FSEO: Few-Shot Evolutionary Optimization via Meta-Learning for Expensive Multi-Objective Optimization
Authors: Xunzhao Yu
Venue: NeurIPS 2025 poster ()
Keywords: Expensive optimization
meta-learning
few-shot optimization
multi-objective optimization
Primary area: optimization

Abstract: Meta-learning has been demonstrated to be useful to improve the sampling efficiency of Bayesian optimization (BO) and surrogate-assisted evolutionary algorithms (SAEAs) when solving expensive optimization problems (EOPs). 
Existing studies mainly focus on either combinations of existing meta-learning modeling methods with optimization algorithms, or the development of meta-learning acquisition functions for specific meta BO. However, the meta-learning models used in the literature are not designed for optimization purpose, and the generalization ability of meta-learning acquisition functions is limited.
In this work, we develop a novel architecture of meta-learning model for optimization purpose and propose a generalized few-shot evolutionary optimization (FSEO) framework to solve EOPs.
We focus on the scenario of expensive multi-objective EOPs (EMOPs) in the context of few-shot optimization as there are few studies on it and its high requirement on surrogate modeling performance.
The surrogates in FSEO framework combines neural network with Gaussian Processes (GPs), their network parameters and some parameters of GPs represent task-independent experience and are meta-learned across related optimization tasks, the remaining GPs parameters are task-specific parameters that represent unique features of the target task.
We demonstrate that our FSEO framework is able to improve the sampling efficiency of existing SAEAs on EMOPs.

FSEO: Few-Shot Evolutionary Optimization via Meta
Learning for Expensive Multi-Objective Optimization
Xunzhao Yu
Department of Economics, University of Warwick Xunzhao Yu@warwick ac uk
Abstract
Meta-learning has been demonstrated to be useful improve the sampling effi- ciency of Bayesian optimization (BO) and surrogate-assisted evolutionary algo- rithms (SAEAs) when solving expensive optimization problems (EOPs). Existing studies mainly focus on either combinations of existing meta-learning modeling methods with optimization algorithms, the development of meta-learning acqui- sition functions for specific meta BO. However, the meta-learning models used in the literature are not designed for optimization purposes, and the generalization ability of meta- meta-leerring acquisition functions is limited. In this work, we develop a novel architecture of meta-learning model for optimization purposes and propose a generalized few-shot evolutionary optimization (FSEO) framework to solve EOPs. We focus on the scenario of expensive multi-ohjective EOPs (EMOPs) in the con- text of few-shot optimization as there are few studies on it and its high requirement on surrogate modeling performance. The surrogates FSEO framework combines neural network with Gaussian Processes (GPs), their network parameters and some parameters of GPs represent task-independent experience and are meta-learned across related optimization tasks, the remaining GPs parameters specifc parameters that represent unique features of the target task. We demonstrate that FSEO is able to improve the sampling efficiency of existing SAEAs on EMOPs.
Introduction
Expensive optimization problems (EOPs) aim to find good as possible solutions within budget of limited solution evaluations. Conventional Bayesian optimization (BO) and surrogate- asssisted evolu- tionary algorithms (SAEAs) have been widely used solve EOPs, but they train surrogate models from scratch. To further improve sampling efficiency and optimization performance, many efforts have been made pre-train surrogates with the prior experience gained from related optimization tasks, resulting in experience-basee based optimization algorithms 2 38 37].
where plenty of expensive related tasks are available and each of them can provide small dataset for experience learning. Therefore, many experience-based optimization approaches, such multi- tasking optimization [47 [22 and transfer optimization [37] 21] 220), are not considered as they cannot learn experience from small related tasks (a detailed clarification of differences between these concepts is available in Appendix I.II). comparison, meta- learning [17] has been proven to be powerful in solving few-shot problems, leading
Scope. This work considers solving EOPs in the context of few-shot problems
subcategory of experience-based
optimization, namely few-shot optimization (FSO) (50]
Motivation. Existing studies FSO are mainly few-shot Bayesian optimization (FSBO) where meta-learning approaches are combined with BO to solve EOPs with only one objective. These studies either employ meta-learning models from the literature directly focus the meta-learning of acquisition functions (AFs) that are customized for BO. In this paper, we develop a novel meta-
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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learning architecture for optimization purposes to enhance modeling performance and propose a generalized few-shot evolutionary optimization (FSEO) framework to address EOPs from the perspective of SAEAs. We demonstrate the generality and applicability of FSEO multi-objective EOPs (EMOPs). FSO on EMOPs has been limited studied but EMOPs have a higher requirement on modeling performance than expensive single-objective optimization. Major contributions are summarized as follows.
A novel leat-leenning method, namely Meta Deep Kernel Learning (MDKL), is developed to gain prior experience from related expensive tasks. Our model architecture and parameter designs make it possible to generate regression-basee surrogate on the prior experience and then continually adapt the surrogate to approximate the target task.
We propose a FSEO framework to solve EOPs from the perspective of SAEAS. FSEO framework is applicable to regression-based SAEAS since FSEO embed our meta-learning models in these SAEAS as their surrogates. In addition, an update strategy is designed to constantly adapt surrogates during optimization. Note that our FSBO framework is general framework but we focus on its performance on EMOPs in this paper.
Experiments are conducted on EMOPs to show that our FSEO framework is effective. Our comprehensive ablation studies reveal the influence of several factors FSEO performance and provide empirical guidance on the application of our FSEO framework.
2 Related Work
Experience- based optimization can be divided into several subcategories according to the techniques of learning prior experience from related tasks. A detailed classification and discussion on these subcategories is available in Appendix I This subsection focuses on related work on FSO.
Wistuba 50 firstly employed meta-learning for few-shot optimization on hyperparameter optimiza- tion (HPO) problems. Subsequent FSO related studies can be grouped into two categories: The first category focuses on improving the performance of few-shot optimization, either by employing different models [27] or by developing novel acquisition functions for BO extends few-shot optimization to more complex optimization problems [56] or applies it to new domains [6. addition, FSO studies in the literature can also be categorized according to their model architectures. Most studies meta-learn parameters for Gaussian Processes (GPs) [48) namely FSBO or Meta Bayesian Optimization (MBO) S4 45 29 40). In addition. [27] meta-learns with
[8] The second category
transformer neural processes and [50 & meta-learn parameters for the architecture of deep kernel
learning (DKL) [49] The MDKL model in our FSEO belongs to the last category as its model
architecture relevant DKL.
Our work differs from existing studies in three points: Firstly, the novel architecture of meta-learning model for optimization purposes. Many studies (50) use existing meta-learning models [30 their surrogates. During the optimization process, these surrogates make predictions with newly observed data, which is a kind of data adaptation rather than model parameter adaptation. The parameters in these models are trained and fixed before the optimization process begins, no further parameter adaptations are made during the optimization, as these meta-learning models are originally designed for regression or classification tasks rather than optimization tasks. In comparison, we develop a meta-learning model, MDKL, for optimization purposes. MDKL has novel model architecture with explicit task-specific parameters, which allows continual adaptations of model parameters and thus improves modeling performance during optimization. Secondly, the generality and broad applicability of FSEO. Existing works are mainly customized for specific algorithms or optimization problems. For example, the meta-learning settings for AFs [46] are not applicable the SAEAs without AFs. However, our FSEO works on the meta-lcarning of surrogates and is applicable to various SAEAS, so our work broadens the scope of existing FSO research. A detailed discussion between BO and SAEA is presented in Appendix A.2 In addition, most existing FSO studies investigated only global optimization, leaving other optimization scenarios such as EMOP still awaiting investigation. In contrast, as our MDKL is designed for optimization and is capable of continually adaptation, we focus on EMOPs which require more effective models than global optimization. Lastly, in-depth ablation studies are lacking in the literature, making it unclear which factors affect the performance of FSO. Our extensive ablation studies fill this gap and we conclude some empirical rules to improve the performance of FSO.

