## 1 Introduction  
Benefitting from high power, excellent beam quality, and high polarization extinction ratio (PER), high-power linearly polarized fiber lasers have gained extensive attention for their wide applications in industrial manufacturing and scientific research, such as coherent beam combination (CBC) [1, 2, 3], nonlinear frequency conversion (NLFC) [4, 5], and gravitational wave detection [6]. CBC of high-power linearly polarized fiber lasers is an ideal technology to realize 10 kW-level lasers. In 2020, [PERSON] et al. [3] realized an ultrafast laser delivering 10.4 kW average power based on a CBC system of twelve ytterbium-doped kW-level linearly polarized fiber lasers. NLFC based on high-power linearly polarized fiber lasers in near-infrared band is the primary means of accessing high-power fiber lasers in other bands such as blue-green laser [4] and ultra-violet (UV) laser [5]. The 1 kW linearly polarized single-frequency fiber lasers are considered to be promising laser sources for the next-generation gravitational wave detectors (GWDs), as the sensitivity of GWDs can be increased by increasing the power of laser sources, as well as the degree of polarization [6]. Polarization-maintaining (PM) fibers are usually employed in fiber amplifiers for the generation of linearly polarized fiber lasers. However, compared with non-PM configurations, PM fibers have lower thresholds of nonlinear effects [7] and transverse mode instability (TMI) [8], and in the process of power amplification, the PER of the PM fiber laser has an overall tendency to deteriorate for thermally induced polarization coupling [9], as a result of which the power scaling of PM fiber amplifiers is more difficult. Active polarization control of non-PM fiber lasers is an adaptive feedback control scheme combined with intelligent algorithms. The concept of active polarization control was first proposed in optical communication [10], and currently it has been fully developed in both polarization controllers and control algorithms [11; 12]. In recent years, the active polarization control of non-PM fiber lasers has shown great potential in high-power linearly polarized fiber lasers. In 2010, [PERSON] et al. [13] demonstrated a 1.4 kW linearly polarized laser with active polarization control in a non-PM fiber amplifier, and applied it in a CBC system. In 2018, [PERSON] et al. [14] reported a fiber amplifier with the PER of 16-17 dB and power up to 2.5 kW in non-PM fiber configuration using the active polarization control. Algorithms are crucial in the active polarization control system, which affect the convergence speed and PER. Various algorithms have been studied in polarization control. In 2008, [PERSON] et al. [15] introduced the simulated annealing (SA) algorithm to polarization control, and realized the continuous conversion of the state of polarization (SOP) and the stable SOP output. In 2009, [PERSON] et al. [16] utilized the fast localization algorithm (FLA) as well as the gradient search algorithm to control the polarization efficiently. In 2013, [PERSON] et al. [17] reported a novel algorithm based on FLA to accelerate the control speed and improve the accuracy. In 2020, [PERSON] et al. [18] proposed a mixed genetic algorithm (GA) and SA algorithm for polarization control, and analyzed the convergence effect theoretically. The above algorithms have not been fully optimized, and show low control bandwidth, low convergence speed, and weak robustness [19]. The stochastic parallel gradient descent (SPGD) algorithm is an optimized gradient descent algorithm with high convergence speed and accuracy, and is preferred in the active polarization control of the high-power fiber laser system. In 2017, [PERSON] et al. [20] and [PERSON] et al. [21] realized linearly polarized output power of 1 kW and 1.43 kW by active polarization control based on the SPGD algorithm, with a PER of 14.5 dB and 11.1 dB, respectively. However, the learning rate, or gain factor, of the SPGD algorithm is fixed.