Automatic Hyper-Parameter Tuning for Black-box LiDAR Odometry
Kenji Koide1 , Masashi Yokozuka1 , Shuji Oishi1 , and Atsuhiko Banno1

Abstract— LiDAR odometry algorithms are complex andinvolve a number of hyper-parameters. The choice of hyperparameters can substantively affect the performance of odometry estimation, and it is necessary to carefully fine-tune thehyper-parameters depending on the sensor, environment, andalgorithm to achieve the best estimation results. While odometry
estimation algorithms are often tuned manually, this is timeconsuming and may also result in a sub-optimal parameter
set. This paper presents an automatic hyper-parameter tuning
approach for LiDAR odometry estimation. By taking advantageof the sequential model-based optimization (SMBO) approach,
we automatically optimize the hyper-parameter set of a blackbox odometry estimation algorithm without detailed knowledgeof the algorithm. In addition, a LiDAR data augmentation
approach is also proposed to prevent overfitting. Through evaluation, we show that the combination of SMBO-based parameter
exploration and data augmentation enables us to efficiently androbustly optimize the hyper-parameter set for several different
odometry estimation algorithms. We also demonstrate that the
optimized parameter set exhibits superior performance withrespect to KITTI dataset and in a real use scenario.

I. INTRODUCTION
LiDAR odometry estimation and SLAM are crucial formany functions in intelligent autonomous systems, such as
localization, mapping, and navigation. A number of odometry estimation and SLAM algorithms have been proposed[1], [2], [3], and the SLAM community has benefited
from these advances. Those algorithms are, however, often
surprisingly complex and involve many hyper-parameters.
Their performance can depend substantively on the choiceof hyper-parameters. It is necessary to carefully fine-tune
the hyper-parameters depending on the sensor, environment,
and algorithm to achieve the best estimation results. Without
appropriate hyper-parameter selection, their accuracy candrastically deteriorate when we try to apply them in a newenvironment or we use a new sensor model [4].
Despite their importance, hyper-parameters tend to be
manually calibrated in odometry estimation algorithms. Manual tuning through trial and error, however, requires alarge amount of human effort to maximize the estimation
performance for large datasets. Furthermore, it requires athorough mechanistic understanding of the algorithm to be
tuned; insufficient understanding and cursory tuning can leadto a parameter set that results in sub-optimal performance.
Although a few studies have proposed automatic hyperparameter tuning methods for LiDAR and visual odometry
estimation methods [5], [6], [7], they are all dedicated to
specific algorithms or environments.
1 All the authors are with the Department of Information Technology
and Human Factors, the National Institute of Advanced Industrial Science and Technology, Umezono 1-1-1, Tsukuba, 3050061, Ibaraki, Japan,