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Background
Preliminaries about meta-learning and DKL are given here. The former is the method of experience learning, the latter is the underlying structure of experience representation.
Meta-Learning in Few-Shot Problems. In the context of few-shot problems, have plenty of related tasks, each task T contributes a couple of small datasets D {(S, 2) namely support dataset S and query dataset Q, respectively. After learning from datasets of random related tasks, support set S, from a new unseen task T- is given and one is asked to estimate the labels or values of query set Q.. The problem is called 1-shot 5-shot when only data point data points provided in S.. A comprehensive definition of few-shot problems is available in 7 44).
Meta-learning methods have been widely used to solve few-shot problems [44]. They learn domain- specific features that are shared among related tasks as experience, such experience is used to understand and interpret the data collected from new tasks encountered in the future.
Deep Kernel Learning (DKL). DKL aims to construct kernels that encapsulate the expressive power of deep architectures for GPs. To create expressive and scalable closed-form covariance kernels, DKL combines the non-paree non-parametric flexibility of kernel methods and the structural properties of deep neural networks. In practice, deep kernel k(x", x hy) transforms the inputs x of base kernel k(x', x (0) through a non-linear mapping given by a deep architecture ofx (w, b):
kxx'; x ly) k(p(x"|w (w, b), 6(x' D)
(I)
where 0 and (w, b) are parameter vectors of the base kernel and the deep architecture, respectively.
Y {0, w, b) is the of all the parameters in this deep kernel. Note that DKL, parameters of deep kernel k(x", x ly) are learned jointly by using the log marginal likelihood function of
GPs as the loss function. Such a joint learning strategy has been shown to make DKL algorithm outperform a combination of deep neural network and a GP model, where a trained GP model is applied to the output layer trained deep neural network
49
Meta-Learning on DKL. An important distinction between DKL, algorithms and the applications of meta-learning DKL is that DKL algorithms learn their deep kernels from single tasks instead of collections of related tasks. This difference alleviates two drawbacks of single task DKL [41] First, the scalability of deep kernels is no longer issue as datasets meta-learning small. Second, the risk of overfitting decreases since diverse data points are sampled across tasks.
Few-Shot Evolutionary Optimization (FSEO) Framework
In this paper, T. denotes the target optimization task, and plenty of small datasets Dj sampled from related tasks Ti are available for experience learning. A complete list of notations is available at the beginning the Appendix.
4.1 Overall Working Mechanism
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Related taok
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Update surropates ity")
Stop
Yes
Figure I: Diagram of our FSEO framework. Methods for handling multiple objectives constraints are dependent on the module "SAEA optimizer'.
As illustrated Fig. [ all modules covering the optimization of target task are included in the blue block. The modules included in the yellow block are associated with related tasks T, and

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Algorithm FSEO Framework.
1: Input: Dj: Datasets collected from related tasks T; i= i=f1....,N! NY: Nm: Number of subsets Dn for meta-learning; [pm|: Size of subsets Dm [Dm S [D; due Dn, C D; Batch size
B; Surrogate learning rates o; [3; Target task T.; An SAEA optimizer Opl; Fitness evaluation budget F Fmmax
2: Experience 7 +- Meta--carming(()) Nm, 1Dm), B,), Alg /
3: S. 6- Sampling Id solutions from T.
4: h(>r") < Adaptation("" S., Iniitialize surrogate."/
5: Set evaluation counter FE = (S.
6: while FE < Emaz do
7: Candidate solution(s) x* + Surrogate-assiste optimization (Opt, h( h(-"))
8: f(x*) + Evaluate x* on T.,
9: S. < S. [(x"
h(yy)) Update(Yy S2. /" Alg. /
11: Update F.E
end while
13: Output: Optimal solutions in S..
experience learning, which distinguishes our FSEO framework from conventional SAEAs and BO. The MDKL, surrogate modeling method consists of two procedures: the meta-leaming procedure and the adaptation procedure. The former learns prior experience from Tr, the latter uses experience to adapt surrogates to fit T.. The framework of FSEO is depicted Alg. [ it consists of the following major steps.
1. Experience learning:
Before expensive optimization begins, meta-learning procedure is performed to train task-independent parameters 70 for MDKL surrogates (line 2). Nr, datasets (Dml..... Dm, N., collected from N related tasks {T TN are used train 7", y the experience that represents the domain-specific features of related tasks.
2. Initialize surrogates with experience: Optimization begins when target optimization task is given. An initial dataset S. sampled (line to adapt task-specific parameters 7 on the basis of experience y"" After that, MDKL surrogates are updated (line 4).
3. Reproduction: MDKL surrogates h(("") are combined with SAEA optimizer Opt to search for optimal solution(s) x" on h((")) (line 7). This implemented by replacing the original rregression-baseds surrogates in SAEA with h(y").
4. Update archive and surrogates:
New optimal solution(s) x" evaluated on target task T. (line 8). The evaluated solutions will be added to dataset S. (line 9) which serves as an archive. Then, surrogate adaptation triggered, surrogates h((r") are updated (line 10).
5. Stop criterion:
Once the evaluation budget has run out, the evolutionary optimization process terminates, outputting the optimal solutions in dataset S.. Otherwise, the algorithm returns to Step 3.
4.2 Learning and Using Experience by MDKL
MDKI., the domain-specific features of related tasks are used as experience, which are represented by the mask-nndependent parameters y learned across related tasks. To make MDKL more capable of expressing complex Nomain-sspecine features, the base kernel k(x², 0) in GP is combined with neural network of (w, b) to construct deep kernel (see Eq. The modeling of MDKL model
consists of two procedures: the meta-learning procedure and the adaptation procedure. To illustrate them clearly, present frameworks for both procedures and explain them in detail.
Meta-learning procedure: Learning experience
Our MDKI. model uses the kernel in [22] as its base kernel:
1(x' x cxp(
10 -x1. ).t)
(2)

