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This paper examines the close interplay between cooperation and adaptation for distributed detection schemes over fully decentralized networks. The combined attributes of cooperation and adaptation are necessary to enable networks of detectors to continually learn from streaming data and to continually track drifts in the state of nature when deciding in favor of one hypothesis or another. The results in this paper establish a fundamental scaling law for the steady-state probabilities of miss detection and false alarm in the slow adaptation regime, when the agents interact with each other according to distributed strategies that employ small constant step-sizes. The latter are critical to enable continuous adaptation and learning. This paper establishes three key results. First, it is shown that the output of the collaborative process at each agent has a steady-state distribution. Second, it is shown that this distribution is asymptotically Gaussian in the slow adaptation regime of small step-sizes. Third, by carrying out a detailed large deviations analysis, closed-form expressions are derived for the decaying rates of the false-alarm and miss-detection probabilities. Interesting insights are gained from these expressions. In particular, it is verified that as the step-size μ decreases, the error probabilities are driven to zero exponentially fast as functions of 1μ, and that the exponents governing the decay increase linearly in the number of agents. It is also verified that the scaling laws governing the errors of detection and the errors of estimation over the network behave very differently, with the former having exponential decay proportional to 1μ, while the latter scales linearly with decay proportional to μ. Moreover, and interestingly, it is shown that the cooperative strategy allows each agent to reach the same detection performance, in terms of detection error exponents, of a centralized stochastic-gradient solution. The results of this paper are illustrated by applying them to canonical distributed detection problems.
Jian Wang, Lesya Shchutska, Olivier Schneider, Yiming Li, Yi Zhang, Aurelio Bay, Guido Haefeli, Christoph Frei, Frédéric Blanc, Tatsuya Nakada, Michel De Cian, François Fleuret, Elena Graverini, Renato Quagliani, Federico Betti, Andrea Merli, Aravindhan Venkateswaran, Vitalii Lisovskyi, Katharina Müller, Sebastian Schulte, Veronica Sølund Kirsebom, Elisabeth Maria Niel, Mingkui Wang, Zhirui Xu, Chao Wang, Lei Zhang, Ho Ling Li, Mark Tobin, Minh Tâm Tran, Niko Neufeld, Matthew Needham, Marc-Olivier Bettler, Maurizio Martinelli, Vladislav Balagura, Donal Patrick Hill, Liang Sun, Pietro Marino, Mirco Dorigo, Xiaoxue Han, Liupan An, Federico Leo Redi, Plamen Hristov Hopchev, Maxime Schubiger, Hang Yin, Guido Andreassi, Violaine Bellée, Preema Rennee Pais, Pavol Stefko, Tara Nanut, Maria Elena Stramaglia, Yao Zhou, Tommaso Colombo, Vladimir Macko, Guillaume Max Pietrzyk, Evgenii Shmanin, Simone Meloni, Xiaoqing Zhou, Surapat Ek-In, Carina Trippl, Sara Celani, Marco Guarise, Serhii Cholak, Dipanwita Dutta, Zheng Wang, Yong Yang, Yi Wang, Hao Liu, Hans Dijkstra, Gerhard Raven, Peter Clarke, Frédéric Teubert, Giovanni Carboni, Victor Coco, Shuai Liu, Adam Davis, Paolo Durante, Yu Zheng, Renjie Wang, Anton Petrov, Maxim Borisyak, Feng Jiang, Chen Chen, Zhipeng Tang, Xuan Li, Alexey Boldyrev, Almagul Kondybayeva, Hossein Afsharnia
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Olivier Schneider, Yiming Li, Mingkui Wang, Chao Wang, Tagir Aushev, Sun Hee Kim, Donghyun Kim, Lei Li