We consider the problem of distributed inference where agents in a network observe a stream of private signals generated by an unknown state, and aim to uniquely identify this state from a finite set of hypotheses. We focus on scenarios where communication between agents is costly, and takes place over channels with finite bandwidth. To reduce the frequency of communication, we develop a novel event-triggered distributed learning rule that is based on the principle of diffusing low beliefs on each false hypothesis. Building on this principle, we design a trigger condition under which an agent broadcasts only those components of its belief vector that have adequate innovation, to only those neighbors that require such information. We prove that our rule guarantees convergence to the true state exponentially fast almost surely despite sparse communication, and that it has the potential to significantly reduce information flow from uninformative agents to informative agents. Next, to deal with finite-precision communication channels, we propose a distributed learning rule that leverages the idea of adaptive quantization. We show that by sequentially refining the range of the quantizers, every agent can learn the truth exponentially fast almost surely, while using just $1$ bit to encode its belief on each hypothesis. For both our proposed algorithms, we rigorously characterize the trade-offs between communication-efficiency and the learning rate.
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Linear Mixed Effects (LME) models have been widely applied in clustered data analysis in many areas including marketing research, clinical trials, and biomedical studies. Inference can be conducted using maximum likelihood approach if assuming Normal distributions on the random effects. However, in many applications of economy, business and medicine, it is often essential to impose constraints on the regression parameters after taking their real-world interpretations into account. Therefore, in this paper we extend the classical (unconstrained) LME models to allow for sign constraints on its overall coefficients. We propose to assume a symmetric doubly truncated Normal (SDTN) distribution on the random effects instead of the unconstrained Normal distribution which is often found in classical literature. With the aforementioned change, difficulty has dramatically increased as the exact distribution of the dependent variable becomes analytically intractable. We then develop likelihood-based approaches to estimate the unknown model parameters utilizing the approximation of its exact distribution. Simulation studies have shown that the proposed constrained model not only improves real-world interpretations of results, but also achieves satisfactory performance on model fits as compared to the existing model.
Voronoi coverage control is a particular problem of importance in the area of multi-robot systems, which considers a network of multiple autonomous robots, tasked with optimally covering a large area. This is a common task for fleets of fixed-wing Unmanned Aerial Vehicles (UAVs), which are described in this work by a unicycle model with constant forward-speed constraints. We develop event-based control/communication algorithms to relax the resource requirements on wireless communication and control actuators, an important feature for battery-driven or otherwise energy-constrained systems. To overcome the drawback that the event-triggered algorithm requires continuous measurement of system states, we propose a self-triggered algorithm to estimate the next triggering time. Hardware experiments illustrate the theoretical results.
Gradient quantization is an emerging technique in reducing communication costs in distributed learning. Existing gradient quantization algorithms often rely on engineering heuristics or empirical observations, lacking a systematic approach to dynamically quantize gradients. This paper addresses this issue by proposing a novel dynamically quantized SGD (DQ-SGD) framework, enabling us to dynamically adjust the quantization scheme for each gradient descent step by exploring the trade-off between communication cost and convergence error. We derive an upper bound, tight in some cases, of the convergence error for a restricted family of quantization schemes and loss functions. We design our DQ-SGD algorithm via minimizing the communication cost under the convergence error constraints. Finally, through extensive experiments on large-scale natural language processing and computer vision tasks on AG-News, CIFAR-10, and CIFAR-100 datasets, we demonstrate that our quantization scheme achieves better tradeoffs between the communication cost and learning performance than other state-of-the-art gradient quantization methods.
