Consensus is one of the most fundamental distributed computing problems. In particular, it serves as a building block in many replication based fault-tolerant systems and in particular in multiple recent blockchain solutions. Depending on its exact variant and other environmental assumptions, solving consensus requires multiple communication rounds. Yet, there are known optimistic protocols that guarantee termination in a single communication round under favorable conditions. In this paper we present a generic optimizer than can turn any consensus protocol into an optimized protocol that terminates in a single communication round whenever all nodes start with the same predetermined value and no Byzantine failures occur (although node crashes are allowed). This is regardless of the network timing assumptions and additional oracle capabilities assumed by the base consensus protocol being optimized. In the case of benign failures, our optimizer works whenever the number of faulty nodes @math . For Byzantine behavior, our optimizer's resiliency depends on the validity variant sought. In the case of classical validity, it can accommodate @math Byzantine failures. With the more recent external validity function assumption, it works whenever @math . Either way, our optimizer only relies on oral messages, thereby imposing very light-weight crypto requirements.
Zyzzyva is a client driven protocol @cite_24 which terminates after @math communication rounds (including the communication between the client and the replicas) whenever the client receives identical replies from all @math replicas. Our optimizer obtains termination in a single communication round among the replicas even when upto @math of them may crush or be slow. This is by relying on all-to-all communication, and ensuring fast termination only when the preferred value is included in the first @math replies. Also, our optimizer is generic while Zyzzyva and FaB are specialized solutions.
@cite_24
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We present Zyzzyva, a protocol that uses speculation to reduce the cost and simplify the design of Byzantine fault tolerant state machine replication. In Zyzzyva, replicas respond to a client's request without first running an expensive three-phase commit protocol to reach agreement on the order in which the request must be processed. Instead, they optimistically adopt the order proposed by the primary and respond immediately to the client. Replicas can thus become temporarily inconsistent with one another, but clients detect inconsistencies, help correct replicas converge on a single total ordering of requests, and only rely on responses that are consistent with this total order. This approach allows Zyzzyva to reduce replication overheads to near their theoretical minimal. We present Abstract (ABortable STate mAChine replicaTion), a new abstraction for designing and reconfiguring generalized replicated state machines that are, unlike traditional state machines, allowed to abort executing a client’s request if “something goes wrong.” Abstract can be used to considerably simplify the incremental development of efficient Byzantine fault-tolerant state machine replication ( BFT ) protocols that are notorious for being difficult to develop. In short, we treat a BFT protocol as a composition of Abstract instances. Each instance is developed and analyzed independently and optimized for specific system conditions. We illustrate the power of Abstract through several interesting examples. We first show how Abstract can yield benefits of a state-of-the-art BFT protocol in a less painful and error-prone manner. Namely, we develop AZyzzyva, a new protocol that mimics the celebrated best-case behavior of Zyzzyva using less than 35p of the Zyzzyva code. To cover worst-case situations, our abstraction enables one to use in AZyzzyva any existing BFT protocol. We then present Aliph, a new BFT protocol that outperforms previous BFT protocols in terms of both latency (by up to 360p) and throughput (by up to 30p). Finally, we present R-Aliph, an implementation of Aliph that is robust, that is, whose performance degrades gracefully in the presence of Byzantine replicas and Byzantine clients. Modern Byzantine fault-tolerant state machine replication (BFT) protocols involve about 20,000 lines of challenging C++ code encompassing synchronization, networking and cryptography. They are notoriously difficult to develop, test and prove. We present a new abstraction to simplify these tasks. We treat a BFT protocol as a composition of instances of our abstraction. Each instance is developed and analyzed independently. To illustrate our approach, we first show how our abstraction can be used to obtain the benefits of a state-of-the-art BFT protocol with much less pain. Namely, we develop AZyzzyva, a new protocol that mimics the behavior of Zyzzyva in best-case situations (for which Zyzzyva was optimized) using less than 24 of the actual code of Zyzzyva. To cover worst-case situations, our abstraction enables to use in AZyzzyva any existing BFT protocol, typically, a classical one like PBFT which has been tested and proved correct. We then present Aliph, a new BFT protocol that outperforms previous BFT protocols both in terms of latency (by up to 30 ) and throughput (by up to 360 ). The development of Aliph required two new instances of our abstraction. Each instance contains less than 25 of the code needed to develop state-of-the-art BFT protocols. We consider the problem of learning an unknown Markov Decision Process (MDP) that is weakly communicating in the infinite horizon setting. We propose a Thompson Sampling-based reinforcement learning algorithm with dynamic episodes (TSDE). At the beginning of each episode, the algorithm generates a sample from the posterior distribution over the unknown model parameters. It then follows the optimal stationary policy for the sampled model for the rest of the episode. The duration of each episode is dynamically determined by two stopping criteria. The first stopping criterion controls the growth rate of episode length. The second stopping criterion happens when the number of visits to any state-action pair is doubled. We establish @math bounds on expected regret under a Bayesian setting, where @math and @math are the sizes of the state and action spaces, @math is time, and @math is the bound of the span. This regret bound matches the best available bound for weakly communicating MDPs. Numerical results show it to perform better than existing algorithms for infinite horizon MDPs.