Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userAsynchronous Distributed Optimization with Redundancy in Cost Functions
95
0
0.0
(
0
)
Added by
Shuo Liu
Publication date
2021
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
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 synchrony can be expensive and even infeasible in real-world applications. We show that waiting for all the agents is unnecessary in many applications of distributed optimization, including distributed machine learning, due to redundancy in the cost functions (or {em data}). Specifically, we consider a generic notion of redundancy named $(r,epsilon)$-redundancy implying solvability of the original multi-agent optimization problem with $epsilon$ accuracy, despite the removal of up to $r$ (out of total $n$) agents from the system. We present an asynchronous DGD algorithm where in each iteration the server only waits for (any) $n-r$ agents, instead of all the $n$ agents. Assuming $(r,epsilon)$-redundancy, we show that our asynchronous algorithm converges to an approximate solution with error that is linear in $epsilon$ and $r$. Moreover, we also present a generalization of our algorithm to tolerate some Byzantine faulty agents in the system. Finally, we demonstrate the improved communication efficiency of our algorithm through experiments on MNIST and Fashion-MNIST using the benchmark neural network LeNet.
rate research
Read More
As numerous machine learning and other algorithms increase in complexity and data requirements, distributed computing becomes necessary to satisfy the growing computational and storage demands, because it enables parallel execution of smaller tasks that make up a large computing job. However, random fluctuations in task service times lead to straggling tasks with long execution times. Redundancy, in the form of task replication and erasure coding, provides diversity that allows a job to be completed when only a subset of redundant tasks is executed, thus removing the dependency on the straggling tasks. In situations of constrained resources (here a fixed number of parallel servers), increasing redundancy reduces the available resources for parallelism. In this paper, we characterize the diversity vs. parallelism trade-off and identify the optimal strategy, among replication, coding and splitting, which minimizes the expected job completion time. We consider three common service time distributions and establish three models that describe scaling of these distributions with the task size. We find that different distributions with different scaling models operate optimally at different levels of redundancy, and thus may require very different code rates.
We study asynchronous finite sum minimization in a distributed-data setting with a central parameter server. While asynchrony is well understood in parallel settings where the data is accessible by all machines -- e.g., modifications of variance-reduced gradient algorithms like SAGA work well -- little is known for the distributed-data setting. We develop an algorithm ADSAGA based on SAGA for the distributed-data setting, in which the data is partitioned between many machines. We show that with $m$ machines, under a natural stochastic delay model with an mean delay of $m$, ADSAGA converges in $tilde{O}left(left(n + sqrt{m}kapparight)log(1/epsilon)right)$ iterations, where $n$ is the number of component functions, and $kappa$ is a condition number. This complexity sits squarely between the complexity $tilde{O}left(left(n + kapparight)log(1/epsilon)right)$ of SAGA textit{without delays} and the complexity $tilde{O}left(left(n + mkapparight)log(1/epsilon)right)$ of parallel asynchronous algorithms where the delays are textit{arbitrary} (but bounded by $O(m)$), and the data is accessible by all. Existing asynchronous algorithms with distributed-data setting and arbitrary delays have only been shown to converge in $tilde{O}(n^2kappalog(1/epsilon))$ iterations. We empirically compare on least-squares problems the iteration complexity and wallclock performance of ADSAGA to existing parallel and distributed algorithms, including synchronous minibatch algorithms. Our results demonstrate the wallclock advantage of variance-reduced asynchronous approaches over SGD or synchronous approaches.
The LOCAL model is among the main models for studying locality in the framework of distributed network computing. This model is however subject to pertinent criticisms, including the facts that all nodes wake up simultaneously, perform in lock steps, and are failure-free. We show that relaxing these hypotheses to some extent does not hurt local computing. In particular, we show that, for any construction task $T$ associated to a locally checkable labeling (LCL), if $T$ is solvable in $t$ rounds in the LOCAL model, then $T$ remains solvable in $O(t)$ rounds in the asynchronous LOCAL model. This improves the result by Casta~neda et al. [SSS 2016], which was restricted to 3-coloring the rings. More generally, the main contribution of this paper is to show that, perhaps surprisingly, asynchrony and failures in the computations do not restrict the power of the LOCAL model, as long as the communications remain synchronous and failure-free.
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 involves proper accounting of information delays, which makes their analysis challenging. This article reviews recent developments in the design and analysis of asynchronous optimization methods, covering both centralized methods, where all processors update a master copy of the optimization variables, and decentralized methods, where each processor maintains a local copy of the variables. The analysis provides insights as to how the degree of asynchrony impacts convergence rates, especially in stochastic optimization methods.
In this paper, a distributed convex optimization algorithm, termed emph{distributed coordinate dual averaging} (DCDA) algorithm, is proposed. The DCDA algorithm addresses the scenario of a large distributed optimization problem with limited communication among nodes in the network. Currently known distributed subgradient methods, such as the distributed dual averaging or the distributed alternating direction method of multipliers algorithms, assume that nodes can exchange messages of large cardinality. Such network communication capabilities are not valid in many scenarios of practical relevance. In the DCDA algorithm, on the other hand, communication of each coordinate of the optimization variable is restricted over time. For the proposed algorithm, we bound the rate of convergence under different communication protocols and network architectures. We also consider the extensions to the case of imperfect gradient knowledge and the case in which transmitted messages are corrupted by additive noise or are quantized. Relevant numerical simulations are also provided.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
