A Correction of Pseudo Log-Likelihood Method
This addresses a technical flaw in algorithms used for bandit problems, which is incremental but important for reliability in applications like social networks and causal inference.
The paper identifies that the pseudo log-likelihood function in prior MLE methods for contextual and causal bandits may be unbounded, leading to ill-defined algorithms, and provides a correction with a counterexample and solution.
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}.