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}.

我们给出一个反例来说明最大伪对数似然估计失败，并提供了解决方案来纠正文章中提出的算法。

一种伪似然方法的修正

A Correction of Pseudo Log-Likelihood Method

In this paper, we propose a novel approach for solving linear numeric
planning problems, called Symbolic Pattern Planning. Given a planning problem
$\Pi$, a bound $n$ and a pattern -- defined as an arbitrary sequence of actions
-- we encode the problem of finding a plan for $\Pi$ with bound $n$ as a
formula with fewer variables and/or clauses than the state-of-the-art rolled-up
and relaxed-relaxed-$\exists$ encodings. More importantly, we prove that for
any given bound, it is never the case that the latter two encodings allow
finding a valid plan while ours does not. On the experimental side, we consider
6 other planning systems -- including the ones which participated in this
year's International Planning Competition (IPC) -- and we show that our planner
Patty has remarkably good comparative performances on this year's IPC problems.

提出了一种名为符号模式规划的解决线性数值规划问题的新方法，通过将规划问题编码为使用较少变量和 / 或子句的公式，以寻找给定边界下与现有编码方法相比无法找到有效计划的计划。实验证明，我们的规划器在国际规划竞赛（IPC）今年的问题上具有显著良好的比较性能。