k.koide@aist.go.jp

In the context of machine learning, sequential model-based
optimization (SMBO), which optimizes a set of parameters
without detailed modeling of the behavior of the system tobe tuned, has attracted attention and has been applied toautomatic hyper-parameter tuning [8], [9], [10]. The SMBO
approach explores the parameter space through an automaticparameter-selection-and-trial loop with a surrogate functionof an expensive evaluation function. It has been shown that
this approach can efficiently optimize the hyper-parametersof models that have high evaluation cost and involve many
hyper-parameters, such as deep neural networks [11].
The purpose of this paper is to put forward an improved
approach for hyper-parameter tuning that can be applied toall odometry estimation algorithms. We first propose an automatic hyper-parameter optimization method for odometry
estimation algorithms based on the SMBO approach. The
proposed approach does not exploit detailed knowledge ofthe algorithm to be tuned but instead treats the system asa black-box. We also propose a data augmentation methodfor LiDAR sequences to prevent overfitting of the optimized
hyper-parameters and find a hyper-parameter set that isrobust to environment changes. Through evaluation, we showthat the proposed hyper-parameter optimization approachconsiderably improves the performance of LiDAR odometry
algorithms for a publicly available dataset, KITTI [12].
The contribution of this paper is three-fold. First, we
propose an automatic and general hyper-parameter tuning
approach for odometry estimation algorithms. Second, adata augmentation method to prevent the parameter tuning
process from overfitting is proposed. Third, we have released
the code, as open source, to automate the odometry tuning
process 1 .
II. RELATED WORKSLAM and odometry estimation algorithms are inherently
very complex and use various hyper-parameters (e.g., point
cloud resolution, feature matching threshold, and keyframeinterval). It is known that some popular SLAM frameworks
like Google cartographer require fine-tuning many hyperparameters that affect each other to achieve the best results[13]. This tuning process requires a thorough understandingof its inner behavior and a large amount of trial and error.
Despite the importance of hyper-parameter tuning, only
a few studies have considered automatic tuning of SLAMrelated algorithms. Nobili et al. proposed a tuning method
for ICP algorithms to improve the LiDAR localization accuracy for a humanoid robot [6]. This method automatically
1 https://github.com/SMRT-AIST/automatic_tuning/tree/developtimizes outlier removal based on the estimated overlap
rate between point clouds. Permeleau et al. performed an
exhaustive parameter-by-parameter exploration to investigate
how changes in parameter values affect ICP registration
results [5]. Zheng optimized the hyper-parameters for avisual SLAM algorithm (e.g., the number of features, patch
size, and edge threshold) using a grid search [7]. There
are also several case studies that propose techniques totune SLAM-related algorithms for specific contexts [14].
However, the above-described methods are all dedicatedto specific sensors and task configurations. We argue thenecessity of an automatic and general hyper-parameter tuning
process that is potentially beneficial to every SLAM-related
algorithm.
In the context of machine learning, hyper-parameter tuning
has been recognized as an important step to maximize theperformance of learning models [15]. Machine learning algorithms commonly use a certain number of hyper-parameters
to control their behavior, and their performance can substantively depend on the choice of the hyper-parameter set.
In classic algorithms that use only a few parameters (e.g.,
RBF SVM parameter selection [16]), parameter tuning isoften undertaken by an exhaustive grid search or a random
search [17]. However, when the number of parameters islarge or computation of the evaluation function is expensive,
it is difficult to obtain a sufficient solution with these naive
methods in a reasonable time. To efficiently optimize many
parameters in an expensive model, the SMBO approach has
been widely used in recent years [18], [19]. This approach
uses a light surrogate function to approximate the costly
evaluation function and effectively explore the parameter
space with the model response prediction calculated with thesurrogate function. Many SMBO algorithms have been proposed, and they are popular in the machine learning domain
because automatic parameter tuning confers clear advantages
over manual alternatives [8], [9], [10]. In particular, deeplearning-based methods, which require tuning many hyperparameters for a very costly training model, have benefited
from SMBO-based automated hyper-parameter tuning [11].
In this work, we apply the SMBO approach to hyperparameter tuning of odometry estimation algorithms. Although we focus on LiDAR odometry estimation, the proposed approach is general and can also be applied to visual
odometry algorithms.
III. METHODOLOGY
A. Problem Definition
Let us assume that we have an odometry estimation
function F that takes D as input data sequences and x
as a set of hyper-parameters, and then outputs estimatedsensor trajectories T ; T = F(D, x). Our goal is to findthe parameter set x̃ that minimizes the evaluation function
G for the estimated trajectories:x̃ = arg min G (F(D, x)) .

(1)xWe use the notation G(x) = G (F (X , x)) in the rest of thispaper for simplicity.

Algorithm 1 Sequential Model-Based Optimization [18]1: H ← []2: for i ∈ [1, · · · , N ] do3:x∗ ← arg max A (S (x, Mi−1 ))x

Evaluate G (x∗ )H ← H ∪ (x∗ , G(x∗ ))6:
Fit Mi to H
return H
4:
5:

