A Correction of Pseudo Log-Likelihood Method
Shi Feng Nuoya Xiong Zhijie Zhang Wei Chen
Pseudo log-likelihood is a type of maximum likelihood estimation (MLE) method
used in various fields including contextual bandits, influence maximization of
social networks, and causal bandits. However, in previous literature
\citep{li2017provably, zhang2022online, xiong2022combinatorial,
feng2023combinatorial1, feng2023combinatorial2}, the log-likelihood function
may not be bounded, which may result in the algorithm they proposed not
well-defined. In this paper, we give a counterexample that the maximum pseudo
log-likelihood estimation fails and then provide a solution to correct the
algorithms in \citep{li2017provably, zhang2022online, xiong2022combinatorial,
feng2023combinatorial1, feng2023combinatorial2}.