Many problems can be solved by iteration by multiple participants (processors, servers, routers etc.). Previous mathematical models for such asynchronous iterations assume a single function being iterated by a fixed set of participants. We will call such iterations static since the system's configuration does not change. However in several real-world examples, such as inter-domain routing, both the function being iterated and the set of participants change frequently while the system continues to function. In this paper we extend Uresin & Dubois's work on static iterations to develop a model for this class of "dynamic" or "always on" asynchronous iterations. We explore what it means for such an iteration to be implemented correctly, and then prove two different conditions on the set of iterated functions that guarantee the full asynchronous iteration satisfies this new definition of correctness. These results have been formalised in Agda and the resulting library is publicly available.
This paper addresses the distributed convergence detection problem in asynchronous iterations. A modified recursive doubling algorithm is investigated in order to adapt to the non-power-of-two case. Some convergence detection algorithms are illustrated based on the reduction operation. Finally, a concluding discussion about the implementation and the applicability is presented.
Asynchronous iterations arise naturally in parallel computing if one wants to solve large problems with a minimization of the idle times. This paper presents an original model of asynchronous iterations for a time-domain decomposition method, namely the parareal method. The asynchronous parareal algorithm is here applied to European option pricing, and numerical experiments performed on a parallel supercomputer, illustrate the performance and efficiency of this new method.
LAAS-CNRS（LAAS-法国国家科学研究中心）；Université de Toulouse（图卢兹大学）；CNRS（法国国家科学研究中心）
We describe several features of parallel or distributed asynchronous iterative algorithms such as unbounded delays, possible out of order messages or flexible communication. We concentrate on the concept of macroiteration sequence which was introduced in order to study the convergence or termination of asynchronous iterations. A survey of asynchronous iterations for convex optimization problems is also presented. Finally, a new result of convergence for parallel or distributed asynchronous iterative algorithms with flexible communication for convex optimization problems and machine learning is…
This paper proposes a simple topological characterization of a large class of fair adversarial models via affine tasks: sub-complexes of the second iteration of the standard chromatic subdivision. We show that the task computability of a model in the class is precisely captured by iterations of the corresponding affine task. Fair adversaries include, but are not restricted to, the models of wait-freedom, t-resilience, and $k$-concurrency. Our results generalize and improve all previously derived topological characterizations of the ability of a model to solve distributed tasks.
Iterative graph algorithms often compute intermediate values and update them as computation progresses. Updated output values are used as inputs for computations in current or subsequent iterations; hence the number of iterations required for values to converge can potentially reduce if the newest values are asynchronously made available to other updates computed in the same iteration. In a multi-threaded shared memory system, the immediate propagation of updated values can cause memory contention that may offset the benefit of propagating updates sooner. In some cases, the benefit of a smalle…
Asynchronous iterations are more and more investigated for both scaling and fault-resilience purpose on high performance computing platforms. While so far, they have been exclusively applied within space domain decomposition frameworks, this paper advocates a novel application direction targeting time-decomposed time-parallel approaches. Specifically, an asynchronous iterative model is derived from the Parareal scheme, for which convergence and speedup analysis are then conducted. It turned out that Parareal and async-Parareal feature very close convergence conditions, asymptotically equivalen…
In this paper, we address the problem of designing a distributed application meant to run both classical and asynchronous iterations. MPI libraries are very popular and widely used in the scientific community, however asynchronous iterative methods raise non-negligible difficulties about the efficient management of communication requests and buffers. Moreover, a convergence detection issue is introduced, which requires the implementation of one of the various state-of-the-art termination methods, which are not necessarily highly reliable for most computational environments. We propose here an …
Federated learning (FL) is typically performed in a synchronous parallel manner, where the involvement of a slow client delays a training iteration. Current FL systems employ a participant selection strategy to select fast clients with quality data in each iteration. However, this is not always possible in practice, and the selection strategy often has to navigate an unpleasant trade-off between the speed and the data quality of clients. In this paper, we present Pisces, an asynchronous FL system with intelligent participant selection and model aggregation for accelerated training. To avoid in…
This paper considers the problem of asynchronous distributed multi-agent optimization on server-based system architecture. In this problem, each agent has a local cost, and the goal for the agents is to collectively find a minimum of their aggregate cost. A standard algorithm to solve this problem is the iterative distributed gradient-descent (DGD) method being implemented collaboratively by the server and the agents. In the synchronous setting, the algorithm proceeds from one iteration to the next only after all the agents complete their expected communication with the server. However, such s…
Consider a set of networked agents endowed with private cost functions and seeking to find a consensus on the minimizer of the aggregate cost. A new class of random asynchronous distributed optimization methods is introduced. The methods generalize the standard Alternating Direction Method of Multipliers (ADMM) to an asynchronous setting where isolated components of the network are activated in an uncoordinated fashion. The algorithms rely on the introduction of randomized Gauss-Seidel iterations of a Douglas-Rachford operator for finding zeros of a sum of two monotone operators. Convergence t…
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 …
We present a study of the effectiveness of asynchronous incomplete LU factorization preconditioners for the time-implicit solution of compressible flow problems while exploiting thread-parallelism within a compute node. A block variant of the asynchronous fine-grain parallel preconditioner adapted to a finite volume discretization of the compressible Navier-Stokes equations on unstructured grids is presented, and convergence theory is extended to the new variant. Experimental (numerical) results on the performance of these preconditioners on inviscid and viscous laminar two-dimensional steady-…
