The increasing prevalence of personal devices motivates the design of algorithms that can leverage their computing power, together with the data they generate, in order to build privacy-preserving and effective machine learning models. However, traditional distributed learning algorithms impose a uniform workload on all participating devices, most often discarding the weakest participants. This not only induces a suboptimal use of available computational resources, but also significantly reduces the quality of the learning process, as data held by the slowest devices is discarded from the procedure. This paper proposes HgO, a distributed learning scheme with parameterizable iteration costs that can be adjusted to the computational capabilities of different devices. HgO encourages the participation of slower devices, thereby improving the accuracy of the model when the participants do not share the same dataset. When combined with a robust aggregation rule, HgO can tolerate some level of Byzantine behavior, depending on the hardware profile of the devices (we prove, for the first time, a trade-off between Byzantine tolerance and hardware heterogeneity). We also demonstrate the convergence of HgO, theoretically and empirically, without assuming any specific partitioning of the data over the devices. We present an exhaustive set of experiments, evaluating the performance of HgO on several classification tasks and highlighting the importance of incorporating slow devices when learning in a Byzantine-prone environment with heterogeneous participants.

We consider the problem of making a multi-agent system (MAS) resilient to Byzantine failures through replication. We consider a very general model of MAS, where randomness can be involved in the behavior of each agent. We propose the first universal scheme to make such a MAS Byzantine-resilient.

Modern machine learning architectures distinguish servers and workers. Typically, a d-dimensional model is hosted by a server and trained by n workers, using a distributed stochastic gradient descent (SGD) optimization scheme. At each SGD step, the goal is to estimate the gradient of a cost function. The simplest way to do this is to average the gradients estimated by the workers. However, averaging is not resilient to even one single Byzantine failure of a worker. Many alternative gradient aggregation rules (GARs) have recently been proposed to tolerate a maximum number f of Byzantine workers. These GARs differ according to (1) the complexity of their computation time, (2) the maximal number of Byzantine workers despite which convergence can still be ensured (breakdown point), and (3) their accuracy, which can be captured by (3.1) their angular error, namely the angle with the true gradient, as well as (3.2) their ability to aggregate full gradients. In particular, many are not full gradients for they operate on each dimension separately, which results in a coordinate-wise blended gradient, leading to low accuracy in practical situations where the number (s) of workers that are actually Byzantine in an execution is small (s < < f). We propose Aksel, a new scalable median-based GAR with optimal time complexity (𝒪(nd)), optimal breakdown point (n > 2f) and the lowest upper bound on the expected angular error (𝒪(√d)) among full gradient approaches. We also study the actual angular error of Aksel when the gradient distribution is normal and show that it only grows in 𝒪(√dlog{n}), which is the first logarithmic upper bound ever proven on the number of workers n assuming an optimal breakdown point. We also report on an empirical evaluation of Aksel on various classification tasks, which we compare to alternative GARs against state-of-the-art attacks. Aksel is the only GAR reaching top accuracy when there is actually none or few Byzantine workers while maintaining a good defense even under the extreme case (s = f). For simplicity of presentation, we consider a scheme with a single server. However, as we explain in the paper, Aksel can also easily be adapted to multi-server architectures that tolerate the Byzantine behavior of a fraction of the servers.

We consider the problem of communicating reliably in a dynamic network in the presence of up to k Byzantine failures. It was shown that this problem can be solved if and only if the dynamic graph satisfies a certain condition, that we call "RDC condition". In this paper, we present the first self-stabilizing algorithm for reliable communication in this setting - that is: in addition to permanent Byzantine failures, there can also be an arbitrary number of transient failures. We prove the correctness of this algorithm, provided that the RDC condition is "always eventually satisfied".

In distributed computing, many papers try to evaluate the message complexity of a distributed system as a function of the number of nodes n. But what about the cost of building the distributed system itself? Assuming that we want to reliably connect n nodes, how does the total number of nodes of the network evolve with n? Addressing such a question lies at the heart of achieving scalability in cloud computing. In this paper, we give the explicit description of a distributed system of which any two of then nodes, for any n, remain connected (by a path of alive nodes and channels) with probability at least m, despite the very fact that (a) every other node or channel has an independent probability λ of failing, and (b) the number of channels connected to every node is physically bounded by a constant. We show however that if we also require any two of the n nodes to maintain a balanced message throughput with a constant probability, then O (nlog1+εn) additional intermediary nodes are sufficient, where ε > 0 is an arbitrarily small constant.

