Distributed Gaussian Process for Multi-agent Systems

P. Zhai, R.T. Rajan

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Distributed multi-agent systems (MAS) offer higher robustness and scalability compared to single-agent systems employing centralized solutions. The challenge of learning unknown environmental phenomenons can be regarded as learning a hidden function, which can be modeled through non-parametric methods e.g., Gaussian Processes (GP). Our main challenge is to develop a distributed non-parametric model e.g., GP for environment monitoring. In this work, we specifically focus on developing fully-distributed algorithm for GP hyperparameter optimization. An example of hyperparameter set is θ = {sf , l1, l2} for a squared exponential kernel, where signal variance sf indicates the range of function, and the characteristic lengths l1, l2 indicate the smoothness. We also develop an asynchronous version to deal with heterogeneous processing time of agents. Assuming that local datasets at agents are independent with each other, we approximate hyperparameter optimization by maximizing the sum of local Likelihoods. By further defining a unique θ across the network, the problem can be regarded as a distributed consensus problem. Alternating direction method of multipliers (ADMM) with proximal θ update have been applied by Xie et al. [1], which still requires a center computing unit for auxiliary variable update. We propose a fully-distributed algorithm with centralized update replaced by local consensus. In each iteration, an agent collects auxiliary variables from neighbor agents, and use their average in new iteration. Asynchronous behavior is introduced by allowing fast agents to start new iterations without collecting update from slowest agents. Our proposed algorithm allows agents in the network to perform faster iterations and thus saving time. We perform simulations with artificially generated 2D GP field under pre-defined hyperparameter setting. Noisy measurements are randomly allocated to agents for distributed hyperparameter optimization. Simulation results show that the optimal hyperparameters at agents converge to the expected values...
Original languageEnglish
Title of host publication42nd WIC Symposium on Information Theory and Signal Processing in the Benelux (SITB 2022)
EditorsJérôme Louveaux, François Quitin
Number of pages1
Publication statusPublished - 2022
Event42nd WIC Symposium on Information Theory and Signal Processing in the Benelux - Louvain la Neuve, Belgium
Duration: 1 Jun 20222 Jun 2022
Conference number: 42


Conference42nd WIC Symposium on Information Theory and Signal Processing in the Benelux
Abbreviated titleSITB 2022
CityLouvain la Neuve


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