We present Asynchronous Stochastic Parallel Pose Graph Optimization (ASAPP), the first asynchronous algorithm for distributed pose graph optimization (PGO) in multi-robot simultaneous localization and mapping. By enabling robots to optimize their local trajectory estimates without synchronization, ASAPP offers resiliency against communication delays and alleviates the need to wait for stragglers in the network. Furthermore, ASAPP can be applied on the rank-restricted relaxations of PGO, a crucial class of non-convex Riemannian optimization problems that underlies recent breakthroughs on globally optimal PGO. Under bounded delay, we establish the global first-order convergence of ASAPP using a sufficiently small stepsize. The derived stepsize depends on the worst-case delay and inherent problem sparsity, and furthermore matches known result for synchronous algorithms when there is no delay. Numerical evaluations on simulated and real-world datasets demonstrate favorable performance compared to state-of-the-art synchronous approach, and show ASAPP's resilience against a wide range of delays in practice.
Motion estimation approaches typically employ sensor fusion techniques, such as the Kalman Filter, to handle individual sensor failures. More recently, deep learning-based fusion approaches have been proposed, increasing the performance and requiring less model-specific implementations. However, current deep fusion approaches often assume that sensors are synchronised, which is not always practical, especially for low-cost hardware. To address this limitation, in this work, we propose AFT-VO, a novel transformer-based sensor fusion architecture to estimate VO from multiple sensors. Our framewo…
Asynchronous parallel optimization received substantial successes and extensive attention recently. One of core theoretical questions is how much speedup (or benefit) the asynchronous parallelization can bring us. This paper provides a comprehensive and generic analysis to study the speedup property for a broad range of asynchronous parallel stochastic algorithms from the zeroth order to the first order methods. Our result recovers or improves existing analysis on special cases, provides more insights for understanding the asynchronous parallel behaviors, and suggests a novel asynchronous para…
Several works have shown linear speedup is achieved by an asynchronous parallel implementation of stochastic coordinate descent so long as there is not too much parallelism. More specifically, it is known that if all updates are of similar duration, then linear speedup is possible with up to $Θ(\sqrt n L_{\max}/L_{\overline{\mathrm{res}}})$ processors, where $L_{\max}$ and $L_{\overline{\mathrm{res}}}$ are suitable Lipschitz parameters. This paper shows the bound is tight for almost all possible values of these parameters.
We describe an asynchronous parallel variant of the randomized Kaczmarz (RK) algorithm for solving the linear system $Ax=b$. The analysis shows linear convergence and indicates that nearly linear speedup can be expected if the number of processors is bounded by a multiple of the number of rows in $A$.
We describe an asynchronous parallel stochastic coordinate descent algorithm for minimizing smooth unconstrained or separably constrained functions. The method achieves a linear convergence rate on functions that satisfy an essential strong convexity property and a sublinear rate ($1/K$) on general convex functions. Near-linear speedup on a multicore system can be expected if the number of processors is $O(n^{1/2})$ in unconstrained optimization and $O(n^{1/4})$ in the separable-constrained case, where $n$ is the number of variables. We describe results from implementation on 40-core processor…
Communication delays and synchronization are major bottlenecks for parallel computing, and tolerating asynchrony is therefore crucial for accelerating parallel computation. Motivated by optimization problems that do not satisfy convexity assumptions, we present an asynchronous block coordinate descent algorithm for nonconvex optimization problems whose objective functions satisfy the Polyak-Lojasiewicz condition. This condition is a generalization of strong convexity to nonconvex problems and requires neither convexity nor uniqueness of minimizers. Under only assumptions of mild smoothness of …
