## 1 Introduction
### Related Works  
To the best of the authors' knowledge, the existing works on cooperative relaying FSO systems can be divided into two categories, which are performance analysis and optimization algorithms. In the first category, the system indexes are analyzed and derived, including bit error rate (BER) or symbol error rate (SER) [6, 7], outage probability (OP) [8], channel capacity [9, 10].  
In the second category, studies on optimization algorithms can be viewed as an extension of the first category, where the abovementioned system indexes are either maximized or minimized by optimizing parameters including power allocation [11, 12], relay placement [13, 14] and relay selection [5, 15, 16, 17]. Since this paper focuses on the relay selection issue, the related papers are analyzed. It should be mentioned that either channel state information (CSI) or partial CSI is assumed to be a priori information during the optimization algorithms, which can be estimated or obtained due to the quasi-static channel.  
Ref. [5] has discovered that the best relay can be selected to minimize the BER, according to the channel conditions in source to the relay (S-R) link, the relay to destination (R-D) link and the source to destination (S-D) link. A comprehensive comparison was carried out between three cases, i.e., proactive relay, reactive relays and direct link. In Ref. [15], a relay selection algorithm was proposed as a solution to mitigate channel fading, where two cooperative modes enhanced network capacity, i.e., the intra-relay set and inter-relay set cooperative modes. A link scheduling algorithm was further proposed to improve bandwidth utilization and reduce the occupancy rate of the transceivers by better utilizing the idle FSO links. Ref. [16] investigated a new distributed relay selection algorithm where each relay was allowed to transmit only when its SNR was higher than a given threshold. The threshold was achieved with the gradient algorithm to guarantee the lowest SER. Ref. [17] proposed an improvement to the existing S-R protocol by relay selection, which was better tailored to realistic systems deploying finite-size buffers. It was shown that the proposed scheme could enhance the diversity order without the need of implementing buffers of infinite size that cause infinite delays. The closed-form asymptotic expressions of OP for two-relay networks were also derived.  
With the development and application of machine learning (ML), ML-based relay selection algorithms have become a hot topic. In Ref. [18], a supervised ML-enabling scheme was proposed in order to enable a combined relay selection to avoid high computing latency. In Ref. [19], a model-free primal-dual deep learning algorithm was designed to increase the transmission capacity, and the policy gradient method was applied to the primal update in order to estimate the necessary gradient information. [PERSON]. [20] modeled the CSI in the process of cooperative communications with relay selection as a Markov decision process. A deep \(Q\)-network (DQN) was employed to choose the optimal relay from a plurality of relay nodes, where both the outage probability and mutual information were the objective function.  
It should be noted that the difference between Refs. [18; 19; 20] is that Ref. [18] employed a supervised learning structure, while Refs. [19; 20] utilized a reinforcement learning (RL) structure. The former learns from a labeled dataset, which provides answers that the algorithm can use to evaluate its accuracy on the training data. The latter has the ability of learning strategies to maximize rewards during interactions with the environment. Owing to the fact that the RL approach is committed to maximizing the cumulative reward, it has irreplaceable advantages in dynamic optimization problems.