Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 8: Strong Accept: Technically strong paper, with novel ideas, excellent impact on at least one area, or high-to-excellent impact on multiple areas, with excellent evaluation, resources, and reproducibility, and no unaddressed ethical considerations.
review_content: summary: The paper proposes an algorithm for batch multi-objective Bayesian optimization. The acquisition function uses Chebyshev scalarization. The goal is to solve problems with an infinite size pareto optimal set and find a pareto manifold of solutions. 
strengths_and_weaknesses: Strengths

+The problem setting is interesting. Continuous pareto set There are several real-world problems with a manifold of solutions. The Idea of creating a projection of the manifold based on the preference defined by the practitioner is appealing.
+ the approach is well structured and novel 
+ The paper is well written, and the proposed solution is clear.
+ The paper covered lots of baselines on several synthetic and real-world problems 

Weaknesses: 

+ The practicality of accessing the pareto set manifold in the context of expensive experiments might be questionable.
+ Defining user preference in terms of scalars is challenging in practice and there is no clear way on how to do it
+ The experiment comparison is missing an important relevant algorithm from the preference over objectives literature [1]
+ The contribution of the batch selection is minor and incremental

[1] Abdolshah, Majid, et al. "Multi-objective Bayesian optimization with preferences over objectives." Neurips (2019).

questions: Several applications have an infinite pareto set of solutions. However, in practice, having access to an approximation of the manifold over the input space in the context of expensive evaluations, might not be necessarily useful. Given the cost of the objectives, the budget might be exhausted by the time a good approximation of the manifold is built. At that point of the optimization process, access to the pareto set manifold would not be useful without access to output values. Also relying on only the approximate input space manifold can be very risky in several applications given the uncertainty of the prediction.
limitations: Yes the authors discussed limitations briefly. I suggest including a discussion about the challenges in defining the preference over objectives in the context of black-box functions
review_title: null

final_score: rating: 5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.
review_content: summary: This work proposes a novel method for multi-objective Bayesian optimization (MOBO). The work argues that the proposed method achieves greater sample efficiency and better runtime than existing alternatives. The proposed method leverages the structure of the Pareto set, acknowledging that the Pareto set is typically infinite and the often the result of optimization is a finite approximation. 
strengths_and_weaknesses: The problem of multi-objective optimization of expensive function is important. However, many existing works have already tackled this problem, as noted in the paper. Hence, subsequent efforts can at best achieve incremental gains. The method amounts to 1) using the known connection between an augmented TCH scalarization and pareto optimal points, 2) training a neural network select the next candidate designs (these would be believed to be Pareto optimal if the \hat{f} were set to the posterior mean, but instead this work sets it to a lower confidence bound). 

The paper is generally well-written, but the augmented Chebyshev scalarization is already used by ParEGO with EI. It is unclear why a NN should be used here to select designs (the main novel component). The empirical results show that the proposed methods works quite well, but raises questions. Given that there are no theoretical results, the burden is on the empirical validation and the motivation for the methodology, but both currently fall short of making a compelling case for the utility of this method. 

questions: Why is using NN policy for candidate generation a good idea? What is the benefit?
  * The NN serves as a way to generate candidates. Why not just optimize the acquisition function under one scalarization (or more for generating a batch)?
  * Can you provide an ablation study that removes the NN and simply optimizes the acquisition function? The importance of each the two main contributions---1) using augmented Tchebyshev scalarization with an ideal point and epsilon and 2) using a NN to predict the optimal designs---is currently not clear.
* Regarding batch selection: qParEGO also selects different scalarizations, randomly, for each point in the batch. The proposed batch selection criteria of using HVI (based on the predicted LCB) to select points is not well-motivated. Why not just maximize expected improvement or LCB of HVI? The choice of using HVI for batch selection is a large departure from proposed approach for sequential optimization and is not well-justified
* This work is missing an introduction to Bayesian optimization, which would make it hard for a non-BO expert to read this paper.
* Hypervolume improvement is introduced before hypervolume. I recommend switching this ordering (and potentially introducing these concepts earlier)
* “It would be computationally intensive to find a set to exactly maximize the hypervolume improvement (12). “ This is commonly done in expected hypervolume improvement, albeit with a sequential greedy approximation. I recommend clarifying this statement to state that jointly maximizing B candidates is difficult and therefore sequential greedy selection is typically used (Daulton et al., 2020).
* The pareto set of designs for the ZDT problems exist in a tiny slice of the search space. This biases performance towards the PSL based approach where a NN could very well predict the optimal designs in they are close to together and at least one has been observed. Furthermore, this makes many improvement-based acquisition function hard to optimize. Therefore, using the proposed epsilon adjustment has outsized impact, but this could be done for any acquisition function. In addition, the initial designs used for acquisition optimization are particularly important as often these will be zero. Hence, acquisition optimization is sensitive to the initialization and techniques such as perturbing the best designs observed so far with a small amount of zero-mean Gaussian noise significant influence optimization performance. This feature if ZDT is particularly important because one contribution of this work is the method for generating candidates using PLS with circumvents the classical acquisition optimization. Heuristics such as perturbing the best points with a small amount of zero-mean Gaussian noise should be compared against to understand this paper's contribution.
* Appendix, L198: “qEHVI needs an extremely long runtime  to calculate the expected hypervolume improvement for more than 3 objectives at each step.” Daulton et al., 2020 run qEHVI on vehicle safety with 3 objectives and Daulton et al., 2021 run qEHVI and qNEHVI on car side impact with 4 objectives.
* Why is LaMoo (Zhao et al., 2022) not compared against? 
* Why is qNEHVI (Daulton et al., 2021) not compared against, since is scales better with the batch size than qEHVI?
* Line 76: “expectation improvement” -> expected improvement
* Line 126: Figure 1b does not show “our proposed PSL method also learns an estimated Pareto set Mpsl with the predicted Pareto front fˆ (Mpsl ) to approximate the Pareto set Mps and Pareto front f (Mps ) “
* Line 250: “\hat{f} are the surrogate values” – it is unclear whether this is the posterior mean or the LCB?