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Algorithm 2 Meta-learning(D;, Nm. [Pm], (x)))
1: Input: Dj:
Datasets collected from related tasks Tú, i= (1,,..., N}: Nm: Number of subsets D m for meta-learning; [Dml: Size of subsets Dm- 1Dml I [Di] due to Dm S Dú Batch size B; Learning rate for priors a.
2: Randomly initialize w, b, 0 ,",pp.
3: Set the number of update iterations U Nm/B.
4: for 1 to U do
5:
D'B Randomly select batch of datasets from (Di....,
6: for all D2 in the batch do
7:
Dms k- subset size [Dml from D'
8:
Initialize task-specific increment A0' Ap'.
9:
Compute task-speeific parameters: 0 0" A0' =p + Ap'
10:
Obtain deep kernel k(x', x ly) based GP: h(r), where y= (w.b, 0', p'} (Eq.
Compute the loss function L(D més h(>)) (Eq 12: end for
11:
13: Update w, b. 00,0 via gradient descent: a v L(Dms, h(y)) (Eq.
14:
end for
15:
Output: inseeinndeendeet parameters: Y = {w, b, 0", .p'.
Therefore, the deep kernel will be:
kxx', x2)r) = exp( Σ Uu (elo ((x/// b)
where 7 = [w, b. 0, pp] is a set of deep kernel parameters. ø. w and b denote the neural network and its parameters (see Eq. ( 0, p are parameters of base kernel, details on alternative base kernels are available in 48
The aim of the meta-learning procedure is learn experience " from related tasks (Ti,.... TN including neural network parameters w, b. and mask-independent base kernel parameters 0 ,p' The pseudo-code of the meta-learning procedure is presented in Alg. 2 Ideally, experience 7 is learned from plenty of (Nm) small datasets Dm collected from different related tasks. However, in practice, the number of available related tasks N may be much smaller than Nm- Hence, meta-learning is conducted gradually over U update iterations (line 3). During each update iteration, a small batch of related tasks contribute small datasets [Dm1..... DmB } for meta- meta-nen purposes (lines 5 and 7). Note that if N < Nm. related task T; can be used multiple times in the meta-learning procedure.
For given dataset D Dini denote O 0 + A and p² p Ap' as the task task-specific kernel parameters, where A are the distance we need to move from the task-independent parameters to the task-specific parameters (line 9). The loss function of MDKL. is the negative log-likelihood function, where the likelihood is defined as follows (22]:
(y 1a) R (y 14)
expl
(22))/2
2a
where R is the determinant of the correlation matrix R, each element in the matrix is computed using Eq. 3 3).. y is the fitness vector of D Mean y and variance o² of the prior distribution can be
estimated by:
I'RR'S I'R-T
6= -- - 12) T 1
(5)
n Experience 7 [w, b, 0= pd) is updated by gradient descent (line 13), take 0 as an example:
0h 0"
B Σ
Vo-L(Dmis) h(+)).
After U iterations, 7 has been sufficiently trained by Nm, small datasets D., and will later be used in target task T..
Adaptation procedure: Using experience
The meta-lcarning of experience y enables MDKL to handle family of related tasks in general. To
5

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effectively approximate a specific task T., surrogate h((²)) needs to adapt task-specific increments A and Ap" in the way described in Alg. [] A diagram of the deep kernel implemented in our MDKL. model is illustrated in Fig. 2 From Fig. 2, it is clear that task-independent parameters = b, 0r } are trained on meta data D. During the optimization process, MDKI. adapts task-specific increments A0", Ap" (Algorithm 8, line 3) and combines them with experience 0" resulting in task-specific parameters 0*, p'. Hence, the deep kernel parameter y = {w, b, 0", pp } is available. By invoking Eq. S prediction procedure.
the prior distribution of MDKL is estimated for the following surrogate
Algorithm 3 Adaptation(?", S.;
Input: Current surrogate parameters y"; dataset S, sam- pled from target task TT (Archive); Learning rate for adap- tation B.
Neural network
P. (8, Q.1
2: if y == 7 then
3: Initialize task-specific increments A0", Ap". Compute task-specific parameters: 0* 0F + AO",
ADC
4:
8.
AP" Ap
p' p== pd + Ap'.
5:
Obtain deep kernel k(x', ((xx'xx x ly)) based GP: h(""), ), where
Figure 2: Diagram of our deep kernel implementation. The solid lines depict the training process, the dotted lines depict the infer- ence process. Q. denotes query samples to be evaluated on our surrogates.
>' {w. by 0" .0. pp) (Eq. 3
6: end if
7: Compute the loss function h(x")) (Eq.
8: Update A Ap" using gradient descent:
BV
C(S., h()")).
9: Output: Adapted MDKL h(-").
Surrogate prediction. Due to the nature of GP, when predicting the fitness of solution x", an MDKL surrogate produces a predictive Gaussian distribution (ÿ((x)) (x*)) the predicted mean (x*) ) and covariance g² (x(xx) are specified as (22]:
(xx') + r'R ry - 1n),
(x = 02 'r)-
where r is a correlation vector consisting of covariances between x and S., other variables are explained in (4.
4.3 Surrogate Update Strategy
This subsection describes the update strategy in our FSBO framework. To properly integrate experi- and data from T., update strategy designed to determine whether MDKL surrogate should be adapted in the current iteration or not, ensuring an optimal surrogate update frequency.
As illustrated in Alg. 4 the surrogate update begins when new optimal solution(s) has been evaluated on expensive functions and an updated archive S, is avail- able. For given surrogate h(y"), its mean squared error (MSE) on S. is selected as the update criterion: If the MSE after adaptation 61 (line 4) is larger than the MSE without an adaptation ep (line 2), then the sur- rogate will roll back to the status before the adaptation. This indicates the surrogate update has been refused and f(x")) will not be adapted the current iteration. Otherwise, the adapted surrogate will be chosen (line 6). Note that no matter whether surrogate adaptations are accepted or refused, the resulting surrogates will be treated as updated surrogates, which are employed to assist the SAEA optimizer in the next iteration.
Algorithm 4 Update(y" SS,
I: Input:
Current surrogate parameters y";
Updated archive S.; Learning rate for further adaptations B.
2: eo < MSS((h(T"),S.))
h h(r') + Adaptation("" .S. S..9).
Temporary surrogate, Alg. 3///
4: 61 < MSE(H(Y').S.)
5: if ep then
update 7 = y', obtain new l1(x*).
7: end if Output: Surrogate l((r").
4.4 Discussion on Runtime
The computational complexity introduced by meta-leaming is negligible in the context of few-shot expensive optimization. The time cost model training mainly depends on the size of the dataset used for meta-learning (see Appendix J for complexity analysis of meta- leea-le In few-shot

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optimization, the dataset is typically small, indicating that training meta-learning models is not tmmecconsunnng. contrast. expensive optimization, the time cost of each solution evaluation is much higher than the computational cost of model training. For example, each evaluation of engine performance real-world engine calibration applications may take hours to days [55), similar the evaluation costs reported in other studies on expensive optimization [5]. Therefore, in real-world applications, introducing a meta-learning model is worthwhile even a single expensive evaluation can be saved.
5 Computational Studies
Our computational studies can be divided into three parts:
Appendix D evaluates our meta-learning model performance on two problems and analyzes model component contributions via ablation comparisons with model variants.
2. Sections 5.1 to 5.2 investigate the performance of our FSEO framework in enhancing sampling efficiency. Extensive ablation studies are conducted to provide guidance for practical applications of our FSEO framework.
3. Section |5.3 and Appendix
H demonstrate the performance and broad applicability of our FSEO framework on real-world problems.
For all meta-learning methods used in our experiments, their basic setups are listed in Table 5
5.1 Performance on EMOPs
The experiment in this subsection is designed to answer the question below: With the experience learned from related tasks, can our FSEO framework help an SAEA save 9d solutions without a loss of optimization performance?
5.1.1 Experimental Setups
Optimizaion problems. The computational study conducted on DTLZ test problems [1. All
DTLZ problems have d=10 decision variables and 3 objectives, the setups that have been widely used 35 The details of generating DTLZ variants (related tasks) are provided Appendix C
Comparison algorithms. We test our FSEO framework using an instantiation on MOEA/D-EGO, resulting MOEA/D-FS. Details of the comparison algorithms are given in Appendix E.2
Optimization setups. The parameter setups for this multi-objective optimization experiment are listed in Table During the optimization process, an initial dataset S. sampled using Latin- Hypercube Sampling (LHS) method [28], then extra evaluations are conducted until the evaluation budget has run out. Note that we aim to use related tasks to save 9d evaluations without a loss of SAEA optimization performance. Hence, the total evaluation budgets for MOEA/D-FS and the comparison algorithms are different.
Performance indicators. Since the test problems have objectives, we employ inverted generational distance plus (IGD+) [19] as our performance indicator, where smaller IGD+ values indicate better optimization results. 5000 reference points are generated for computing IGD+ values. More results
in the metrics of IGD [ and HV [61] reported in Appendix E.4
5.1.2 Results and Analysis
The statistical test results are reported in Fig. 3 and Appendix E.3 (Table 7 It can be seen from Fig. 3 that, although 90 fewer evaluations used in surrogate initialization. MOEA/D-FS can still achieve competitive or even smaller IGD+ values than MOEA/D-EGO on all DTTLZ problems except for DTLZ7. In addition, the IGD+ values obtained by MOEA/D-FS drop rapidly, especially during the first few evaluations, implying the experience learned from DTLZ variants is effective. Therefore, in most situations, FSEO framework is able assist MOEA/D-EGO in reaching competitive or even better optimization results, with the number of evaluations used for surrogate initialization reduced from 10d only Id.
'Code available at https://gituub.oom//uuuu// YuSEEO

