This paper discusses hyperparameter optimization within existing autonomous driving algorithms used in autonomous racing competitions. Existing autonomous driving algorithms vary significantly in performance depending on the setting of hyperparameters, making it important to find the right hyperparameter. To address these issues, we propose the Leaky Piece and Conquer Fireworks method, which improves the eficiency of hyperparameter optimization. Experimental results indicate that, on average, the general Fireworks algorithm is approximately 35.5 times faster than Random Search. Furthermore, the Piece and Conquer Fireworks algorithm and the Leaky Piece and Conquer Fireworks algorithm are about 69.9 and 77.9 times faster, respectively.
FGM is an algorithm for autonomous driving by continuously adjusting the steering wheel toward the largest gap. FGM has several hyperparameters, such as the minimum size gap selected, speed in straight lines and curved sections. In this paper, six hyperparameters were used to construct an autonomous driving algorithm.
Fireworks algorithm was used as an algorithm for hyperparameter search. Fireworks algorithm is a sampling-based search algorithm and shows good performance even if the form of the objective function is complex. In addition, Piece and Conquer (PnC) Fireworks algorithm, Leaky Piece and Conquer (Leaky PnC) Fireworks algorithm was proposed and compared with Random Search, general Fireworks algorithm.
The Follow Gap Method (FGM)[
The hyperparameters of the FGM are as follows. PREPROCESS_CONV_SIZE is a hyperparameter that sets how many pieces of data should be converted during pre-processing. BEST_POINT_CONV_SIZE is a hyperparameter representing the CONV value used to find the maximum gap size. MAX_LIDAR_DIST is a hyperparameter indicating how far to look. STRAIGHTTS_SPEED is a hyperparameter indicating a speed in a straight line section. CORNERS_SPEED is a hyperparameter indicating a speed in a curved section.
Fireworks Algorithm[
The Fireworks Algorithm proceeds as follows. 1) Firework Concept: models the solution search process as an object called "firework". Each firework indicates the location of the candidate solutions. 2) Firework Explosion: The key idea of the algorithm is to divide fireworks into several groups, share fireworks among the groups, and improve the solution of discovery. Furthermore, if a better solution is found, more fireworks are dropped at that location, accelerating the process of "exploding" and discovering the solution. 3) Grouping: Fireworks are divided into groups. Each group performs a solution search independently of the other group, and when it finds a new solution, it shares it with the other group. These grouping methods help to explore both global and regional optimal solutions simultaneously. 4) Firework Update: After discovering new solutions, update the location of the firework, and if a better solution is found, drop more ifreworks into that location to improve the solution. 5) Termination condition: The algorithm terminates after meeting the termination condition or after a certain number of repetitions.
In this paper, the Piece and Conquer Fireworks Algorithm and Leaky Piece and Conquer Fireworks Algorithm were proposed based on the existing Fireworks algorithm for explore hyperparameters.
The first algorithm proposed in this paper, Piece and Conquer (PnC) Fireworks Algorithm, means to conquer by piece. A typical Fireworks algorithm finds the optimal hyperparameter using only data that has completed 10 laps if the target lap is 10 laps.
In the PnC Fireworks algorithm, as shown in Figure 1 (Left), the optimal result end points of the lap1 completion piece become the start points of the lap3 completion piece, and the optimal result end points of the lap3 completion piece become the start points of the lap10 completion piece. This is used for navigation of lap10 targeting data fragments of lap1 and data fragments of lap3. As such, the PnC Fireworks algorithm use more data fragments to perform more eficient hyperparameter optimization.
The second algorithm proposed in this paper, Leaky Piece and Conquer (Leaky PnC) Fireworks Algorithm, takes the similar structure with PnC Fireworks Algorithm.
In the Leaky PnC Fireworks algorithm, as shown in Figure 1 (Right), the optimal result end points of the lap1 completion piece are the start points of the lap3 completion piece, and the optimal result end points of the lap3 completion piece are the start points of the lap10 completion piece. This is used for navigation of lap10 targeting data fragments of lap1 and data fragments of lap3. Unlike PnC, Leaky PnC searches for lap3, and even number searches for lap5 when searching for lap3.
In this paper, the driving of the autonomous driving algorithm used a python gym-based
F1TENTH simulator[
In this paper, the number of FGM parameters was set to 6, and the range for each parameter was set as shown in Table 1. The parameters of FGM can also be applied beyond the ranges specified in Table 1, but we have defined the ranges and intervals as shown in Table 1 to enable the determination of relative parameter quality rankings.
The experimental process is as follows: First, we record the performance results for all possible combinations of FGM parameters corresponding to Table 1. In other words, we save 129,600 records of driving performance, given that there are 6 × 4 × 6 × 4 × 15 × 15 = 129,600 possible combinations of FGM parameters. This enables us to establish relative rankings for all 129,600 FGM parameter configurations. Next, based on the recorded performance data, we applied Random search, general Fireworks, PnC Fireworks, and Leaky PnC Fireworks algorithms.
The experiment was performed 30 times for each search algorithm, and the median value of the results executed 30 times was used. This increases the statistical reliability of searchbased algorithm results. Median time(sec) of 30 samples means the time it took to find the optimal parameter. The simulator shows the median value of the results executed when the corresponding algorithm is tested 30 times, and if the simulator accelerates, it can be executed 8 to 10 times faster. Comparison with Random Search (multiple) is a value that indicates how many times faster the corresponding algorithm is compared to Random Search.
Table 2 shows that the Leaky PnC Fireworks algorithm is the best for all three maps: Oschersleben, Silverstone, and Sochi. In the Oschersleben map, the general Fireworks algorithm is 43.9 times faster, the PnC Fire-works algorithm is 90.2 times faster, and the Leaky PnC Fireworks algorithm is 104 times faster than Random Search. In the Silverstone map, the general Fireworks algorithm is 20.1 times faster, the PnC Fireworks algorithm is 42.8 times faster, and the Leaky PnC Fireworks algorithm is 46.1 times faster than Random Search. In the Sochi map, the general Fireworks algorithm is 42.5 times faster, the PnC Fireworks algorithm is 76.7 times faster, and the Leaky PnC Fireworks algorithm is 83.6 times faster than Random Search.
In this paper, the objective was to enhance the performance of FGM through hyperparameter optimization, in other words aiming to improve lap times. Overall, the PnC Fireworks algorithm is about twice as fast as the general Fireworks algorithm, and the Leaky PnC Fireworks algorithm is about 1.1 times faster than the PnC Fireworks algorithm. These experimental results demonstrated that the two types of PnC Firework algorithms proposed in this paper eficiently search for hyperparameters and achieve innovative results in simulations. Furthermore, it is expected to provide important developments in the field of hyperparameter optimization and contribute to the performance improvement of future autonomous driving systems and other complex systems.
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education, Science and Technology (NRF-2021R1G1A1006381).