Adaptive social learning is a useful tool for studying distributed decision-making problems over graphs. This paper investigates the effect of combination policies on the performance of adaptive social learning strategies. Using large-deviation analysis, it first derives a bound on the steady-state error probability and characterizes the optimal selection for the Perron eigenvectors of the combination policies. It subsequently studies the effect of the combination policy on the transient behavior of the learning strategy by estimating the adaptation time in the low signal-to-noise ratio regime. In the process, it is discovered that, interestingly, the influence of the combination policy on the transient behavior is insignificant, and thus it is more critical to employ policies that enhance the steady-state performance. The theoretical conclusions are illustrated by means of computer simulations.

翻译：自适应社会学习是研究图上分布式决策问题的有效工具。本文研究了组合策略对自适应社会学习策略性能的影响。通过大偏差分析，首先推导了稳态错误概率的界，并刻画了组合策略Perron特征向量的最优选择。随后，通过估计低信噪比情况下的自适应时间，研究了组合策略对学习策略暂态行为的影响。有趣的是，在此过程中发现组合策略对暂态行为的影响并不显著，因此采用增强稳态性能的策略更为关键。理论结论通过计算机仿真加以说明。