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Figure 3: IGD+ curves averaged over runs on DTLZ problems. Solid lines are mean values, while shadows are emror regions. MOEA/D-FSs and comparison algorithms initialize their surrogates with 10, 100 samples, respectively. X-axis denotes the extra 50 evaluations allowed the further optimization. Note that 'FS(out)' indicates the target task is excluded from the range of related tasks during the meta-lcarning procedure (see Section 5.2.1).
MOEA/D-FS is less effective on DTLZ7 than on other DTLZ problems. which might be attributed to the discontinuity of the Pareto front on DTLZ7. Note that MOEA/D-FS learns experience from small datasets such as D,,, and S.. The solutions in these small datasets are sampled at random, hence, the probability of having optimal solutions being sampled is small. However, it is difficult to learn the discontinuity of the Pareto front from the sampled non-optimal solutions. a result, the knowledge of 'there are four discrete optimal regions' cannot be learned from such small datasets ((2,,, = 20) collected from related tasks. The performance analysis between MOEA/D-FS and other comparison algorithms is available in Appendix E.3
5.1.3 Further Comparison Experiments with Different Evaluation Budgets
We also compared the performance of our FSEO framework when only 10 evaluations are used for surrogate initialization for comparison algorithms. Consistent results are observed and reported in Table 10 in Appendix E.5 In addition, the performance of our FSEO framework in the context of extremely expensive optimization has been investigated in Appendix (Table 11 and Fig. 7
The question raised at the beginning of this subsection can be answered by the results discussed so far. Due to the integration of the experience learned from related tasks (DTLZ variants), although the evaluation cost of surrogate initialization has been reduced from 10d to 1d, our FSEO framework is still capable of assisting peressioo-bssed SAEAs to achieve competitive even better optimization results in most situations.
5.2
A Ablaioon Studies on Influence of Task Similarity and Dataset Size in Meta-Learning
We conduct ablation studies to investigate the influence of task similarity and that of the dataset size used in meta-learning.
5.2.1 Ablation Study: Influence of Task Similarity
In real-world applications, it optimistic assume that some related tasks are very similar the target task. A more common situation is that all related tasks have limited similarity to the target task. To investigate the relationship between task similarity and FSEO optimization performance, we also test the performance in an 'out-of-range' situation, where the original DTLZ is excluded from the range of DTLZ variants during the MDKL meta-learning procedure. As result, only the DTLZ variants that are quite different from the original DTLZ problem can be used to learn experience. The oaun-e--range" situation eliminates the probability that MDKL. surrogates benefit greatly from the DTLZ variants that are very similar to the original DTLZ problem. Detailed definitions of the

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related tasks used in the 'out-of-range" situation are given in Appendix C Apart from the related tasks used, the remaining experimental setups are the same as the setups described in Section 5.1 For convenience, we denote the situation we tested in Section 5.1 as "in-range" below.
Table 1: Mean IGD+ values and standard deviation (in parentheses) obtained from 30 runs on 7 DTLZ problems. Both MOEA/D- FSs initialize their surrogates with 10 sam- ples, extra 50 evaluations are allowed in the further optimization. '+', +''',,, and '-' de- note the result of the 'out-of-range" situation statistically significantly superior to, al- most equivalent to, and inferior to that of the 'in-range' situation in the Wilcoxon rank sum test (significance level is 0.05), respec- tively. The last two rows count the statistical test results between MOEA/D>FSS and other compared algorithms.
The statistical test results reported in Table show that the 'out-of-range" situation achieves competitive IGD+ values to the 'in-range' situation on all 7 test instances. This suggests that related tasks that are very similar to the target task have a limited impact on the optimization performance of our FSEO framework. Useful experience can be learned from related tasks that are not very similar to the target task. Crucially, when comparing the performance of the out-of-range situation and that of MOEA/D-EGO serve competitive or improved optimization results on 6 DTLZ problems (see Table I the row titled by 'vs MOEA/D-EGO", or Fig. 3). Moreover, it can be seen from the last row of Table 1hhat the 'out-of-range" sit- uation achieves better/coometiiive/wwsss IGD+ values than all compared SAEAS on 31/13/19 test instances. In comparison, the corresponding statistical test re- sults for the 'in-range' situation are 30/15/18. The difference between these statistical test results is not significant.
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A study on the 'out-of-range" situation in the context of extremely expensive multi-objective opti- mization presented in Appendix F2
Consistent results are observed in Table 12 and Fig. 7
Consequently, related tasks that are very similar to the target task are not essential to the optimization performance of our FSEO framework. In the out-oo-raage' situation, our MOEA/D-FS can still achieve competitive or better optimization results than MOEA/D-EGO while using only 1d samples for surrogate initialization.
5.2.2 Ablation Study: Influence of the Size of Datasets Used in Meta-Leernnig
We also investigated the performance of FSEO framework when different sizes of datasets [Dm]] are used in the meta-learning procedure. The experimental setups are the same as the setups of MOEA/D-FS in Section 5.1 except for [Dm]/
is evident from Table that when each DTLZ variant provides |D..| 60 samples for the meta- learning of MDKL surrogates, the performance of both MOEA/D-FSs are improved on 2 or 3 DTLZ problems. Particularly, a significant improvement can be observed from the optimization results of DTLZ7. As we discussed in Section 5.1 the poor performance of our experience-base based optimization on DTLZ7 is caused by the small size of Dm Optimal solutions have few chances to be included in a small Dm, which makes D,,, fail to provide the experience about the discontinuity of optimal regions. In comparison, the experience of 'optimal regions' can be learned from large datasets D,, and thus the optimization results improved significantly.
In conclusion, for our FSEO framework, a large Dm for the meta-learning procedure indicates more useful experience can be learned from related tasks, which further improves the performance of experience-bart based optimization. Therefore, when applying our FSEO framework to real-world optimization problems, it is preferable to collect more data from related tasks for experience learning.
5.3 Performance on Real-World Problems
We also evaluate the performance of our FSEO on real-world problems. In this section, we focus on a Network Architecture Search (NAS) problem, and more computational studies on real-world problems are reported in Appendix H
This NAS problem optimizes the architecture of Transformer

