a thorough analysis of model security is provided as well, and multiple numerical results showcase the superiority of the proposed FedXGB compared with the state-of-the-art models on benchmark datasets.
We study first-order optimization algorithms under the constraint that the descent direction is quantized using a pre-specified budget of $R$-bits per dimension, where $R \in (0 ,\infty)$. We propose computationally efficient optimization algorithms with convergence rates matching the information-theoretic performance lower bounds for: (i) Smooth and Strongly-Convex objectives with access to an Exact Gradient oracle, as well as (ii) General Convex and Non-Smooth objectives with access to a Noisy Subgradient oracle. The crux of these algorithms is a polynomial complexity source coding scheme that embeds a vector into a random subspace before quantizing it. These embeddings are such that with high probability, their projection along any of the canonical directions of the transform space is small. As a consequence, quantizing these embeddings followed by an inverse transform to the original space yields a source coding method with optimal covering efficiency while utilizing just $R$-bits per dimension. Our algorithms guarantee optimality for arbitrary values of the bit-budget $R$, which includes both the sub-linear budget regime ($R < 1$), as well as the high-budget regime ($R \geq 1$), while requiring $O\left(n^2\right)$ multiplications, where $n$ is the dimension. We also propose an efficient relaxation of this coding scheme using Hadamard subspaces that requires a near-linear time, i.e., $O\left(n \log n\right)$ additions.Furthermore, we show that the utility of our proposed embeddings can be extended to significantly improve the performance of gradient sparsification schemes. Numerical simulations validate our theoretical claims. Our implementations are available at https://github.com/rajarshisaha95/DistOptConstrComm.
Training deep neural networks on large datasets can often be accelerated by using multiple compute nodes. This approach, known as distributed training, can utilize hundreds of computers via specialized message-passing protocols such as Ring All-Reduce. However, running these protocols at scale requires reliable high-speed networking that is only available in dedicated clusters. In contrast, many real-world applications, such as federated learning and cloud-based distributed training, operate on unreliable devices with unstable network bandwidth. As a result, these applications are restricted to using parameter servers or gossip-based averaging protocols. In this work, we lift that restriction by proposing Moshpit All-Reduce - an iterative averaging protocol that exponentially converges to the global average. We demonstrate the efficiency of our protocol for distributed optimization with strong theoretical guarantees. The experiments show 1.3x speedup for ResNet-50 training on ImageNet compared to competitive gossip-based strategies and 1.5x speedup when training ALBERT-large from scratch using preemptible compute nodes.
We consider a distributed non-convex optimization where a network of agents aims at minimizing a global function over the Stiefel manifold. The global function is represented as a finite sum of smooth local functions, where each local function is associated with one agent and agents communicate with each other over an undirected connected graph. The problem is non-convex as local functions are possibly non-convex (but smooth) and the Steifel manifold is a non-convex set. We present a decentralized Riemannian stochastic gradient method (DRSGD) with the convergence rate of $\mathcal{O}(1/\sqrt{K})$ to a stationary point. To have exact convergence with constant stepsize, we also propose a decentralized Riemannian gradient tracking algorithm (DRGTA) with the convergence rate of $\mathcal{O}(1/K)$ to a stationary point. We use multi-step consensus to preserve the iteration in the local (consensus) region. DRGTA is the first decentralized algorithm with exact convergence for distributed optimization on Stiefel manifold.
Communication efficient distributed mean estimation is an important primitive that arises in many distributed learning and optimization scenarios such as federated learning. Without any probabilistic assumptions on the underlying data, we study the problem of distributed mean estimation where the server has access to side information. We propose \emph{Wyner-Ziv estimators}, which are communication and computationally efficient and near-optimal when an upper bound for the distance between the side information and the data is known. As a corollary, we also show that our algorithms provide efficient schemes for the classic Wyner-Ziv problem in information theory. In a different direction, when there is no knowledge assumed about the distance between side information and the data, we present an alternative Wyner-Ziv estimator that uses correlated sampling. This latter setting offers {\em universal recovery guarantees}, and perhaps will be of interest in practice when the number of users is large and keeping track of the distances between the data and the side information may not be possible. With this mean estimator at our disposal, we revisit basic problems in decentralized optimization and compression where our Wyner-Ziv estimator yields algorithms with almost optimal performance. First, we consider the problem of communication constrained distributed optimization and provide an algorithm which attains the optimal convergence rate by exploiting the fact that the gradient estimates are close to each other. Specifically, the gradient compression scheme in our algorithm first uses half of the parties to form side information and then uses our Wyner-Ziv estimator to compress the remaining half of the gradient estimates.
