## 2 Related Works  
In this section, we briefly explain some of the MAB algorithms for the transmission rate control in CSMA/CA wireless networks. In [20], the authors introduced the G-ORS algorithm that uses the Kullback-Leibler (KL) divergence measure and graphical unimodality to select the best MCS level for the data transmission. Because each transmission of the data packet results in an outcome of success or failure, it is modeled as a Bernoulli trial, and the KL divergence \(d\) between the two Bernoulli distributions with means of \(p\) and \(q\) can be measured as follows:  
\[d(p,q)=p\log\frac{p}{q}+(1-p)\log\frac{1-p}{1-q}. \tag{3}\]  
If the graphical unimodality is not used, the algorithm becomes a variant of the KL-UCB algorithm. In [21], the authors proposed the MTS algorithm to control the data transmission rates of wireless nodes based on Thompson sampling. Thompson sampling computes the success probability distribution of each arm \(i\) of a given MAB problem using a beta distribution of which the probability density function \(f\) is defined using parameters \(\alpha_{i},\beta_{i}>0\) as follows:\[f(x;\alpha_{i},\beta_{i})=\frac{x^{\alpha_{i}-1}(1-x)^{\beta_{i}-1}}{B(\alpha_{i},\beta_{i})},x\in[0,1]. \tag{4}\]  
Here, \(B(\alpha_{i},\beta_{i})\) is the beta function, which is defined as follows:  
\[B(\alpha,\beta)=\frac{\Gamma(\alpha)\Gamma(\beta)}{\Gamma(\alpha+\beta)}, \tag{5}\]  
where \(\Gamma(\cdot)\) is the gamma function. The two parameters \(\alpha_{i}\) and \(\beta_{i}\) are used to record the histories of the successes and failures of the transmissions from each MCS level \(i\). Whenever a transmission with an MCS level \(i\) is successful, \(\alpha_{i}\) is increased by one; otherwise, \(\beta_{i}\) is increased by one. In [22], the authors proposed the CoTS algorithm to improve the MTS algorithm by incorporating a graphical unimodality to reduce the size of the search space. However, finding an adequate graphical unimodality graph for wireless networks with many MCS levels (including multiple streams) in dynamically changing wireless networks is another challenge that needs to be addressed. In [26], the authors proposed to use the received signal strength indicator (RSSI) for a Thompson sampling-based MAB algorithm. It reduces the search space by considering only the data rates suitable for the measured RSSI range. In [27], the authors proposed to consider only a compact set of optimal data rates [28] decided from the configuration of a given wireless network. In addition, it also uses a threshold-based approach to further reduce the search space by using the transmission success histories of data rates for a Thompson sampling-based MAB algorithm. In [29], the authors proposed a two-stage approach for a Thompson sampling-based MAB algorithm. In the first stage, a group of data rates that could include the optimal MCS is identified, and then, in the second stage, the optimal MCS is searched only in the reduced search space. However, in this paper, we do not consider these search space reduction techniques to focus on the effect of the proposed use of the logarithmic transmission rates. In contrast to most classical MAB problems, the main characteristic of wireless communication networks is that they are inherently non-stationary. The status of a wireless communication channel can change quickly, particularly when wireless nodes are moving and/or when multiple wireless nodes interfere each other. To solve non-stationary MAB problems, in [30], the authors proposed discounted-UCB (D-UCB), which discounts the amount of rewards and number of selection times of arms with a discount parameter \(\gamma\in(0,1)\). In [31], the authors proposed sliding-window UCB (SW-UCB) that uses a sliding window \(\tau\) and counts only the last \(\tau\) events in addition to the discounting when it computes the empirical averages of the rewards of the arms.