Distributed decision-making over networks involves multiple agents collaborating to achieve a common goal. In the social learning process, where agents aim at inferring an unknown state from a stream of local observations, the probability of error in their decisions converges to zero exponentially in the asymptotic regime. The rate of this convergence, known as the error exponent, is influenced by the combination policy employed by the network. This work addresses the challenge of identifying the optimal combination policies to maximize the error exponent. We establish an upper bound on the achievable error exponents by the social learning rule and provide the conditions for the combination policy to reach this upper bound. By implementing the optimized policy, we enhance the error exponent, leading to improved accuracy and efficiency in the distributed decision-making process.

This paper studies the probability of error associated with the social machine learning framework, which involves an independent training phase followed by a cooperative decision-making phase over a graph. This framework addresses the problem of classifying a stream of unlabeled data in a distributed manner. In this work, we examine the classification task with limited observations during the decision-making phase, which requires a non-asymptotic performance analysis. We establish a condition for consistent training and derive an upper bound on the probability of error for classification. The results clarify the dependence on the statistical properties of the data and the combination policy used over the graph. They also establish the exponential decay of the probability of error with respect to the number of unlabeled samples.

Traditional social learning frameworks consider environments with a homogeneous state where each agent receives observations conditioned on the same hypothesis. In this work, we study the distributed hypothesis testing problem for graphs with a community structure, assuming that each cluster receives data conditioned on some different true state. This situation arises in many scenarios, such as when sensors are spatially distributed, or when individuals in a social network have differing views or opinions. We show that the adaptive social learning strategy is not only superior in nonstationary environments, but also allows each cluster to discover its own truth.

We consider a collaborative decision-making frame-work where heterogeneous agents receive streaming and partially informative observations. We consider two asynchronous scenarios that differ based on the agents' participation patterns and the fusion center's policies. By using hypothetical interventions on individual agents to conduct credit assignment, we attribute causal impact scores to each agent for the joint decision. By further employing these scores in a guided theoretical analysis, we compare the fusion center's two policies by evaluating their vulnerability to adversarial attacks, robustness against moderate deviations, and fairness.

Non-Bayesian social learning is a framework for distributed hypothesis testing aimed at learning the true state of the environment. Traditionally, the agents are assumed to receive observations conditioned on the same true state, although it is also possible to examine the case of heterogeneous models across the graph. One important special case is when heterogeneity is caused by the presence of malicious agents whose goal is to move the agents toward a wrong hypothesis. In this letter, we propose an algorithm that allows discovering the true state of every individual agent based on thesequenceof their beliefs. In so doing, the methodology is also able to locate malicious behavior.

Social learning algorithms provide a model for the formation and propagation of opinions over social networks. However, most studies focus on the case in which agents share their information synchronously over regular intervals. In this work, we analyze belief convergence and steady-state learning performance for both traditional and adaptive formulations of social learning under asynchronous behavior by the agents, where some of the agents may decide to abstain from sharing any information with the network at some time instants. We also show how to recover the underlying graph topology from observations of the asynchronous network behavior.

This paper studies the non-asymptotic classification performance of the social machine learning strategy. This strategy involves an independent training phase followed by a cooperative inference phase to classify a growing number of samples. By considering instead a finite number of samples, we provide an upper bound for the probability of misclassification. This bound helps characterize the generalization ability of the social machine learning strategy, in terms of the statistical properties of the classification problem and the combination policy among the distributed classifiers. The analysis establishes the exponential decay of the probability of error with the number of samples when the training phase is consistent.

The adaptive social learning paradigm deals with the opinion formation process by a network of communicating agents in a dynamic environment. In this study, we show that a sequence of publicly exchanged beliefs allows users to discover rich information about the underlying model. In particular, it is shown that it is possible (i) to identify the influence of each individual agent to the objective of truth learning, (ii) to discover how well-informed each agent is, and (iii) to learn the underlying network topology.

We consider a distributed binary hypothesis testing setup where multiple nodes send quantized information to a central processor, which is oblivious to the nodes’ statistics. We study the regime where the missed detection (type-II error) probability decays exponentially and the false alarm (type-I error) probability vanishes. For memoryless quantization, we characterize a tradeoff curve that yields a lower bound for the feasible region of type-II error exponents and the average number of bits sent under the null hypothesis. Moreover, we show that the tradeoff curve is approached at high rates with lattice quantization.

We study a social learning scheme where at every time instant, each agent chooses to receive information from one of its neighbors at random. We show that under this sparser communication scheme, the agents learn the truth eventually and the asymptotic convergence rate remains the same as the standard algorithms, which use more communication resources. We also derive large deviation estimates of the log-belief ratios for a special case where each agent replaces its belief with that of the chosen neighbor.