---

Table 2: Mean IGD+ values and standard deviation (in parentheses) obtained from 30 runs on DTLZ problems. 10 samples are used for initialization and extra 50 evaluations are allowed in the further optimization. [Dmm] is the size of the dataset collected from each related task.
Problem
In-range
Out-of-runge
|Pm.|=20
|Pu|=60
|2,01=20
|Pm|=60
DTLZI
(.73e+
9.930=1(1.87++1)
DTLZ2
[.43e-12.29ee2)
1.24c-1(2.11e-2
1.4ee-((175e-2)+
1.29e-1
DTLZS
1.9e+2 (1)
1.98+2 (2.21e+1)
L99c+
1.9c+=2(1.19+tI)
DTLZA
4,44e-1(1.35ee 1)=
3.17e-1(5.68e-
1996c-(8863e-22))
15.36-1(5.386-2)
DTL.5
1.3e-1(2.24e
9,966-222..88e222
1.03e- (02.-1(2.39e22))) 2y0s
((27-3()))33e22)
DTLZ6
1.1le+05.77e-I)e
1.04c+066.66-
1.17e40(6.88e 1)es
1.22=-06641e-11
DTLZ3
2.47e+0(1
7.49c- (2.61ee1)
2.86c+0(1 87c+0)+
6.96e 1(2.4ee-1)
+/7/-
3/4/0
4/--
2/5/0
44
in terms of two objectives: error and flops Fig. 4 illustrates the result, detailed experimental setups are available in Appendix G
Fig. 4 fillustrates the optimization results in terms of Hypervolume (HV) values, a large HV value indicates a good performance. We can observe that MOEA/D-FS, LLogEHVI, K-RVEA, and
0.875
Demiis
EXOCATIC
0.600
0.225
ORIA
DirHVEI are preferable to the remaining compar- ison algorithms in this NAS problem. However, we should note that MOEA/D-FS uses only ld samples from the target task to initialize surro- gates. Due to the small initialization dataset, at the early stage, the initial HV value of MOEA/D- FS is smaller than the initial HV values of other comparison algorithms (see Fig. 4.. With our meta-learning models, MOFA/D-FS adapts to the target task rapidly and it achieves a competitive HV value within 50 additional evaluations, which is a substantial improvement in optimization performance when compared to the performance of its underlying example algorithm, MOEA/D- EGO. This implies that MOEA/D-FS has saved 82 more evaluations than comparison algorithms by learning experience from related tasks and also has improved the performance of underlying optimization algorithm simultaneously. Therefore, the effectiveness of our FSEO framework on this real-world EMOP demonstrated.
0.750
MODAD-PS (AMSS)
0.925
48
NA3: transtormer archuestuuee optimecaton
Figure 4: NAS comparison results. MOEA/D- FS and comparison algorithms initialize their surrogates with 18, 100 samples, respectively. MOEA/D-FS reaches competitive results while 82 evaluations are saved.
6 Conclusion and Future Work
Conclusion. We present a FSEO framework to address EMOPs from the perspective of SAEAS. A novel meta-learning approach MDKL is proposed to learn prior experience from related expensive tasks. MDKL model is designed for optimization and has explicit task-specific parameters, which allows continually update of task-specific parameters during the optimization process. Empirical experiments show that the FSEO framework is able to improve sampling efficiency and save expensive evaluations for existing regression-based SAEAS. Ablation studies reveal the influence between optimization performance and solutions similarity as well as the size of datasets for meta-learning.
Limitation and future work. The limitations of this work can be summarized the following two points, they widely exist in the literature: First, we do not have a mathematical definition of related tasks. As a result, the boundary between related and unrelated tasks is not clear, making it difficult to perform theoretical analysis on task similarity. Second, the proposed framework is currently for regression-bars based SAEAs only. A detailed discussion this point is available in Appendix B
Future work could focus on quantifying task similarity by proposing metric to measure similarity between tasks. With an appropriate task similarity measure, systematic studies on few-shot optimiza- tion and experience-barr based optimization could be conducted. In addition, a few-shot optimization framework for other SAEA categories can also be a future work.
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Reviews:
[{"review_id": "7npiwRHDAB", "reviewer": "Reviewer_Nr53", "summary": "In this paper, the authors propose a meta-learning-based approach for few-shot, expensive multi-objective optimization problems. The method leverages the meta-learning framework, which is well-suited for few-shot scenarios, and introduces additional components to handle the challenges of multi-objective optimization. A kernel function is used to learn from related tasks and is integrated with a neural network to capture more complex relationships. The learned knowledge is then transferred to task-specific parameters. Additionally, the authors propose a surrogate update strategy based on the mean squared error (MSE) of a given surrogate model. If the updated surrogate performs worse than the previous one, the model reverts to the earlier version. To demonstrate the effectiveness of their approach, the authors present extensive numerical results.", "questions": "How many related tasks are needed to train a good model, and how long does it take?\n\nCan you explain more on the model-parameter adapt and data adapt part?", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\n1: The authors effectively adopt the meta-learning framework to address multi-objective optimization problems.\n2: The surrogate update strategy is interesting, as it introduces a new way to evaluate update directions and discard less effective ones.\n3: Compared with the vanilla meta learning, the author more effectively uses prior experience.\n\nWeakness:\n1:The meta-learning approach is computationally intensive. The authors should provide a discussion of the associated computational cost and training time.\n2: The author claims this method is the model parameter adpation. However, the meta learning itself also a model adaption. I don't see the novelty claimed in this paper. It is more like an more effective meta learning method. It will be helpful if author can explain more on that.", "was_revised": false, "final_justification": "", "rebuttal": "Weakness 1\n\nGood point. We will revise our paper to highlight the following discussion.  \n\nIn expensive optimization, the time cost of each solution evaluation is much higher than the computational cost of model training.\nAt the end of Section 5.3.2, we provide a brief discussion on runtime using a real-world engine application as an example, illustrating how costly an engine performance evaluation can be.\nIn contrast, the time cost of model training mainly depends on the size of the dataset used for meta-learning (see Appendix L for a complexity analysis of meta-learning). However, in the context of few-shot optimization, the dataset size is small, indicating that the computational cost of model training is trivial compared to the cost of solution evaluations.\n\n- - -\nWeakness 2\n\nIndeed, one of our novelties is a more effective meta-learning method which has a novel architecture for continual parameter adaptation. The key point is when and how to adapt models.\n\nExisting meta-learning based optimization methods use models that meta-learned for regression purpose rather than optimization. As a result, the model parameters are adapted only during the meta-learning process. In the optimization process, these models are updated with new data collected from the target task but no further adaptation of model parameters typically occurs.\nOne of our novelties is the meta-learning model architecture that designed for optimization purpose, this architecture allows the model parameters to be continuously adapted throughout the optimization process.\n\n- - -\nQuestion 1:\n\nThe performance of the model depends on several factors, including the number of related tasks, the similarity among those tasks, and the amount of data available for each task. If we define a ‘good' model as one that can effectively improve the optimization efficiency of a target task, then even a small number of related tasks (e.g., 5-10) may be sufficient. However, the actual improvement in efficiency also strongly depends on factors such as task similarity and the quantity of data within each task.\n\nAs for the training time, it would not take a long time due to the small size of datasets in the context of few-shot optimization. In our empirical studies, the meta-learning process takes only a few minutes. Compared to the costly evaluation in expensive optimization (hours to days), the time cost of meta-learning is negligible.\n\n- - -\nQuestion 2:\n\nThe parameters in our meta-learning model consist of two parts: task-independent parameters and task-specific parameters (as illustrated in Fig. 1 of our paper).\nDuring the meta-learning procedure, the task-independent parameters are meta-learned using related tasks.\nIn the optimization procedure, the task-specific parameters are adapted using data from the target task.\n\nIn contrast, meta-learning models originally designed for regression tasks do not include explicit task-specific parameters. In their optimization process, adaptation is typically achieved by updating the data used to compute the correlation matrix $R$ (see Equation 4 in our paper), rather than by adjusting model parameters.\n\nPlease let us know if any part remains unclear or which specific point you are confused about, and we would be happy to clarify further."}, {"review_id": "eP86ISnLmX", "reviewer": "Reviewer_Z9sy", "summary": "The paper proposes a few-shot optimization approach for multi-objective optimization. It consists in learning a parameterized deep kernel learning model that learn surrogate for optimization. The approach is using the meta-learning procedure to estimate the parameters of the deep kernel learning to from the few samples available so far, in order to achieve good performance for multi-objective optimization. The approach is evaluated first on synthetic multi-objective optimization benchmark (DTLZ) and then on two more realistic problems (neural architecture search and engine calibration). Results show performance on par with the best approaches for each problem, while reducing the number of samples used for reaching good solutions for the optimization tasks.", "questions": "- Can you provide a clear context, providing a better overview of related work and how the current contribution differ from related work and constitue a meaningful contribution to the field? I found the discussion in Sec. 2 to be difficult to follow and not that helpful to proper position the work, there is a lot of very specific details without provide a clear high-level picture.\n- Can you provide a clear statement of the significance of the proposal and the reach of it? Said otherwise, “why should I care” about the current proposal.", "limitations": "The proposal is quite algorithmic and has not clear and direct limitations and negative impact on society. Therefore, that point is not applicable to the paper.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n- A sound proposal for few shot optimization, the overall method makes sense.\n- Good set of experiments to characterize the approach.\n- Results are generally comparable to state-of-the-art, except for some cases.\n\nWeaknesses:\n- Rather niche topic, the impact of the proposal is rather limited.