The need for scalable numerical solutions has motivated the development of asynchronous parallel algorithms, where a set of nodes run in parallel with little or no synchronization, thus computing with delayed information. This paper studies the convergence of the asynchronous parallel algorithm ARock under potentially unbounded delays. ARock is a general asynchronous algorithm that has many applications. It parallelizes fixed-point iterations by letting a set of nodes randomly choose solution coordinates and update them in an asynchronous parallel fashion. ARock takes some recent asynchronous …
INRIA（法国国家信息与自动化研究所）；École Normale Supérieure, Paris（巴黎高等师范学院）；Université de Montréal（蒙特利尔大学）
As datasets continue to increase in size and multi-core computer architectures are developed, asynchronous parallel optimization algorithms become more and more essential to the field of Machine Learning. Unfortunately, conducting the theoretical analysis asynchronous methods is difficult, notably due to the introduction of delay and inconsistency in inherently sequential algorithms. Handling these issues often requires resorting to simplifying but unrealistic assumptions. Through a novel perspective, we revisit and clarify a subtle but important technical issue present in a large fraction of …
INRIA - Sierra Project-team（法国国家信息与自动化研究所 - Sierra 项目组）；École normale supérieure, Paris（巴黎高等师范学院）
We describe ASAGA, an asynchronous parallel version of the incremental gradient algorithm SAGA that enjoys fast linear convergence rates. Through a novel perspective, we revisit and clarify a subtle but important technical issue present in a large fraction of the recent convergence rate proofs for asynchronous parallel optimization algorithms, and propose a simplification of the recently introduced "perturbed iterate" framework that resolves it. We thereby prove that ASAGA can obtain a theoretical linear speedup on multi-core systems even without sparsity assumptions. We present results of an …
Although first-order stochastic algorithms, such as stochastic gradient descent, have been the main force to scale up machine learning models, such as deep neural nets, the second-order quasi-Newton methods start to draw attention due to their effectiveness in dealing with ill-conditioned optimization problems. The L-BFGS method is one of the most widely used quasi-Newton methods. We propose an asynchronous parallel algorithm for stochastic quasi-Newton (AsySQN) method. Unlike prior attempts, which parallelize only the calculation for gradient or the two-loop recursion of L-BFGS, our algorithm…
We present complexity and numerical results for a new asynchronous parallel algorithmic method for the minimization of the sum of a smooth nonconvex function and a convex nonsmooth regularizer, subject to both convex and nonconvex constraints. The proposed method hinges on successive convex approximation techniques and a novel probabilistic model that captures key elements of modern computational architectures and asynchronous implementations in a more faithful way than state-of-the-art models. In the companion paper we provided a detailed description on the probabilistic model and gave conver…
We propose a new asynchronous parallel block-descent algorithmic framework for the minimization of the sum of a smooth nonconvex function and a nonsmooth convex one, subject to both convex and nonconvex constraints. The proposed framework hinges on successive convex approximation techniques and a novel probabilistic model that captures key elements of modern computational architectures and asynchronous implementations in a more faithful way than current state-of-the-art models. Other key features of the framework are: i) it covers in a unified way several specific solution methods; ii) it acco…
Fudan University（复旦大学）；Columbia University（哥伦比亚大学）；University of California, Los Angeles（加州大学洛杉矶分校）
In this paper, we propose AsyncQVI, an asynchronous-parallel Q-value iteration for discounted Markov decision processes whose transition and reward can only be sampled through a generative model. Given such a problem with $|\mathcal{S}|$ states, $|\mathcal{A}|$ actions, and a discounted factor $γ\in(0,1)$, AsyncQVI uses memory of size $\mathcal{O}(|\mathcal{S}|)$ and returns an $\varepsilon$-optimal policy with probability at least $1-δ$ using $$\tilde{\mathcal{O}}\big(\frac{|\mathcal{S}||\mathcal{A}|}{(1-γ)^5\varepsilon^2}\log(\frac{1}δ)\big)$$ samples. AsyncQVI is also the first asynchronous…
In machine learning, asynchronous parallel stochastic gradient descent (APSGD) is broadly used to speed up the training process through multi-workers. Meanwhile, the time delay of stale gradients in asynchronous algorithms is generally proportional to the total number of workers, which brings additional deviation from the accurate gradient due to using delayed gradients. This may have a negative influence on the convergence of the algorithm. One may ask: How many workers can we use at most to achieve a good convergence and the linear speedup? In this paper, we consider the second-order converg…
