There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

物件導向軟體之架構(Object-Oriented Software Construction)探討

In 1974 an article appeared in Science magazine with the dry-sounding title “Judgment Under Uncertainty: Heuristics and Biases” by a pair of psychologists who were not well known outside their discipline of decision theory. In it Amos Tversky and Daniel Kahneman introduced the world to Prospect Theory, which mapped out how humans actually behave when faced with decisions about gains and losses, in contrast to how economists assumed that people behave. Prospect Theory turned Economics on its head by demonstrating through a series of ingenious experiments that people are much more concerned with losses than they are with gains, and that framing a choice from one perspective or the other will result in decisions that are exactly the opposite of each other, even if the outcomes are monetarily the same. Prospect Theory led cognitive psychology in a new direction that began to uncover other human biases in thinking that are probably not learned but are part of our brain’s wiring.

Thinking fast and slow.

This paper describes a new replication algorithm that is able to tolerate Byzantine faults. We believe that Byzantinefault-tolerant algorithms will be increasingly important in the future because malicious attacks and software errors are increasingly common and can cause faulty nodes to exhibit arbitrary behavior. Whereas previous algorithms assumed a synchronous system or were too slow to be used in practice, the algorithm described in this paper is practical: it works in asynchronous environments like the Internet and incorporates several important optimizations that improve the response time of previous algorithms by more than an order of magnitude. We implemented a Byzantine-fault-tolerant NFS service using our algorithm and measured its performance. The results show that our service is only 3% slower than a standard unreplicated NFS.

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Practical Byzantine fault tolerance

Speculation is frequent in distributed computing It is even the norm in distributed algorithms that are designed for practical purposes Yet, speculation is difficult and it has, so far, led to algorithms that are intricate and hard to reason about, let aside prove and test The reason is simple: speculation involves different execution paths that are usually intermingled in the same algorithm, adding to the difficulties of concurrency and communication, inherent to generalpurpose distributed computing

Foundations of speculative distributed computing

Machine Learning (ML) solutions are nowadays distributed and are prone to various types of component failures, which can be encompassed in so-called Byzantine behavior. This paper introduces LiuBei, a Byzantine-resilient ML algorithm that does not trust any individual component in the network (neither workers nor servers), nor does it induce additional communication rounds (on average), compared to standard non-Byzantine resilient algorithms. LiuBei builds upon gradient aggregation rules (GARs) to tolerate a minority of Byzantine workers. Besides, LiuBei replicates the parameter server on multiple machines instead of trusting it. We introduce a novel filtering mechanism that enables workers to filter out replies from Byzantine server replicas without requiring communication with all servers. Such a filtering mechanism is based on network synchrony, Lipschitz continuity of the loss function, and the GAR used to aggregate workers' gradients. We also introduce a protocol, scatter/gather, to bound drifts between models on correct servers with a small number of communication messages. We theoretically prove that LiuBei achieves Byzantine resilience to both servers and workers and guarantees convergence. We build LiuBei using TensorFlow, and we show that LiuBei tolerates Byzantine behavior with an accuracy loss of around 5% and around 24% convergence overhead compared to vanilla TensorFlow. We moreover show that the throughput gain of LiuBei compared to another state-of-the-art Byzantine-resilient ML algorithm (that assumes network asynchrony) is 70%.

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Fast Machine Learning with Byzantine Workers and Servers

We study Byzantine collaborative learning, where $n$ nodes seek to collectively learn from each others' local data. The data distribution may vary from one node to another. No node is trusted, and $f < n$ nodes can behave arbitrarily. We prove that collaborative learning is equivalent to a new form of agreement, which we call averaging agreement. In this problem, nodes start each with an initial vector and seek to approximately agree on a common vector, which is close to the average of honest nodes' initial vectors. We present two asynchronous solutions to averaging agreement, each we prove optimal according to some dimension. The first, based on the minimum-diameter averaging, requires $ n \geq 6f+1$, but achieves asymptotically the best-possible averaging constant up to a multiplicative constant. The second, based on reliable broadcast and coordinate-wise trimmed mean, achieves optimal Byzantine resilience, i.e., $n \geq 3f+1$. Each of these algorithms induces an optimal Byzantine collaborative learning protocol. In particular, our equivalence yields new impossibility theorems on what any collaborative learning algorithm can achieve in adversarial and heterogeneous environments.

Collaborative Learning in the Jungle

In this work, we present transaction polymorphism, a synchronization technique that consists of providing more control to the programmer than traditional (i.e., monomorphic) transactions to achieve comparable performance to generic lock-based and lock-free solutions.We prove the following results: (i) Lock-based synchronization enables strictly higher concurrency than monormophic transactions. (ii) Polymorphic transactions enable strictly higher concurrency than monomorphic transactions. The former result indicates that there exist some transactional programs that will never perform as well as their lock-based counterparts, whatever improvement could be made at the hardware level to diminish the overhead associated with transactional accesses. The latter result shows, however, that transaction polymorphism is a promising solution to cope with this issue.

Brief announcement: transaction polymorphism

This paper gives an overview of an open object oriented framework for reliable distributed computing named BAST. BAST provides abstractions for building reliable distributed protocols such as atomic commitment and total order broadcast. It is an object oriented framework in the sense that reliable distributed protocols can be built simply through inheritance and callback implementations. It is open in the sense that both existing protocols and their implementations can be customized for specific application needs.

Rachid Guerraoui

Papers

Foundations of speculative distributed computing

Fast Machine Learning with Byzantine Workers and Servers

Collaborative Learning in the Jungle

Brief announcement: transaction polymorphism

An open framework for reliable distributed computing