\n- The experimental methodology is dubious, as the variants used to train the model are based on DTLZ benchmark, which is then used to assess the model. There are leakage risks, and performances are probably overestimated. I think the meta-training / meta-testing should be done over distincts DTLZ problems, the one used in training not be used again in testing. A leave-one-out methodology over can allow to make a better evaluation. Even with the extra experiments with task similarity used to avoid using close tasks for training-testing, I still think there are potential leakage issues that reduce confidence we can have over the results.\n- The proposal is not improving performances much, so it is not clear that the extra complexity added with the meta-learning worth it.\n- Related work section is not very helpful, not providing clear context to position the work.\n- Overall text quality can be improved, the writing is not always very clear. Careful proofreading would improve the quality of the paper.", "was_revised": true, "final_justification": "I have read the rebuttal comments from the authors. These are fine but are not providing significant points that would change my judgement on the paper. I maintain my evaluation.", "rebuttal": "Weakness 1:\n\nThe topic of addressing expensive optimization problems using meta-learning has gained popularity in recent years [1-2]. However, most existing studies focus on the simplest setting: Single-objective optimization, while other common scenarios such as multi-objective optimization remain underexplored. \nFurthermore, many of these works are specific and lack generalization capability. \nIn contrast, our work introduces an efficient meta-learning model and a generalized optimization framework for expensive multi-objective optimization. In our humble opinion, it has the potential to make a broader impact than previous related studies.\n\n>[1] Wang, Zi, et al. ”Pre-Trained Gaussian Processes for Bayesian Optimization.\" Journal of Machine Learning Research, 2024. \n\n>[2] Pan, Jiarong, et al. “MALIBO: Meta-Learning for Likelihood-Free Bayesian Optimization.\" ICML, 2024. \n\n- - -\nWeakness 2:\n\nOur experimental methodology follows the methodology used in several classic meta-learning studies [1-2]. \nEssentially, meta-learning aim to extract common features from related tasks. However, different DTLZ problems often have distinct features. For example, DTLZ3 is a multimodal problem while DLTZ4 is unimodal but scaled. Therefore, it may not be appropriate to treat DTLZ3 and DTLZ4 as related tasks.\nIn our humble opinion, the methodology suggested by the reviewer might be more aligned with transfer learning rather than meta-learning. A discussion on the difference between transfer learning and meta-learning is available in Appendix A.1. \nNote that some studies [3] use the term 'meta-learning' more broadly to refer to all experience-based optimization methods that leverage data from related tasks. However, in this work, we adopt the definition of meta-learning as presented in [1].\n\n>[1] Finn, Chelsea, et al. \"Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks.\" ICML, 2017.\n\n>[2] Patacchiola, Massimiliano, et al. \"Bayesian Meta-Learning for the Few-Shot Setting via Deep Kernels.\" NeurIPS, 2020.\n\n>[3] Wang, Zi, et al. ”Pre-Trained Gaussian Processes for Bayesian Optimization.\" Journal of Machine Learning Research, 2024.\n- - - \n\nWeakness 3:\n\nGood point. We have revised our manuscript and added the following discussion to further clarify the relationship between performance and the complexity of meta-learning:\n\nThe computational complexity introduced by meta-learning is negligible in the context of expensive optimization. Since the dataset used for meta-learning is typically small, training the meta-learning model is not time-consuming. In contrast, evaluating a single solution can be extremely costly. For example, an engine performance evaluation in our real-world application may take hours to days, similar to the evaluation costs reported in other studies on expensive optimization [1].\nTherefore, in real-world applications, introducing a meta-learning model is worthwhile if even a single expensive evaluation can be saved.\n\nFrom our experiments, it is evident that our few-shot optimization framework saves 9\\$d$ evaluations, while still achieving competitive, or even superior, optimization results (e.g., in terms of IGD+ values) in most cases.\n\n>[1] Wang, Zi, et al. “Pre-Trained Gaussian Processes for Bayesian Optimization.\" Journal of Machine Learning Research, 2024.\n\n- - -\n\nWeakness 4:\n\nSee our response to Question 1.\n\n- - -\n\nWeakness 5:\n\nThanks for your suggestion. We have carefully gone through the entire manuscript to improve the text quality. We believe the revised version is clearer than the one initially submitted.\n\n- - -\n\nQuestion 1\n\nThank you for your suggestion. We have revised the related work section and added the following overview to the second paragraph of Section 2.\n\nWistuba firstly employed meta-learning for few-shot optimization on hyperparameter optimization (HPO) problems. Subsequent related studies can be grouped into three categories:\n\n1. The first category focuses on improving the performance of few-shot optimization, either by employing different models [2] or by developing novel acquisition functions for BO [3]. \n\n2. The second category extends few-shot optimization to more complex optimization problems [4] or applies it to new domains [5-6].\n\n3. The third category explores the use of related tasks in other experience-based optimization methods, such as transfer optimization [7] and multi-task optimization [8], which are distinct from FSO.\n\nHowever, many studies use existing meta-learning models from the literature, these models are not designed for optimization purpose. As a result, these models may be less efficient when applied to optimization problems. In addition, many acquisition functions are working for specific BO, limiting their generality.\nMoreover, current research on few-shot optimization focuses primarily on the simplest case, single-objective optimization. However, multi-objective optimization is common in real-world applications and presents greater challenges.\n\nIn response to these gaps, our work proposes an efficient meta-learning model for optimization purpose and a generalized framework with broad applicability. In particular, we aim to fill the gap in multi-objective few-shot optimization.\nThe difference between our work and related work is described in the third paragraph of Section 2.\n\n>[1] Wistuba, Martin, and Josif Grabocka. “Few-Shot Bayesian Optimization with Deep Kernel Surrogates.\" ICLR, 2021. \n\n>[2] Maraval, Alexandre, et al. \"End-to-End Meta-Bayesian Optimization with Transformer Neural Processes.\" NeurIPS 2023.\n\n>[3] Hsieh, Bing-Jing, et al. ”Reinforced Few-Shot Acquisition Function Learning for Bayesian Optimization.\" NeurIPS, 2021.\n\n>[4] Zhang, Huan, et al. “Solving Expensive Optimization Problems in Dynamic Environments with Meta-Learning.\" IEEE Trans on Cybernetics, 2024.\n\n>[5] Chakrabarty, Ankush. ”Optimizing Closed-Loop Performance with Data from Similar Systems: A Bayesian Meta-Learning Approach.\" CDC, 2022.\n\n>[6] Chen, Wenlin, et al. “Meta-learning Adaptive Deep Kernel Gaussian Processes for Molecular Property Prediction.\" NeurIPS, 2022.\n\n>[7] Bai, Tianyi, et al. ”Transfer Learning for Bayesian Optimization: A Survey.\" arXiv, 2023.\n\n>[8] Wang, Zi, et al. “Pre-Trained Gaussian Processes for Bayesian Optimization.\" Journal of Machine Learning Research, 2024.\n\n- - -\nQuestion 2\n\nIn short, the significance of our work can be summarized as follows:\n\n1. We fill the gap in multi-objective optimization for few-shot optimization, which is crucial as multi-objective optimization problems widely exist in real-world applications.\n\n2. We propose a novel meta-learning model specifically designed for optimization. It can be efficiently and continuously adapted during the optimization process.\n\n3. Our FSEO framework is compatible with a variety of optimization algorithms and is not limited to a specific Bayesian optimization method."}, {"review_id": "OHFDV8WDib", "reviewer": "Reviewer_jiRL", "summary": "This paper introduces FSEO, a few-shot optimization framework based on meta-learning to solve expensive multi-objective optimization problems (EMOPs). The proposed framework uses a novel meta-learning surrogate model called Meta Deep Kernel Learning (MDKL), which combines neural networks with Gaussian Processes. The framework aims to improve the sample efficiency of surrogate-assisted evolutionary algorithms (SAEAs) by leveraging prior experience learned from small datasets of related tasks\nA meta learned surrogate that enables continual adaptation to new tasks\nA generalized framework for use in few-shot scenarios\nframework is shown to reduce the number of function evaluations needed while achieving comparable or better optimization performance compared to standard methods", "questions": "Please refer to the strengths and weakness section to address questions.", "limitations": "Please refer to the strengths and weakness section to address questions.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\nThe paper clearly targets a few-shot setting for expensive multi-objective optimization which is still an active area of research.  MDKL supports continual adaptation of task-specific parameters, which is architecturally significant.  Experiments were conducted on real world tasks where significant improvements have been shown. he paper includes controlled ablations for Task similarity (in-range vs. out-of-range).\n\nWeakness:\n\nThere is missing comparisons for other recent meta learning baselines.  There is no comparison to other meta-learning frameworks that target optimization (e.g., meta-acquisition functions or meta-BO on EMOPs), such as MALIBO, PREBO, or transfer-SAEA methods\nSynthetic results are only reported on DTLZ problems (DTLZ1–DTLZ7), which are standard but limited, No large-scale or high-dimensional EMOP benchmarks. \nThere are no much information on hyperparameters for reproduciability purpose, please direct me in rebuttal if I am missing them \nWhile IGD+ curves and error bands are provided in synthetic benchmarks (Figure 3), no error bars or statistical significance tests are shown.", "was_revised": true, "final_justification": "I went through the reviewers comments, and I am upgrading my review.", "rebuttal": "Weakness 1:\n\nThank you for pointing out this issue. \nWe should have made it clearer that we actually have comparisons with meta-learning baselines in our modeling experiments (see Appendix D).\nIt is worth noting that many few-shot optimization methods use similar meta-learning models but differ in the strategies built around them. Additionally, some studies use the term 'meta-learning' more broadly to refer to all experience-based optimization methods that leverage data from related tasks (e.g., [1]). As a result, these 'meta-learning' methods may not serve as direct baselines in the specific context of few-shot optimization.\nA discussion on the differences between various experience-based optimization methods is provided in Appendix A.1.