Stochastic convergence of parallel asynchronous adaptive first-order methods
Université de Toulouse, INP, IRIT, Toulouse, France（图卢兹大学，INP，IRIT，法国图卢兹）；IA Artificial and Natural Intelligence Toulouse Institute (ANITI)（图卢兹3IA人工智能与自然智能研究所（ANITI））；NAXYS, University of Namur, Namur, Belgium（NAXYS，纳慕尔大学，比利时纳慕尔）
Motivated by large-scale optimization problems arising in the context of machine learning, there have been several advances in the study of asynchronous parallel and distributed optimization methods during the past decade. Asynchronous methods do not require all processors to maintain a consistent view of the optimization variables. Consequently, they generally can make more efficient use of computational resources than synchronous methods, and they are not sensitive to issues like stragglers (i.e., slow nodes) and unreliable communication links. Mathematical modeling of asynchronous methods i…
In the realm of big data and machine learning, data-parallel, distributed stochastic algorithms have drawn significant attention in the present days.~While the synchronous versions of these algorithms are well understood in terms of their convergence, the convergence analyses of their asynchronous counterparts are not widely studied. In this paper, we propose and analyze a {\it distributed, asynchronous parallel} SGD in light of solving an arbitrary consistent linear system by reformulating the system into a stochastic optimization problem as studied by Richtárik and Takác in [35]. We compare …
Two characteristics that make convex decomposition algorithms attractive are simplicity of operations and generation of parallelizable structures. In principle, these schemes require that all coordinates update at the same time, i.e., they are synchronous by construction. Introducing asynchronicity in the updates can resolve several issues that appear in the synchronous case, like load imbalances in the computations or failing communication links. However, and to the best of our knowledge, there are no instances of asynchronous versions of commonly-known algorithms combined with inertial accel…
University of Rochester（罗切斯特大学）；IBM T. J. Watson Research Center（IBM T. J. 沃森研究中心）；ETH Zurich（苏黎世联邦理工学院）；Tencent AI Lab（腾讯人工智能实验室）
Most commonly used distributed machine learning systems are either synchronous or centralized asynchronous. Synchronous algorithms like AllReduce-SGD perform poorly in a heterogeneous environment, while asynchronous algorithms using a parameter server suffer from 1) communication bottleneck at parameter servers when workers are many, and 2) significantly worse convergence when the traffic to parameter server is congested. Can we design an algorithm that is robust in a heterogeneous environment, while being communication efficient and maintaining the best-possible convergence rate? In this pape…
Iowa State University（爱荷华州立大学）；University of Kentucky（肯塔基大学）
PARyOpt is a python based implementation of the Bayesian optimization routine designed for remote and asynchronous function evaluations. Bayesian optimization is especially attractive for computational optimization due to its low cost function footprint as well as the ability to account for uncertainties in data. A key challenge to efficiently deploy any optimization strategy on distributed computing systems is the synchronization step, where data from multiple function calls is assimilated to identify the next campaign of function calls. Bayesian optimization provides an elegant approach to o…
We show that asymptotically, completely asynchronous stochastic gradient procedures achieve optimal (even to constant factors) convergence rates for the solution of convex optimization problems under nearly the same conditions required for asymptotic optimality of standard stochastic gradient procedures. Roughly, the noise inherent to the stochastic approximation scheme dominates any noise from asynchrony. We also give empirical evidence demonstrating the strong performance of asynchronous, parallel stochastic optimization schemes, demonstrating that the robustness inherent to stochastic appro…
Large-scale non-convex optimization problems are expensive to solve due to computational and memory costs. To reduce the costs, first-order (computationally efficient) and asynchronous-parallel (memory efficient) algorithms are necessary to minimize non-convex functions in machine learning. However, asynchronous-first-order methods applied within non-convex settings run into two difficulties: (i) parallelization delays, which affect convergence by disrupting the monotonicity of first-order methods, and (ii) sub-optimal saddle points where the gradient is zero. To solve these two difficulties, …