We consider the distributed resource selection problem in Vehicle-to-vehicle (V2V) communication in the absence of a base station. Each vehicle autonomously selects transmission resources from a pool of shared resources to disseminate Cooperative Awareness Messages (CAMs). This is a consensus problem where each vehicle has to select a unique resource. The problem becomes more challenging when---due to mobility---the number of vehicles in vicinity of each other is changing dynamically. In a congested scenario, allocation of unique resources for each vehicle becomes infeasible and a congested resource allocation strategy has to be developed. The standardized approach in 5G, namely semi-persistent scheduling (SPS) suffers from effects caused by spatial distribution of the vehicles. In our approach, we turn this into an advantage. We propose a novel DIstributed Resource Allocation mechanism using multi-agent reinforcement Learning (DIRAL) which builds on a unique state representation. One challenging issue is to cope with the non-stationarity introduced by concurrently learning agents which causes convergence problems in multi-agent learning systems. We aimed to tackle non-stationarity with unique state representation. Specifically, we deploy view-based positional distribution as a state representation to tackle non-stationarity and perform complex joint behavior in a distributed fashion. Our results showed that DIRAL improves PRR by 20% compared to SPS in challenging congested scenarios.
There has been an increasing necessity for scalable optimization methods, especially due to the explosion in the size of datasets and model complexity in modern machine learning applications. Scalable solvers often distribute the computation over a network of processing units. For simple algorithms such as gradient descent the dependency of the convergence time with the topology of this network is well-known. However, for more involved algorithms such as the Alternating Direction Methods of Multipliers (ADMM) much less is known. At the heart of many distributed optimization algorithms there exists a gossip subroutine which averages local information over the network, and whose efficiency is crucial for the overall performance of the method. In this paper we review recent research in this area and, with the goal of isolating such a communication exchange behaviour, we compare different algorithms when applied to a canonical distributed averaging consensus problem. We also show interesting connections between ADMM and lifted Markov chains besides providing an explicitly characterization of its convergence and optimal parameter tuning in terms of spectral properties of the network. Finally, we empirically study the connection between network topology and convergence rates for different algorithms on a real world problem of sensor localization.
As the modern world becomes increasingly digitized and interconnected, distributed signal processing has proven to be effective in processing its large volume of data. However, a main challenge limiting the broad use of distributed signal processing techniques is the issue of privacy in handling sensitive data. To address this privacy issue, we propose a novel yet general subspace perturbation method for privacy-preserving distributed optimization, which allows each node to obtain the desired solution while protecting its private data. In particular, we show that the dual variables introduced in each distributed optimizer will not converge in a certain subspace determined by the graph topology. Additionally, the optimization variable is ensured to converge to the desired solution, because it is orthogonal to this non-convergent subspace. We therefore propose to insert noise in the non-convergent subspace through the dual variable such that the private data are protected, and the accuracy of the desired solution is completely unaffected. Moreover, the proposed method is shown to be secure under two widely-used adversary models: passive and eavesdropping. Furthermore, we consider several distributed optimizers such as ADMM and PDMM to demonstrate the general applicability of the proposed method. Finally, we test the performance through a set of applications. Numerical tests indicate that the proposed method is superior to existing methods in terms of several parameters like estimated accuracy, privacy level, communication cost and convergence rate.
Resolution level and reconstruction quality in nano-computed tomography (nano-CT) are in part limited by the stability of microscopes, because the magnitude of mechanical vibrations during scanning becomes comparable to the imaging resolution, and the ability of the samples to resist beam damage during data acquisition. In such cases, there is no incentive in recovering the sample state at different time steps like in time-resolved reconstruction methods, but instead the goal is to retrieve a single reconstruction at the highest possible spatial resolution and without any imaging artifacts. Here we propose a joint solver for imaging samples at the nanoscale with projection alignment, unwarping and regularization. Projection data consistency is regulated by dense optical flow estimated by Farneback's algorithm, leading to sharp sample reconstructions with less artifacts. Synthetic data tests show robustness of the method to Poisson and low-frequency background noise. Applicability of the method is demonstrated on two large-scale nano-imaging experimental data sets.
