A New Approach for Distributed Hypothesis Testing with Extensions to Byzantine-Resilience

Abstract

We study a setting where a group of agents, each receiving partially informative private signals, seek to collaboratively learn the true underlying state of the world (from a finite set of hypotheses) that generates their joint observation profiles. To solve this problem, we propose a distributed learning rule that differs fundamentally from existing approaches, in that it does not employ any form of "belief-averaging". Instead, agents update their beliefs based on a min-rule. Under standard assumptions on the observation model and the network structure, we establish that each agent learns the truth asymptotically almost surely. As our main contribution, we prove that with probability 1, each false hypothesis is ruled out by every agent exponentially fast at a network-independent rate that is strictly larger than existing rates. We then develop a computationally-efficient variant of our learning rule that is provably resilient to agents who do not behave as expected (as represented by a Byzantine adversary model) and deliberately try to spread misinformation.

A Communication-Efficient Algorithm for Exponentially Fast Non-Bayesian Learning in Networks

“…In this context, our objectives in this paper are to develop an understanding of (i) the amount of leeway that the above problem affords in terms of sparsifying inter-agent communications without compromising the objective of learning the truth, and (ii) the trade-offs between sparse communication and the rate of learning. To this end, we recall the following definition from [11] that will prove useful in our subsequent developments. Definition 1.…”

“…Our analysis subsumes the special case when communication occurs at every time-step, i.e., when a = 1, which corresponds to the scenario studied in our previous work [11]. While the general approach in [11] was shown to be robust to worst-case adversarial attack models, a convergence-rate analysis of the same was missing. A significant contribution of this paper is to fill this gap by establishing that when a = 1, the asymptotic learning rates resulting from our proposed algorithm are network-structure independent, and a strict improvement over the rates provided by existing algorithms in the literature.…”

“…We develop and analyze a simple time-triggered learning rule that builds on our recent work on distributed hypothesis testing [11]. Specifically, the data-aggregation step of our algorithm involves a min-protocol as opposed to the consensusbased averaging schemes intrinsic to existing linear [6], [7] and log-linear [8]- [10] learning rules.…”

“…We use the lower bounds derived in (4), (5) as a proxy when referring to the corresponding asymptotic learning rates 4. Recently, in[16], we showed that this result continues to hold even if the underlying graph changes with time, but satisfies a mild joint-strong connectivity condition.…”

Event-Triggered Distributed Inference

“…The problem described above arises in a variety of contexts ranging from detection and object recognition using autonomous robots, to statistical inference and learning over multiple processors, to sequential decision-making in social networks. As such, the distributed inference/hypothesis testing problem enjoys a rich history [1][2][3][4][5][6][7][8], where a variety of techniques have been proposed over the years, with more recent efforts directed towards improving the convergence rate. These techniques can be broadly classified in terms of the mechanism used to aggregate data: while consensus-based linear [1,2] and log-linear [3][4][5][6] rules have been extensively studied, [7] and [8] propose a min-protocol that leads to the best known (asymptotic) learning rate for this problem.…”