limitations: The paper briefly touches on limitations in the last paragraph, but those limitations are for MOBO in general rather than focusing on this methodology. The paper would benefit from a discussion of worst-case behavior or situations were the method might fail or struggle would be good to include. Negative societal impacts are not discussed.
review_title: null

final_score: rating: 5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.
review_content: summary: This paper presents a new Pareto set learning method to approximate the whole Pareto set for expensive multi-objective Bayesian optimization. it first generated a model that maps any trade-off preferences to their corresponding Pareto solutions with scalarization, then uses a batched acquisition search with the learned Pareto set model. 
strengths_and_weaknesses: The expensive multi-objective Bayesian optimization problems studied in this paper are a long-standing concern in the field of Bayesian optimization, and this paper presents a new algorithm for this. The main problem is that all the problems tested in the experiments have been proven to be quite simple. Moreover, the dimensionality of the test problem does not exceed 6. These raise concerns about the effectiveness of the algorithm proposed in this paper because the tested problems are too simple.
questions: The setting of the test problems is strange. The experiments on other test problems from the ZDT and DTLZ suites need to be added.
limitations: The impact of the aggregation function on the algorithm needs to be analyzed.
review_title: null

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: In the context of expensive multi-objective black-box optimization, this article proposes to construct a surrogate model of the Pareto set. It is a neural network built upon surrogate models of the objectives, here Gaussian processes. The interest is first to help decision makers to navigate the estimated Pareto set and front. Then it is useful for selecting batches on candidates for sequential optimization, using the existing expected hypervolume improvement. The method is benchmarked over different classical test functions, against appropriate baselines.
strengths_and_weaknesses: Strength:
- the method integrates the structure of the Pareto set to help optimize the qEHVI criterion;
- the Pareto set model is useful for working with practitioners. The method to build it with backpropagation is original.
- the results are convincing in terms of speed and sample efficiency.

Weaknesses:
- models for the Pareto sets have been proposed in the multi-objective literature.
- it uses the qEHVI criterion.
- the behavior on disconnected Pareto front is not shown.
- a few aspects could be clarified, see Questions below.
questions: Could you show the learned Pareto front and set on a case where they are disconnected?
Appendix line 57: Is it still Expected improvement in this form?
Appendix C5: could you define the what ''uncertainty'' means here?
limitations: Limitations are discussed.
review_title: null

Meta-review: metareview: This paper studied the problem of (batch) multi-objective Bayesian optimization (BO). It considers a novel perspective to solve problems with an infinite size pareto optimal set by finding a pareto manifold of solutions. The acquisition strategy uses Chebyshev scalarization. The key idea is to learn a mapping from preferences (i.e., scalarization parameters) to the Pareto optimal solution and use it to guide the acquisition strategy and BO process to approximate the Pareto set. Experimental results demonstrate the effectiveness of the proposed approach.

All reviewers agreed about the novel perspective from which the multi-objective BO problem was studied, but also raised some concerns and questions. The authors gave satisfactory responses to most of the review comments and revised the paper to improve it. Two reviewers strongly supported accepting the paper and two of them gave borderline accept. Authors satisfactorily addressed the main concern of one of them (i.e., test problems are too simple). Some of the comments from Reviewer MK65 needs further work, which is acknowledged by the authors. 

The overall approach is novel, advances scalarization based multi-objective BO, produced good results, and has the potential to generate good interest in the BO community. Therefore, I recommend acceptance.
confidence: Certain
Decision: Accept