The most naive and common ways to find x̃ are an
exhaustive grid search and a random search [17]. They arestraightforward to implement and are often used when thenumber of parameters is small. As the number of parameters
increases, however, the required number of evaluations grows
exponentially. The evaluation of a parameter set G(x) is quite
expensive in LiDAR odometry estimation, and these naive
methods cannot sufficiently explore the parameter space andfind a good parameter set in a reasonable time.
B. Sequential Model-Based Optimization
SMBO [18] is a technique to efficiently explore theparameter space with fewer evaluations. SMBO uses a lightweight surrogate function S(x, Mi ) that approximates thecostly evaluation function G (x) based on a model Mi fitted
to the evaluation history H. It then explores the parameter
space by sampling the parameter set x∗ that maximizes anacquisition criterion A (see Algorithm 1).
The expected improvement (EI) [20] has been widely used
as an acquisition criterion. EI is the expectation that y =G(x) negatively exceeds a threshold y ∗ :Z ∞EIy∗ :=max (y ∗ − y, 0) pMi (y|x)dy.
(2)−∞

A parameter set sample x∗ that maximizes EIy∗ can befound using the tree-structured Parzen estimator (TPE); thisis popular in automatic hyper-parameter tuning frameworks[9], [10]. TPE models p(x|y) instead of directly modelingp(y|x). It defines p(x|y) using two density functions l(x)and g(x):(l(x) if y < y ∗p(x|y) =(3)
g(x) otherwise,
where l(x) is composed of the evaluation results whereG(x) < y ∗ , and g(x) is composed of the other evaluation
results. The quantile γ for the evaluation results such thatp(y < y ∗ ) = γ is chosen as y ∗ , and Kernel density
estimation is used to model l(x) and g(x).
By substituting Eq. (3) into Eq. (2), we obtain the following equation (see [18] for the detailed derivation):
−1

g(x)
(1 − γ).
(4)
EIy∗ (x) ∝ γ +l(x)Eq. 4 indicates that we can obtain x∗ by finding x thatmaximizes g(x)/l(x). Sampling-based techniques are used
to find x∗ in the parameter space.

TABLE I: Averaged translational RTEs [%] for KITTI
MethodLeGO-LOAM
hdl graph slam
SuMa

ConfigBaseline
Tuned
Baseline
Tuned
Baseline
Tuned

00
1.77
3.01
1.78
1.36
1.12
1.06

01
39.9
3.76
17.3
6.88
13.2
10.5

Training set
02
03
04
05
Avg.*
06
07
6.78
1.50
1.02
1.20
9.90
0.99
1.11
2.39
2.09
1.01
1.65
2.62 (-7.28)
1.30
1.45
2.45
1.62
2.34
1.38
4.60
1.00
0.84
1.58
1.06
1.18
0.93
2.29 (-2.31)
0.83
1.47
1.52
1.55
0.53
1.44
3.37
0.68
0.77
1.40
1.25
0.60
1.13
2.80 (-0.57)
0.66
0.71
* Values in parentheses are with respect to the baseline.

08
1.75
2.41
1.73
1.64
1.72
1.86

Test set
09
1.47
1.93
2.01
1.38
1.36
0.98

10
1.92
2.25
2.54
3.08
2.21
1.97

Avg. *
1.53
2.03 (+0.50)
1.69
1.61 (-0.07)
1.45
1.39 (-0.06)

TABLE II: Averaged translational RTEs [%] without KITTI 01 and 02
MethodLeGO-LOAM

hdl graph slam

SuMa

Configuration
Baseline
Tuned
Tuned w. D.A.
Baseline
Tuned
Tuned w. D.A.
Baseline
Tuned
Tuned w. D.A.

Training set
00
03
04
05
Avg. *
06
07
1.77
1.50 1.02
1.20
1.52
0.99
1.11
1.60
1.51 1.14
0.98
1.37 (-0.15)
1.03
1.07
1.80
1.52 1.03
0.99
1.47 (-0.05)
0.99
1.07
1.78
1.62 2.34
1.38
1.67
1.00
0.84
1.37
1.64 1.90
1.05
1.32 (-0.35)
0.98
0.60
1.48
1.91 1.87
1.16
1.43 (-0.24)
0.96
0.66
1.12
1.55 0.53
1.55
1.22
0.68
0.77
1.05
1.24 0.61
1.24
1.08 (-0.17)
0.63
0.72
1.13
1.28 0.57
1.14
1.11 (-0.11)
0.67
0.82
* Values in parentheses are with respect to the baseline.