Deep learning has recently emerged as a disruptive technology to solve challenging radio resource management problems in wireless networks. However, the neural network architectures adopted by existing works suffer from poor scalability, generalization, and lack of interpretability. A long-standing approach to improve scalability and generalization is to incorporate the structures of the target task into the neural network architecture. In this paper, we propose to apply graph neural networks (GNNs) to solve large-scale radio resource management problems, supported by effective neural network architecture design and theoretical analysis. Specifically, we first demonstrate that radio resource management problems can be formulated as graph optimization problems that enjoy a universal permutation equivariance property. We then identify a class of neural networks, named \emph{message passing graph neural networks} (MPGNNs). It is demonstrated that they not only satisfy the permutation equivariance property, but also can generalize to large-scale problems while enjoying a high computational efficiency. For interpretablity and theoretical guarantees, we prove the equivalence between MPGNNs and a class of distributed optimization algorithms, which is then used to analyze the performance and generalization of MPGNN-based methods. Extensive simulations, with power control and beamforming as two examples, will demonstrate that the proposed method, trained in an unsupervised manner with unlabeled samples, matches or even outperforms classic optimization-based algorithms without domain-specific knowledge. Remarkably, the proposed method is highly scalable and can solve the beamforming problem in an interference channel with $1000$ transceiver pairs within $6$ milliseconds on a single GPU.
In federated learning, communication cost is often a critical bottleneck to scale up distributed optimization algorithms to collaboratively learn a model from millions of devices with potentially unreliable or limited communication and heterogeneous data distributions. Two notable trends to deal with the communication overhead of federated algorithms are gradient compression and local computation with periodic communication. Despite many attempts, characterizing the relationship between these two approaches has proven elusive. We address this by proposing a set of algorithms with periodical compressed (quantized or sparsified) communication and analyze their convergence properties in both homogeneous and heterogeneous local data distribution settings. For the homogeneous setting, our analysis improves existing bounds by providing tighter convergence rates for both strongly convex and non-convex objective functions. To mitigate data heterogeneity, we introduce a local gradient tracking scheme and obtain sharp convergence rates that match the best-known communication complexities without compression for convex, strongly convex, and nonconvex settings. We complement our theoretical results and demonstrate the effectiveness of our proposed methods by several experiments on real-world datasets.
We propose Federated Accelerated Stochastic Gradient Descent (FedAc), a principled acceleration of Federated Averaging (FedAvg, also known as Local SGD) for distributed optimization. FedAc is the first provable acceleration of FedAvg that improves convergence speed and communication efficiency on various types of convex functions. For example, for strongly convex and smooth functions, when using $M$ workers, the previous state-of-the-art FedAvg analysis can achieve a linear speedup in $M$ if given $M$ rounds of synchronization, whereas FedAc only requires $M^{\frac{1}{3}}$ rounds. Moreover, we prove stronger guarantees for FedAc when the objectives are third-order smooth. Our technique is based on a potential-based perturbed iterate analysis, a novel stability analysis of generalized accelerated SGD, and a strategic tradeoff between acceleration and stability.
In Byzantine robust distributed or federated learning, a central server wants to train a machine learning model over data distributed across multiple workers. However, a fraction of these workers may deviate from the prescribed algorithm and send arbitrary messages. While this problem has received significant attention recently, most current defenses assume that the workers have identical data. For realistic cases when the data across workers are heterogeneous (non-iid), we design new attacks which circumvent current defenses, leading to significant loss of performance. We then propose a simple bucketing scheme that adapts existing robust algorithms to heterogeneous datasets at a negligible computational cost. We also theoretically and experimentally validate our approach, showing that combining bucketing with existing robust algorithms is effective against challenging attacks. Our work is the first to establish guaranteed convergence for the non-iid Byzantine robust problem under realistic assumptions.
Tuning hyperparameters for machine learning algorithms is a tedious task, one that is typically done manually. To enable automated hyperparameter tuning, recent works have started to use techniques based on Bayesian optimization. However, to practically enable automated tuning for large scale machine learning training pipelines, significant gaps remain in existing libraries, including lack of abstractions, fault tolerance, and flexibility to support scheduling on any distributed computing framework. To address these challenges, we present Mango, a Python library for parallel hyperparameter tuning. Mango enables the use of any distributed scheduling framework, implements intelligent parallel search strategies, and provides rich abstractions for defining complex hyperparameter search spaces that are compatible with scikit-learn. Mango is comparable in performance to Hyperopt, another widely used library. Mango is available open-source and is currently used in production at Arm Research to provide state-of-art hyperparameter tuning capabilities.
In this paper, we study distributed algorithms for large-scale AUC maximization with a deep neural network as a predictive model. Although distributed learning techniques have been investigated extensively in deep learning, they are not directly applicable to stochastic AUC maximization with deep neural networks due to its striking differences from standard loss minimization problems (e.g., cross-entropy). Towards addressing this challenge, we propose and analyze a communication-efficient distributed optimization algorithm based on a {\it non-convex concave} reformulation of the AUC maximization, in which the communication of both the primal variable and the dual variable between each worker and the parameter server only occurs after multiple steps of gradient-based updates in each worker. Compared with the naive parallel version of an existing algorithm that computes stochastic gradients at individual machines and averages them for updating the model parameters, our algorithm requires a much less number of communication rounds and still achieves a linear speedup in theory. To the best of our knowledge, this is the \textbf{first} work that solves the {\it non-convex concave min-max} problem for AUC maximization with deep neural networks in a communication-efficient distributed manner while still maintaining the linear speedup property in theory. Our experiments on several benchmark datasets show the effectiveness of our algorithm and also confirm our theory.