\n \n> [1] Wang, Zi, et al. ”Pre-Trained Gaussian Processes for Bayesian Optimization.\" Journal of Machine Learning Research, 2024.\n\n- - -\nWeakness 2:\n\nThis is a good suggestion. We have read the recommended papers and conducted additional research on this topic.\n\nWe should clarify that our work focuses specifically on few-shot multi-objective optimization. While some existing studies on meta-learning-based optimization exist (e.g., MALIBO), they primarily target single-objective optimization or other types of experience-based optimization. As such, these frameworks are not directly comparable to our approach in the context of multi-objective optimization problems.\nWe have included a discussion on the distinctions among various experience-based optimization methods in Appendix A.1, such as multi-task optimization, multi-form optimization, transfer optimization, and few-shot optimization.\n\nRelated work on multi-objective optimization is very limited, and some of them are limited on specific optimization applications [1], which motivated us to develop a generalized framework for multi-objective optimization.\n\n> [1] Watanabe, Shuhei, et al. \"Speeding up multi-objective hyperparameter optimization by task similarity-based meta-learning for the tree-structured parzen estimator.\" IJCAI, 2023.\n\n- - -\nWeakness 3:\n\nGreat point.\nThe DTLZ benchmark includes seven problems with different but common features, which helps evaluate the performance of multi-objective optimization algorithms. However, as the reviewer noted, these benchmark problems may not fully capture the complexity of real-world applications.\n\nTo address this limitation and strengthen our empirical studies, we followed the practice in the literature by including several real-world problems to demonstrate the robustness of our method. The results on these real-world applications are reported in Section 5.3.\nAdditionally, our modeling experiments in Appendix D include both synthetic and real-world applications.\n\n- - -\nWeakness 4:\n\nThank you for pointing out this issue.\nAs a pioneering study in few-shot multi-objective optimization, our work focuses on designing an efficient and general framework for the most common multi-objective optimization scenarios found in real-world expensive optimization applications. Accordingly, we followed the practice of existing studies [1-4] and did not include specific problem features such as large-scale or dynamic settings within the scope of this work.\n\nWe understand the importance of considering higher-dimensional problems, and we will leave it for one subsequent work (just like other studies that focus on this challenging issue [5-7]). We will make this clear in the revised paper. \n>[1] Wang, Zi, et al. ”Pre-Trained Gaussian Processes for Bayesian Optimization.\" Journal of Machine Learning Research, 2024. \n\n>[2] Pan, Jiarong, et al. “MALIBO: Meta-Learning for Likelihsood-Free Bayesian Optimization.\" ICML, 2024. \n\n>[3] Tu et al. ”Joint Entropy Search for Multi-Objective Bayesian Optimization.” NeurIPS, 2022. \n\n>[4] Wistuba, Martin, and Josif Grabocka. “Few-Shot Bayesian Optimization with Deep Kernel Surrogates.\" ICLR, 2021.\n\n> [5] Wu, Yupeng, et al. “High-Dimensional Causal Bayesian Optimization.” ECAI, 2024. \n\n> [6] Ramchandran, Siddharth, et al. “High-Dimensional Bayesian Optimisation with Gaussian Process Prior Variational Autoencoders.” ICLR, 2025. \n\n> [7] Zhou, MengChu, et al. “Evolutionary Optimization Methods for High-Dimensional Expensive Problems: A Survey.” IEEE/CAA Journal of Automatica Sinica, 2024.\n\n- - -\nWeakness 5:\n\nThank you for your comment.\nWe provide the hyperparameter details in Tables 4 and 5 (Appendix E.1), and we have cited relevant references to show that these settings are commonly used in the literature.\nWe will revise the paper to clarify this point more effectively.\n\n- - -\nWeakness 6:\n\nThanks for your comment. \nStatistical tests corresponding to Figure 3 are reported in Appendix E.3, Table 6.\nIn addition, statistical test results for two different metrics, IGD and HV, are presented in Tables 7 and 8.\nWe will revise our paper to improve clarity and make key information easier to find."}, {"review_id": "s0aTkDSr1m", "reviewer": "Reviewer_jgNV", "summary": "This paper introduces FSEO, a framework for solving expensive multi-objective optimization problems (EMOPs) using few-shot meta-learning. At its core, the method builds a meta-learned surrogate model (MDKL) that combines a deep kernel architecture with Gaussian Processes. The surrogate is trained across a set of related tasks to learn task-independent parameters and then adapted online to each new target task with limited samples (as few as 1d evaluations). The surrogate is integrated into regression-based surrogate-assisted evolutionary algorithms (SAEAs), with MOEA/D-EGO used as a case study.\nThe authors validate their approach across synthetic DTLZ benchmarks and real-world tasks, including neural architecture search and engine calibration, and conduct ablation studies to explore the effects of task similarity and dataset size.", "questions": "1. Without an acquisition function, how does the evolutionary component balance uncertainty? Is the MDKL variance ever used directly in search?\n2. Do you have any quantitative measures of task similarity across DTLZ variants or real tasks (e.g., using function landscapes or mutual information)?\n3. How expensive is the adaptation step computationally? Could you report runtime per update or total time vs. baseline?\n4. In DTLZ7, you mention MDKL fails due to discontinuity. Have you considered hybrid approaches (e.g., combining meta-learned GP with density estimators)?\n5. Have you tried plugging MDKL into other SAEAs like RVEA or ParEGO? If not, are there any anticipated challenges?\n\n\nSuggestions for Improvement\n\n* Add a second SAEA to test generality of the FSEO framework.\n* Provide runtime measurements (total time, per-update cost, adaptation vs. inference).\n* Discuss whether task-specific adaptation ever overfits in low-data settings.\n* Add theoretical discussion or intuition about why MDKL generalizes across tasks.", "limitations": "yes", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 4, "originality": 4, "strengths_and_weaknesses": "Strengths\n\n* The need for few-shot sample-efficient optimization is strong, especially in high-cost engineering and machine learning settings.\n* FSEO is a modular enhancement that can be plugged into any regression-based SAEA, not tied to a specific optimizer.\n* MDKL introduces task-specific parameter adaptation during optimization, improving over frozen meta-learned surrogates used in past few-shot BO literature.\n* Comprehensive evaluation and the \"out-of-range\" setting shows that FSEO remains effective even when test tasks fall outside the meta-training distribution.\n\nWeaknesses\n\n* Performance inconsistency: Results on DTLZ4, DTLZ6, and especially DTLZ7 show that FSEO can struggle with non-uniform or discontinuous Pareto fronts — an important limitation.\n* No theoretical guarantees: The paper does not provide formal analysis (e.g., regret bounds, convergence guarantees) to support when/why MDKL works or fails.\n* Generalization to other SAEAs not demonstrated: All experiments focus on MOEA/D-EGO. Claims of framework generality would be stronger if results on a second SAEA were included.\n* Compute/resource use is under-reported: Adaptation cost per iteration and overall runtime are not measured, even though MDKL retraining happens repeatedly.", "was_revised": true, "final_justification": "My concerns have all been resolved, so I’ll keep my score as it is.", "rebuttal": "Question 1\n\nGood point.\nOur framework includes meta-learning models and a model update strategy. However, the acquisition function is a component of the optimizer and can vary depending on which optimization algorithm the FSEO framework is applied to.\n\n- - -\nQuestion 2\n\nWe estimate task similarity across variants based on the difference between their parameters, following the approach used in several classic meta-learning studies [1-2]. As suggested by the reviewer, using function landscapes could be a promising idea in this regard. We will add figures to analyze the task similarity across variants based on the difference of function landscapes.\n\n>[1] Finn, Chelsea, et al. ”Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks.\" ICML, 2017\n\n>[2] Patacchiola, Massimiliano, et al. “Bayesian Meta-Learning for the Few-Shot Setting via Deep Kernels.\" NeurIPS, 2020.\n\n- - -\nQuestion 3\n\nWe will revise our paper to include the following discussion on runtime.\n\nThe computational cost of the adaptation step is minimal, and we did not observe a noticeable increase in runtime during the optimization process. This is expected because:\n1. We did not increase the number of surrogate models in SAEAs.\n2. No additional data from the target task was introduced during the adaptation step.\n3. In the context of few-shot optimization, the dataset used for adaptation is small, so the model updates are not computationally intensive.\n\nOverall, in expensive optimization problems, the cost of evaluating a solution typically outweighs the runtime of the optimization algorithm itself.\n\n- - -\nQuestion 4\n\nThis is a great suggestion.\nAs a pioneering study on multi-objective few-shot optimization, our current work does not yet explore additional techniques to address the limitations of meta-learning models on problems with specific characteristics (e.g., discontinuities). We will revise our paper to clarify that enhancing optimization performance through methods such as hybrid approaches is a promising direction for future work.\n\n- - -\nQuestion 5:\n\nGood suggestion.\nWe should make it clearer that we integrated MDKL with another SAEA in Section 5.3.2. This section is intended to demonstrate the generality and broad applicability of our algorithm, and we did not encounter any unexpected challenges.\n\n- - -\nWeakness 1:\n\nWe should make it clearer that although FSEO did not achieve better optimization results on DTLZ4 and DTLZ6, the results were obtained using only 1\\$d$ evaluations, indicating 9\\$d$ evaluations were saved. This reflects a significant improvement in efficiency for expensive optimization. \nAdditionally, the results in Table 9 (Appendix E.5) further demonstrate that FSEO performs well on DTLZ4 and DTLZ6.\n\n- - - \nWeakness 2 (Suggestion 4):\n\nGood suggestion. We will revise our paper and add the following intuition to explain why MDKL generalizes across tasks.\n\nFor related tasks, we assume that the parameters of their distributions are located within a cluster in the parameter space. If two parameter vectors are very close to each other in this space, the corresponding tasks are considered highly similar. Therefore, the purpose of the meta-learning procedure is to move the task-independent parameter vector toward the center of this cluster. Once meta-learning is complete, it becomes easier to approximate the parameter vector of the target distribution based on the position of the meta-learned parameter vector.\n\n- - -\nWeakness 3 (Suggestion 1):\n\nSee our response to Question 5.\n\n- - -\nWeakness 4 (Suggestion 2):\n\nSee our response to Question 3."}]