SMBO algorithms are available in several hyper parameter
optimization frameworks [8], [9], and in this work, we utilize
the TPE implementation in optuna [10], a hyper parameter
optimization library, to find the best hyper-parameter set x̃.
C. Data Augmentation
Although the SMBO approach enables us to efficiently
explore the parameter space, it tends to find an aggressive
hyper-parameter set to minimize the trajectory errors in the
training set and suffer from overfitting. In particular, forodometry estimation, the number of training sequences ismuch smaller compared to usual machine learning tasks, andoverfitting can be a critical problem. Inspired by the recent
success for data augmentation in the context of deep learning[21], we propose the following three data augmentation
techniques to avoid overfitting:1) Random range noise: For each point in an input point
cloud, we sample a random range of noise in a typicalnoise range for a 3D LiDAR: r ∼ N (µ = 0, σ =0.025) [m] and add it to the point.
2) Random transformation: For each input frame, we
randomly sample a transformation, where the translation ktk ∼ N (0, 0.05) [m] and the rotation angleθ ∼ N (0, 0.25) [°], and apply it to the point cloudand its inverse to the ground truth pose.
3) Reversing order: We reverse the data order for half of
the augmented sequences.
By introducing perturbations with these data augmentation
techniques, we aim to let SMBO find a parameter set thatcan robustly deal with noise and environment changes. We
generate four augmented sequences for each input data
sequence.
IV. E XPERIMENT
A. Evaluation on KITTI

08
1.75
1.71
1.73
1.73
1.37
1.51
1.72
1.55
1.62

Test set
09
1.47
5.51
1.46
2.01
1.61
1.54
1.36
0.94
1.30

10
1.92
2.10
1.84
2.54
1.78
1.69
2.21
1.70
1.96

Avg. *
1.52
2.42 (+0.90)
1.51 (-0.01)
1.69
1.34 (-0.35)
1.37 (-0.32)
1.45
1.21 (-0.24)
1.37 (-0.08)

1) Evaluation setting: To show that there is scope to
improve the estimation accuracy with hyper-parameter tuning
for many odometry estimation methods, we carried out anevaluation on the KITTI dataset [12]. Following [12] and[2], we used relative trajectory errors (RTEs) [22] averaged
over sub-trajectories of 100 to 800 m lengths as the metricfor evaluation. We utilized evo 2 to calculate the RTEs.
The sequences 00 to 05 were used for hyper-parameter
optimization, while the remaining sequences were used forvalidation.
We ran LeGO-LOAM [1], hdl graph slam [3], and SuMa
[2] on the KITTI dataset and evaluated their RTEs. We used
manually tuned parameter sets as the baselines. It is worth
mentioning that the baseline parameter set of SuMa is finetuned for the KITTI dataset in [2]. Then, we optimized theparameter sets for these frameworks with the TPE-based
SMBO approach. The list of tuned parameters and theirranges are available on our project page 3 . The numberof SMBO evaluation trials was set to 128. For the CPUbased frameworks (LeGO-LOAM and hdl graph slam), we
ran eight trials in parallel to speed up the optimization
process. Parameter optimization was completed in aboutfour hours. However, optimization of SuMa, which utilizes
GPU computation, took about 12 hours. This is because its
processing speed decreases significantly when multiple trials
are run in parallel due to GPU scheduling issues, and wethus had to run a single trial at a time.
2) Optimizing parameters using the entire KITTI: Table
I shows the RTEs for the baseline and tuned parameter
sets. We can see that the RTEs for all the methods forthe training set were significantly improved after fine-tuning(LeGO-LOAM: −7.28%, hdl graph slam: −2.31%, SuMa:
2 https://github.com/MichaelGrupp/evo
3 https://github.com/SMRT-AIST/automatic_tuning/
blob/devel/parameters.md

Fig. 1: Parameters for LeGO-LOAM sampled by TPE-based SMBO during parameter optimization. The blue dashed lines
indicate the sample densities.