In reinforcement learning, agents learn by performing actions and observing their outcomes. Sometimes, it is desirable for a human operator to interrupt an agent in order to prevent dangerous situations from happening. Yet, as part of their learning process, agents may link these interruptions, that impact their reward, to specific states and deliberately avoid them. The situation is particularly challenging in a multi-agent context because agents might not only learn from their own past interruptions, but also from those of other agents. Orseau and Armstrong defined safe interruptibility for one learner, but their work does not naturally extend to multi-agent systems. This paper introduces dynamic safe interruptibility, an alternative definition more suited to decentralized learning problems, and studies this notion in two learning frameworks: joint action learners and independent learners. We give realistic sufficient conditions on the learning algorithm to enable dynamic safe interruptibility in the case of joint action learners, yet show that these conditions are not sufficient for independent learners. We show however that if agents can detect interruptions, it is possible to prune the observations to ensure dynamic safe interruptibility even for independent learners.

We consider the following problem: two nodes want to reliably communicate in a dynamic multihop network where some nodes have been compromised, and may have a totally arbitrary and unpredictable behavior. These nodes are called Byzantine. We consider the two cases where cryptography is available and not available. We prove the necessary and sufficient condition (that is, the weakest possible condition) to ensure reliable communication in this context. Our proof is constructive, as we provide Byzantine-resilient algorithms for reliable communication that are optimal with respect to our impossibility results. In a second part, we investigate the impact of our conditions in three case studies: participants interacting in a conference, robots moving on a grid and agents in the subway. Our simulations indicate a clear benefit of using our algorithms for reliable communication in those contexts.

We consider the problem of reliably broadcasting messages in a network where some nodes are likely to fail. We consider the most general failure model: the Byzantine model, where the failing nodes have an arbitrary behavior, and may actively try to destabilize the network. We focus on totally decentralized solutions. Most existing solutions require high network connectivity, and are not adapted to sparsely connected networks. A typical example is the grid, where each node has at most four neighbors. In this paper, we propose a new broadcast protocol adapted to such networks. This protocol is based on interconnected subsets called control zones, that filter the diffusion of false messages. We give a methodology to determine a set of nodes that always communicate reliably, depending on the placement of Byzantine nodes. We then use this methodology to perform an experimental evaluation on square and hexagonal grids, in the presence of randomly distributed Byzantine failures. We show that our protocol significantly improves the communication probability, compared to existing solutions.

We consider the problem of reliably broadcasting messages in a multi-hop network where nodes can fail in some unforeseen manner. We consider the most general failure model: the Byzantine model, where failing nodes may exhibit arbitrary behavior, and actively try to harm the network. Previous approaches dealing with permanent Byzantine failures limit either the number of Byzantine nodes or their density. In dense network, the density criterium is the allowed fraction of Byzantine neighbors per correct node. In sparse networks, density has been defined as the distance between Byzantine nodes. In this context, we first propose a new algorithm for networks whose communication graph can be decomposed into cycles: e.g., a torus can be decomposed into square cycles, a planar graph into polygonal cycles, etc. Our algorithm ensures reliable broadcast when the distance between permanent Byzantine failures is greater than twice the diameter of the largest cycle of the decomposition. Then, we refine the first protocol to make it Byzantine fault tolerant for transient faults (in addition to permanent Byzantine faults). This additional property is guaranteed by means of self-stabilization, which permits to recover from any arbitrary initial state. This arbitrary initial state can be seen as the result of every node being Byzantine faulty for a short period of time (hence the transient qualification). This second protocol thus tolerates permanent (constrained by density) and transient (unconstrained) Byzantine failures. When the maximum degree and cycle diameter are both bounded, both solutions perform in a time that remains proportional to the network diameter.

We consider the problem of reliably broadcasting information in a multi hop asynchronous network that is subject to Byzantine failures. That is, some nodes of the network can exhibit arbitrary (and potentially malicious) behavior. Existing solutions provide deterministic guarantees for broadcasting between all correct nodes, but require that the communication network is highly-connected (typically, 2k+1 connectivity is required, where k is the total number of Byzantine nodes in the network). In this paper, we investigate the possibility of Byzantine tolerant reliable broadcast between most correct nodes in low-connectivity networks (typically, networks with constant connectivity). In more details, we propose a new broadcast protocol that is specifically designed for low-connectivity networks. We provide sufficient conditions for correct nodes using our protocol to reliably communicate despite Byzantine participants. We present experimental results that show that our approach is especially effective in low-connectivity networks when Byzantine nodes are randomly distributed.