Consensus Instances Research Articles

A pragmatic approach for comparing species distribution models to increasing confidence in managing piping plover habitat

AbstractConservation management often requires decision‐making without perfect knowledge of the at‐risk species or ecosystem. Species distribution models (SDMs) are useful but largely under‐utilized due to model uncertainty. We used an ensemble modeling approach of two independently derived SDMs to explicitly address common modeling impediments and directly inform conservation decision‐making for piping plovers in a heavily populated mid‐Atlantic (USA) coastal zone. We summarized previously published Bayesian network and maximum entropy models to highlight similarities and differences in structure, and we compared the relative importance of predictors used. Despite differences in analytical approach, relative importance of factors driving nest‐site selection was consistent. Models demonstrated considerable agreement when comparing a binary (suitable/unsuitable) measure of suitability. Instances of model consensus (i.e., overlapping areas of predicted piping plover nesting habitat between models) provide a stronger “signal” in model results, reducing uncertainty related to biases or errors associated with either model. We tested model accuracy using a common dataset of plover nests initiated within the focal areas between 2013 and 2015, and we examined congruency in model outputs. Nearly, 90% of all nests occurred in areas predicted suitable by at least one model, and at least 33% of the total nests were predicted in areas suitable by both. Because models predominantly agreed on what drives piping plover nest‐site selection, areas predicted suitable by a single model should not be discounted. This case study demonstrates how models can effectively inform conservation planning by explicitly identifying the management objective, presenting robust evidence to allow managers to evaluate outcomes of alternative management decisions, and clearly communicating results that address real‐world conservation problems. Our results can greatly increase the piping plover management community's ability to prioritize candidate sites for future protection, manage existing nesting habitat appropriately, and make a compelling case for conservation actions against competing land use objectives.

A Paxos based algorithm to minimize the overhead of process recovery in consensus

Consensus is a fundamental abstraction in distributed systems and its solvability is widely discussed in the literature. In message passing distributed systems where there is a need to solve sequential instances of consensus, it is possible that some processes become faulty during one instance and recover later in another instance. Though consensus algorithms should be equipped both to handle process failures and process recovery, only a little amount of work has been done in the literature to handle process recovery. Handling process recovery is not trivial because a recovered process may broadcast a new message which could hamper the progress made by other processes towards achieving consensus in their current round, and thereby forcing them to start a new round. Therefore algorithms that are not designed to handle process recovery require $${\text {O}}\bigl (f\bigr )$$ rounds or $${\text {O}}\bigl (f\delta \bigr )$$ time to achieve consensus, where at most f processes can recover and $$\delta $$ is the message delay in the system. But Dutta et al. (in: International conference on dependable systems and networks (DSN’05), pp 22–27), 2005. https://doi.org/10.1109/DSN.2005.54 ) showed that the overhead of handling process recovery is constant and their algorithm takes $$17\delta $$ time to achieve consensus. In this work, we introduce a new Paxos based algorithm that lowers the upper bound to $$11\delta $$ . We also show that if all process failures are initial, the upper bound can be further reduced to $$5\delta $$ . Our algorithm selectively enables processes executing lower rounds to decide irrespective of the presence of higher rounds in the system, minimizing the effect of recovered processes starting a higher round.

Scalable Multitask Policy Gradient Reinforcement Learning

Policy search reinforcement learning (RL) allows agents to learn autonomously with limited feedback. However, such methods typically require extensive experience for successful behavior due to their tabula rasa nature. Multitask RL is an approach, which aims to reduce data requirements by allowing knowledge transfer between tasks. Although successful, current multitask learning methods suffer from scalability issues when considering large number of tasks. The main reasons behind this limitation is the reliance on centralized solutions. This paper proposes to a novel distributed multitask RL framework, improving the scalability across many different types of tasks. Our framework maps multitask RL to an instance of general consensus and develops an efficient decentralized solver. We justify the correctness of the algorithm both theoretically and empirically: we first proof an improvement of convergence speed to an order of O(1/k) with k being the number of iterations, and then show our algorithm surpassing others on multiple dynamical system benchmarks.

Consensus, Authority, and the Interpretive Community in the Thought of Muḥammad b. Jarīr al-Ṭabarī

Examination of al-Ṭabarī’s oeuvre as a whole reveals certain patterns that cut across fields. The following article addresses the concept of ḥujja, which is related to his understanding of consensus. It has been pointed out that al-Ṭabarī uses the term ḥujja (‘proof’) with two quite different meanings in his Qur'anic commentary, Jāmiʿ al-bayān. In one sense, ḥujja designates a proof such as a Qur'anic verse, a ḥadīth report, or an instance of consensus. In the second sense, ḥujja refers to particular people, scholars of the past whom al-Ṭabarī considers the most prominent authorities in a particular field. Al-Ṭabarī uses the term in a similar fashion in the extant sections of his legal work Ikhtilāf al-fuqahāʾ, and examination of the two works in combination reveals regularities in al-Ṭabarī’s understanding of hermeneutics across fields, including law, Qur'anic variants (qirāʾāt), and Qur'anic exegesis (tafsīr). His use of the term ḥujja implies that he conceived of the interpretive community in tafsīr and other fields as comprised of two tiers, a lower tier of all competent scholars and an upper tier—the ḥujja—of those scholars whose opinions were instrumental in shaping discourse in the field in question.