−0.57%). In particular, the RTEs for sequences 01 and 02,
which were the most difficult sequences in KITTI, involving
forest-like environments with baselines that tend to yieldcorrupted estimates, were greatly improved. However, forsome of the other sequences in the training set and thesequences in the test set, the RTEs deteriorated. This isbecause, to improve the RTEs for the difficult sequences (01and 02), the SMBO selected more conservative parameters,
which resulted in worse RTEs for the other sequences.
This finding testifies to the importance of the metric used
for optimization. Although the SMBO approach enables us
to improve the performance of a system for a specific metric,
the results do not always reflect intuitive impressions of thegoodness of the system (Discussed later in Sec V).
Fig. 1 shows the parameters for LeGO-LOAM sampledduring parameter optimization. The blue dashed lines show
the sampling densities estimated using kernel density estimation. We can see that the SMBO took more samples
from regions where the RTE was expected to be smalland efficiently explored the parameter space to find thebest parameter set. While some parameters have a clear
relationship between the parameter value and the RTE value
and appear straightforward to optimize (e.g., edge thresholdand segment valid point num), some other parameters produce relatively complex RTE distributions (e.g., nearest feature search distance and surf threshold) that would be
more difficult to optimize manually.
3) Optimizing parameters for urban scenes: To evaluate the peak performance of these frameworks in termsof accuracy in a typical urban environment, we removed
sequences 01 and 02, which involve forest-like environments,from the training set and ran the parameter optimization
again. The results are shown in Table II. In this case,
SMBO chose the parameters that fitted better to the typicalurban scenes in KITTI, and the RTEs for hdl graph slamand SuMa were greatly improved for both the training
and test sets (hdl graph slam: (−0.35%, −0.35%), SuMa:(0.17%, 0.24%) for the training and test sets, respectively).
While the RTE for LeGO-LOAM was also improved for the
training set (−0.15%), it deteriorated substantively for thetest set (+0.90%). This suggests that an overly aggressive
parameter set was selected to improve the RTE for the
training set, and resulted in overfitting.
Next we generated four data sequences for each training sequence with the proposed data augmentation techniques and optimized the parameter sets for the augmented training dataset (see Table II). Although theparameter sets optimized with data augmentation haveslightly inferior RTEs compared to those optimized without data augmentation, we can see that the proposed data
augmentation enables all the methods including LeGOLOAM to improve the RTEs for both the training andtest sets (LeGO-LOAM: (−0.05%, −0.01%) hdl graph slam:(−0.24%, −0.32%), SuMa: (−0.11%, −0.08%)). This suggests that perturbations injected in the augmented dataset
lead SMBO to choose a robust parameter set and help toprevent overfitting.

START/END
START/END

Imagery©2020 Google, Map data ©2020

Imagery©2020 Google, Map data ©20205m(a) Environment 1

5m(b) Environment 2

Fig. 2: Experimental environments.
TABLE III: Odometry drift errors for LeGO-LOAM in real environments
Configuration
Baseline
Tuned
Tuned w. D.A.

Training set (Env1)
Trans. [m]Rot. [°]
0.104 ± 0.029
0.027 ± 0.009
0.078 ± 0.035
0.028 ± 0.010
0.098 ± 0.042
0.033 ± 0.009

Test set (Env1)
Trans. [m]Rot. [°]
0.102 ± 0.006
0.030 ± 0.006
0.214 ± 0.058
0.060 ± 0.015
0.092 ± 0.020
0.021 ± 0.009