Federated learning aims to jointly learn statistical models over massively distributed remote devices. In this work, we propose FedDANE, an optimization method that we adapt from DANE, a method for classical distributed optimization, to handle the practical constraints of federated learning. We provide convergence guarantees for this method when learning over both convex and non-convex functions. Despite encouraging theoretical results, we find that the method has underwhelming performance empirically. In particular, through empirical simulations on both synthetic and real-world datasets, FedDANE consistently underperforms baselines of FedAvg and FedProx in realistic federated settings. We identify low device participation and statistical device heterogeneity as two underlying causes of this underwhelming performance, and conclude by suggesting several directions of future work.
We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving empirical risk minimization (ERM) problems with a nonsmooth regularization term. Our algorithm is applicable to both the primal and the dual ERM problem. Current second-order and quasi-Newton methods for this problem either do not work well in the distributed setting or work only for specific regularizers. Our algorithm uses successive quadratic approximations of the smooth part, and we describe how to maintain an approximation of the (generalized) Hessian and solve subproblems efficiently in a distributed manner. When applied to the distributed dual ERM problem, unlike state of the art that takes only the block-diagonal part of the Hessian, our approach is able to utilize global curvature information and is thus magnitudes faster. The proposed method enjoys global linear convergence for a broad range of non-strongly convex problems that includes the most commonly used ERMs, thus requiring lower communication complexity. It also converges on non-convex problems, so has the potential to be used on applications such as deep learning. Computational results demonstrate that our method significantly improves on communication cost and running time over the current state-of-the-art methods.
Communication overhead is one of the key challenges that hinders the scalability of distributed optimization algorithms. In this paper, we study local distributed SGD, where data is partitioned among computation nodes, and the computation nodes perform local updates with periodically exchanging the model among the workers to perform averaging. While local SGD is empirically shown to provide promising results, a theoretical understanding of its performance remains open. We strengthen convergence analysis for local SGD, and show that local SGD can be far less expensive and applied far more generally than current theory suggests. Specifically, we show that for loss functions that satisfy the Polyak-{\L}ojasiewicz condition, $O((pT)^{1/3})$ rounds of communication suffice to achieve a linear speed up, that is, an error of $O(1/pT)$, where $T$ is the total number of model updates at each worker. This is in contrast with previous work which required higher number of communication rounds, as well as was limited to strongly convex loss functions, for a similar asymptotic performance. We also develop an adaptive synchronization scheme that provides a general condition for linear speed up. Finally, we validate the theory with experimental results, running over AWS EC2 clouds and an internal GPU cluster.
This paper proposes a novel family of primal-dual-based distributed algorithms for smooth, convex, multi-agent optimization over networks that uses only gradient information and gossip communications. The algorithms can also employ acceleration on the computation and communications. We provide a unified analysis of their convergence rate, measured in terms of the Bregman distance associated to the saddle point reformation of the distributed optimization problem. When acceleration is employed, the rate is shown to be optimal, in the sense that it matches (under the proposed metric) existing complexity lower bounds of distributed algorithms applicable to such a class of problem and using only gradient information and gossip communications. Preliminary numerical results on distributed least-square regression problems show that the proposed algorithm compares favorably on existing distributed schemes.
Distributed optimization is essential for training large models on large datasets. Multiple approaches have been proposed to reduce the communication overhead in distributed training, such as synchronizing only after performing multiple local SGD steps, and decentralized methods (e.g., using gossip algorithms) to decouple communications among workers. Although these methods run faster than AllReduce-based methods, which use blocking communication before every update, the resulting models may be less accurate after the same number of updates. Inspired by the BMUF method of Chen & Huo (2016), we propose a slow momentum (SlowMo) framework, where workers periodically synchronize and perform a momentum update, after multiple iterations of a base optimization algorithm. Experiments on image classification and machine translation tasks demonstrate that SlowMo consistently yields improvements in optimization and generalization performance relative to the base optimizer, even when the additional overhead is amortized over many updates so that the SlowMo runtime is on par with that of the base optimizer. We provide theoretical convergence guarantees showing that SlowMo converges to a stationary point of smooth non-convex losses. Since BMUF can be expressed through the SlowMo framework, our results also correspond to the first theoretical convergence guarantees for BMUF.