## 1 Introduction
RL is also used in navigation systems to optimize routes and make decisions based on real-time data. However, there are some potential challenges in applying RL. One challenge is the long time it takes for RL algorithms to converge and learn something meaningful. This restricts the use of RL techniques in real-time learning scenarios. Another challenge is the need for large numbers of data for training RL models. RL algorithms require extensive exploration of the environment to learn optimal policies, which can be time-consuming and resource-intensive. Additionally, RL algorithms may struggle with partial observability and uncertainty in complex environments, which can affect their performance and ability to make accurate decisions [14; 15]. The non-convex problem and coupling constraints, as studied in this paper, pose considerable challenges to finding an optimal solution. In order to address this, we propose a novel MIMO precoding scheme based on RL, which provides a highly effective approach for jointly optimizing both the precoding and detection matrix of the transceiver and receiver, respectively. The proposed RL-based solution offers a number of key advantages over traditional optimization methods, such as greater flexibility and the adoption of the variation of system dynamics. Specifically, the RL framework allows the system to learn from past experiences and optimize the transmission and reception processes in an iterative and adaptive manner. Overall, our findings highlight the potential of RL-based methods for addressing complex optimization problems in FSO communication systems. In this study, a joint precoder and combiner optimization based on RL is proposed. We analyze the bit error rate (BER) performance at different system parameters and compare it with the conventional schemes. The simulation results show that our scheme is able to obtain a lower BER performance compared to the conventional scheme. The main contributions of this research include:  
1. Our proposal involves the introduction of a state-of-the-art NLOS UV MIMO system, which is capable of photon-counting while operating under the influence of Poisson shot noise. To optimize the system performance, we formulate a novel optimization problem that addresses the design of both the precoding and combining matrices, utilizing the well-established minimum mean square error (MMSE) criterion. 2. By employing a methodical approach to deriving and reformulating key aspects of our expected MMSE precoding design, we successfully transform it into an optimization problem that is conducive to efficient computation using the multi-agent deep deterministic policy gradient (MADDPG) algorithm [16]. Through this novel approach, we are able to attain the global optimal precoding matrix and combining matrix. 3. The proposed system exhibits strong robustness. To evaluate the efficacy of our approach in realistic settings, we conducted experiments considering varying degrees of channel state information (CSI). The simulation results indicate our scheme is capable of achieving a BER of less than \(10^{-4}\) even when the CSI is imperfect. The rest of this paper is organized as follows. The related work is presented in Section 2. Section 3 introduces the system model. In Section 4, we present the RL-based precoder and combiner design, in which a specific expression of the optimization problem is given by a detailed mathematical derivation. In Section 5, we propose a method to solve the optimization problem based on the MADDPG algorithm. The simulation results are given in Section 6. Finally, we conclude in Section 7.