B. Evaluation in a Real Environment
To show that the proposed approach can be applied to apractical situation, we recorded five LiDAR data sequenceswith Velodyne VLP16 in environment 1 shown in Fig. 2 andoptimized the LeGO-LOAM parameter set. For validation,
we recorded two more sets of three sequences in environment
1 and 2, respectively.
To evaluate the odometry drift, we aligned the last frameof each sequence with the first frame using ICP, and thencompared the obtained relative pose with the last sensor poseof the estimated sensor trajectory. In this evaluation, we madeSMBO minimize the sum of the translation and rotation poseerrors: G(x) = errort [m] + errorr [rad].
Table III shows the evaluation results. Although the estimation accuracy for the training set was greatly improvedby hyper-parameter optimization, the accuracy for the test
set in environment 1 deteriorated due to overfitting. With
the proposed data augmentation, although the errors forthe training set were slightly worse compared to the casewithout data augmentation, we achieved the best results forthe test sets. This shows that the proposed combination of
SMBO-based hyper-parameter tuning and data augmentation
is effective for improving the accuracy of LiDAR odometry
while retaining its robustness in practical situations.
V. D ISCUSSION
A. Evaluation MetricAs shown in Sec. IV-A, the SMBO approach enables us to
improve the performance of odometry estimation algorithms
with respect to a specific metric. However, the optimization results do not always reflect the intuitive goodness of

Test set (Env2)
Trans. [m]Rot. [°]
0.170 ± 0.053
0.015 ± 0.003
0.135 ± 0.046
0.022 ± 0.003
0.083 ± 0.029
0.022 ± 0.008

the system. While the averaged RTE is widely used forodometry evaluation in the literature, it does not represent
some important aspects of odometry estimation (e.g., thebalance between accuracy and robustness). We believe that itis necessary to create a new metric that reflects other aspectsof odometry estimation (e.g., robustness to sensor motionand environment change) to better capture the performanceof odometry estimation systems.
B. Data Augmentation
While we proposed basic data augmentation techniquesfor LiDAR odometry datasets, there is scope to investigate
more advanced techniques. When we injected a large amountof noise into the augmented dataset (e.g., translation noise
ktk ∼ N (0, 0.25) [m] and rotation noise θ ∼ N (0, 2.5)[°]), that made SMBO choose a very conservative parameter
set and resulted in deteriorated RTEs on not only the test
set but also the training set. It is desirable to develop data
augmentation techniques to safely inject large perturbations
without jeopardizing the accuracy of odometry estimations.
We consider that techniques used in deep learning (e.g.,
randomly erasing some parts of input data [23], data generation with adversarial networks [24]) could be a way tosafely increase the variety in the training dataset. We also
consider that recent simulation-based LiDAR data generation
techniques [25] are promising for enlarging the training
dataset and striking a balance between the accuracy androbustness of odometry estimation.
C. Optimization TimeParameter optimization using SuMa [2] for the augmented
dataset took about two days. It would require a much longeramount of time if we optimized the hyper-parameters on alarge dataset (e.g., a city-scale dataset). As described in Sec.
IV-A, we can process each trial of the SMBO in parallel, andthis significantly reduces the optimization time. However,with GPU-based algorithms like SuMa, it is difficult to run
multiple trials in parallel due to GPU scheduling issues, andthus it is not possible to reduce the optimization time in thesame way.
For parameter tuning of deep neural networks, trial pruning based on learning curve evaluation is often used [26]. We
consider that a similar approach to terminate unpromising
trials by evaluating only a few of the first sequences would
be effective for accelerating the entire parameter optimization
process.
VI. C ONCLUSION
This paper proposed an automatic hyper-parameter tuning
approach for LiDAR odometry estimation algorithms. The
proposed approach utilized the TPE-based SMBO techniqueto efficiently explore the parameter space to maximize an
evaluation metric without detailed knowledge of the algorithm to be tuned. The experimental results show thatthe proposed data augmentation techniques enable us toprevent overfitting during parameter optimization and obtaina parameter set for robust and accurate odometry estimation.
Although we explored the possibility of hyper-parametertuning to improve odometry estimation performance, as
discussed in Sec. V, we consider that there is scope to makethe automatic hyper-parameter tuning more efficient andpractical (e.g., developing new metric, data augmentation,and trial pruning strategies). Furthermore, we would be able
to obtain greater performance gains by adaptively changing
the hyper-parameters depending on the circumstances insteadof using fixed pre-optimized parameters; we plan to focus on
this in future work.
ACKNOWLEDGMENT*This work was supported in part by a project commissioned by the New Energy and Industrial Technology
Development Organization (NEDO).
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