Recent several years have witnessed the surge of asynchronous (async-) parallel computing methods due to the extremely big data involved in many modern applications and also the advancement of multi-core machines and computer clusters. In optimization, most works about async-parallel methods are on unconstrained problems or those with block separable constraints. In this paper, we propose an async-parallel method based on block coordinate update (BCU) for solving convex problems with nonseparable linear constraint. Running on a single node, the method becomes a novel randomized primal-dual BCU…
Stochastic gradient methods (SGMs) are the predominant approaches to train deep learning models. The adaptive versions (e.g., Adam and AMSGrad) have been extensively used in practice, partly because they achieve faster convergence than the non-adaptive versions while incurring little overhead. On the other hand, asynchronous (async) parallel computing has exhibited significantly higher speed-up over its synchronous (sync) counterpart. Async-parallel non-adaptive SGMs have been well studied in the literature from the perspectives of both theory and practical performance. Adaptive SGMs can also …
Finding a fixed point to a nonexpansive operator, i.e., $x^*=Tx^*$, abstracts many problems in numerical linear algebra, optimization, and other areas of scientific computing. To solve fixed-point problems, we propose ARock, an algorithmic framework in which multiple agents (machines, processors, or cores) update $x$ in an asynchronous parallel fashion. Asynchrony is crucial to parallel computing since it reduces synchronization wait, relaxes communication bottleneck, and thus speeds up computing significantly. At each step of ARock, an agent updates a randomly selected coordinate $x_i$ based …
Sandia National Laboratories（桑迪亚国家实验室）；Xilinx Inc.（赛灵思公司）
Bayesian optimization (BO) is a flexible and powerful framework that is suitable for computationally expensive simulation-based applications and guarantees statistical convergence to the global optimum. While remaining as one of the most popular optimization methods, its capability is hindered by the size of data, the dimensionality of the considered problem, and the nature of sequential optimization. These scalability issues are intertwined with each other and must be tackled simultaneously. In this work, we propose the Scalable$^3$-BO framework, which employs sparse GP as the underlying surr…
Cornell University（康奈尔大学）；Uber AI Labs（优步人工智能实验室）；National University of Singapore（新加坡国立大学）
This paper describes Plumbing for Optimization with Asynchronous Parallelism (POAP) and the Python Surrogate Optimization Toolbox (pySOT). POAP is an event-driven framework for building and combining asynchronous optimization strategies, designed for global optimization of expensive functions where concurrent function evaluations are useful. POAP consists of three components: a worker pool capable of function evaluations, strategies to propose evaluations or other actions, and a controller that mediates the interaction between the workers and strategies. pySOT is a collection of synchronous an…
We introduce and analyze stochastic optimization methods where the input to each gradient update is perturbed by bounded noise. We show that this framework forms the basis of a unified approach to analyze asynchronous implementations of stochastic optimization algorithms.In this framework, asynchronous stochastic optimization algorithms can be thought of as serial methods operating on noisy inputs. Using our perturbed iterate framework, we provide new analyses of the Hogwild! algorithm and asynchronous stochastic coordinate descent, that are simpler than earlier analyses, remove many assumptio…
We introduce the Stochastic Asynchronous Proximal Alternating Linearized Minimization (SAPALM) method, a block coordinate stochastic proximal-gradient method for solving nonconvex, nonsmooth optimization problems. SAPALM is the first asynchronous parallel optimization method that provably converges on a large class of nonconvex, nonsmooth problems. We prove that SAPALM matches the best known rates of convergence --- among synchronous or asynchronous methods --- on this problem class. We provide upper bounds on the number of workers for which we can expect to see a linear speedup, which match t…