Distributed algorithms to solve linear equations in multi-agent networks have attracted great research attention and many iteration-based distributed algorithms have been developed. The convergence speed is a key factor to be considered for distributed algorithms, and it is shown dependent on the spectral radius of the iteration matrix. However, the iteration matrix is determined by the network structure and is hardly pre-tuned, making the iterative-based distributed algorithms may converge very slowly when the spectral radius is close to 1. In contrast, in centralized optimization, the Conjugate Gradient (CG) is a widely adopted idea to speed up the convergence of the centralized solvers, which can guarantee convergence in fixed steps. In this paper, we propose a general distributed implementation of CG, called DCG. DCG only needs local communication and local computation, while inheriting the characteristic of fast convergence. DCG guarantees to converge in $4Hn$ rounds, where $H$ is the maximum hop number of the network and $n$ is the number of nodes. We present the applications of DCG in solving the least square problem and network localization problem. The results show the convergence speed of DCG is three orders of magnitude faster than the widely used Richardson iteration method.
We consider training models on private data that are distributed across user devices. To ensure privacy, we add on-device noise and use secure aggregation so that only the noisy sum is revealed to the server. We present a comprehensive end-to-end system, which appropriately discretizes the data and adds discrete Gaussian noise before performing secure aggregation. We provide a novel privacy analysis for sums of discrete Gaussians and carefully analyze the effects of data quantization and modular summation arithmetic. Our theoretical guarantees highlight the complex tension between communication, privacy, and accuracy. Our extensive experimental results demonstrate that our solution is essentially able to match the accuracy to central differential privacy with less than 16 bits of precision per value.
As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.
Unsupervised multi-object representation learning depends on inductive biases to guide the discovery of object-centric representations that generalize. However, we observe that methods for learning these representations are either impractical due to long training times and large memory consumption or forego key inductive biases. In this work, we introduce EfficientMORL, an efficient framework for the unsupervised learning of object-centric representations. We show that optimization challenges caused by requiring both symmetry and disentanglement can in fact be addressed by high-cost iterative amortized inference by designing the framework to minimize its dependence on it. We take a two-stage approach to inference: first, a hierarchical variational autoencoder extracts symmetric and disentangled representations through bottom-up inference, and second, a lightweight network refines the representations with top-down feedback. The number of refinement steps taken during training is reduced following a curriculum, so that at test time with zero steps the model achieves 99.1% of the refined decomposition performance. We demonstrate strong object decomposition and disentanglement on the standard multi-object benchmark while achieving nearly an order of magnitude faster training and test time inference over the previous state-of-the-art model.
Influence maximization is the task of selecting a small number of seed nodes in a social network to maximize the spread of the influence from these seeds, and it has been widely investigated in the past two decades. In the canonical setting, the whole social network as well as its diffusion parameters is given as input. In this paper, we consider the more realistic sampling setting where the network is unknown and we only have a set of passively observed cascades that record the set of activated nodes at each diffusion step. We study the task of influence maximization from these cascade samples (IMS), and present constant approximation algorithms for this task under mild conditions on the seed set distribution. To achieve the optimization goal, we also provide a novel solution to the network inference problem, that is, learning diffusion parameters and the network structure from the cascade data. Comparing with prior solutions, our network inference algorithm requires weaker assumptions and does not rely on maximum-likelihood estimation and convex programming. Our IMS algorithms enhance the learning-and-then-optimization approach by allowing a constant approximation ratio even when the diffusion parameters are hard to learn, and we do not need any assumption related to the network structure or diffusion parameters.
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.
Most Deep Reinforcement Learning (Deep RL) algorithms require a prohibitively large number of training samples for learning complex tasks. Many recent works on speeding up Deep RL have focused on distributed training and simulation. While distributed training is often done on the GPU, simulation is not. In this work, we propose using GPU-accelerated RL simulations as an alternative to CPU ones. Using NVIDIA Flex, a GPU-based physics engine, we show promising speed-ups of learning various continuous-control, locomotion tasks. With one GPU and CPU core, we are able to train the Humanoid running task in less than 20 minutes, using 10-1000x fewer CPU cores than previous works. We also demonstrate the scalability of our simulator to multi-GPU settings to train more challenging locomotion tasks.
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