Author rebuttal:

Meta-review: This paper develops a novel meta-learning model for optimization purposes and proposes a generalized few-shot evolutionary optimization (FSEO) method for expensive multi-objective optimization problems. The proposed FSEO uses meta deep kernel learning (MDKL), which combines neural networks with Gaussian processes (GP). The surrogate is trained across related tasks to learn task-independent parameters and adapted to a new target task. The experimental evaluation on benchmark problems demonstrates that FSEO outperforms baseline methods.

The proposed meta-learning framework can adequately address the challenges in expensive multi-objective optimization problems. The weaknesses are that the proposed method requires a relatively high computational cost and lacks a theoretical discussion.  

After the authors' rebuttal and discussion, all reviewers gave a positive score. The proposed meta-learning framework and surrogate update strategy are sound. The effectiveness of the proposed method is empirically validated through experiments.
The weaknesses and room for improvement might exist in this paper, which might be a reason that several reviewers did not raise the scores. However, based on the reviewers' comments and discussion, I believe that the strengths of this paper outweigh its weaknesses. Therefore, I recommend accepting this paper.

I encourage the authors to revise the paper based on the reviewers' comments to improve the quality of the paper, e.g., the clarity of the novelty of the proposed method, justification of the experimental settings, and the extra computational cost.
Decision: Accept (poster)