Quantitative Analysis of Consensus Algorithms

Consensus is one of the key problems in fault-tolerant distributed computing. Although the solvability of consensus is now a well-understood problem, comparing different algorithms in terms of efficiency is still an open problem. In this paper, we address this question for round-based consensus algorithms using communication predicates, on top of a partial synchronous system that alternates between good and bad periods (synchronous and nonsynchronous periods). Communication predicates together with the detailed timing information of the underlying partially synchronous system provide a convenient and powerful framework for comparing different consensus algorithms and their implementations. This approach allows us to quantify the required length of a good period to solve a given number of consensus instances. With our results, we can observe several interesting issues, such as the number of rounds of an algorithm is not necessarily a good metric for its performance.

Continuous consensus with ambiguous failures

Continuous consensus (CC) is the problem of maintaining up-to-date and identical copies of a “core” of information about the past at all correct processes in the system (Mizrahi and Moses, 2008 [6]). This is a primitive that supports simultaneous coordination among processes, and eliminates the need for issuing separate instances of consensus for different tasks. Recent work has presented new simple and efficient optimum protocols for continuous consensus in the crash and (sending) omissions failure models. For every pattern of failures, these protocols maintain at each and every time point a core that subsumes that maintained by any other continuous consensus protocol. This paper considers the continuous consensus problem in the face of harsher failures: general omissions and authenticated Byzantine failures. Computationally efficient optimum protocols for CC do not exist in these models if P ≠ N P . A variety of CC protocols are presented. The first is a simple protocol that enters every interesting event into the core within t + 1 rounds (where t is the bound on the number of failures), provided there are a majority of correct processes. The second is a protocol that achieves similar performance so long as n > t (i.e., there is always guaranteed to be at least one correct process). The final protocol makes use of active failure monitoring and failure detection to include events in the core much faster in many runs of interest. Its performance is established based on a nontrivial property of minimal vertex covers in undirected graphs. The results are adapted to the authenticated Byzantine failure model, in which it is assumed that faulty processes are malicious, but correct processes have unforgeable signatures. Finally, the problem of uniform CC is considered. It is shown that a straightforward version of uniform CC is not solvable in the setting under study. A weaker form of uniform CC is defined, and protocols achieving it are presented.

The k-simultaneous consensus problem

This paper introduces and investigates the k-simultaneous consensus task: each process participates at the same time in k independent consensus instances until it decides in any one of them. It is shown that the k-simultaneous consensus task is equivalent to the k-set agreement task in the wait-free read/write shared memory model, and furthermore k-simultaneous consensus possesses properties that k-set does not. In particular we show that the multivalued version and the binary version of the k-simultaneous consensus task are wait-free equivalent. These equivalences are independent of the number of processes. Interestingly, this provides us with a new characterization of the k-set agreement task that is based on the fundamental binary consensus problem.

Implementing uniform reliable broadcast with binary consensus in systems with fair-lossy links

When implementing multivalued consensus using binary consensus, previous algorithms assume the availability of uniform reliable broadcast, which is not implementable in systems with fair-lossy links. In this paper, we show that with binary consensus we can implement uniform reliable broadcast directly in systems with fair-lossy links, and thus the separate assumption of the availability of uniform reliable broadcast is not necessary. We further prove that, when binary consensus instances are available only as black boxes, any implementation of uniform reliable broadcast in the fair-lossy link model requires the invocation of an infinite number of binary consensus instances even if no process ever broadcasts any messages, and this is true even when multivalued consensus is used.

Bounded cost algorithms for multivalued consensus using binary consensus instances

In this paper, we present two bounded cost algorithms that solve multivalued consensus using binary consensus instances. Our first algorithm uses ⌈ log 2 n ⌉ number of binary consensus instances where n is the number of processes, while our second algorithm uses at most 2 k ˜ binary consensus instances, where k ˜ is the maximum length of the binary representation of all proposed values in the run. Both algorithms are significant improvements over the previous algorithm in [A. Mostefaoui, M. Raynal, F. Tronel, From binary consensus to multivalued consensus in asynchronous message-passing systems, Information Processing Letters 73 (5–6) (2000) 207–212], where the number of binary consensus instances needed to solve one multivalued consensus is unbounded.

Optimal Amortized Distributed Consensus

In this paper we study the behavior of deterministic algorithms when consensus is needed repeatedly, say k times. We show that it is possible to achieve consensus with the optimal number of processors (n > 3t), and when k is large enough, with optimal amortized cost in all other measures: the number of communication rounds r*, the maximal message size m*, and the total bit complexity b*. More specifically, we achieve the following amortized bounds for k consensus instances: r* = O(1 + t/k), b* = O(nt + nt3/k), and m* = O(1 + t2/k). When k ≥ t2, then r* and m* are O(1) and b*= O(nt), which is optimal.