Venue: ICLR 2023 Conference

Reviews:

final_score: rating: 3: reject, not good enough
review_content: summary_of_the_paper: This paper extends the simple linear scalarization method in multi-objective optimization to the GflowNets setting. Two variants of GflowNets are proposed and extensive empirical experiments are provided, which verifies the effectiveness of them.
strength_and_weaknesses: Strengths:
+ The idea of extending gflow nets to the multi-objective setting is novel and interesting.
+ Multi-objective gflow nets are useful in drug discovery.

Weaknesses:
+ The extension of weighted sum scalarization to glow nets seems incremental, which lacks novelty.
+ The understanding of multi-objective of this paper is limited. Some of the assertions are overclaimed. For example, weighted sum scalarization is only one simple way to do multi-objective optimization (MOO). It has many drawbacks, especially when non-convex Pareto front is encountered. But in Section 2.1, the authors claim solving weighted sum scalarization equals solving MOO. More precise background knowledge on MOO should be incorporated.
+ The study of the active version of gflow nets is not very clearly motivated.



clarity,_quality,_novelty_and_reproducibility: Clarity: The presentation is good. But at the knowledge level, this paper does not study the background of MOO well.

Quality: Fairly good.

Novelty: The novelty is limited from the technical level, as weighted sum scalarization seems too simple in MOO. But it seems good from the application level with respect to drug discovery

Reproducibility: Good.

summary_of_the_review: More technical depth of MOO should be incorporated. The technical contribution of extending MOO to GlowNets seems to be limited. The motivation of the study should be more precisely described.
review_title: null

final_score: rating: 8: accept, good paper
review_content: summary_of_the_paper: The paper leverages GFlowNet to solve the Multi-Objective Optimization problem. The authors derive two versions of the algorithm, regular and active learning variants. The authors empirically demonstrate that the proposed algorithms outperform existing methods almost on every considered benchmark and perform reasonably on DNA sequence design tasks. The method as expected performs very well in terms of generating a diverse set of candidates.
strength_and_weaknesses: Strength

* The authors successfully applied conditional GFlowNet (for the first time) to the Multi-Objective Optimization problem.
* The author generalizes the GFlowNet active learning algorithm for the Multi-Objective Optimization problem case. 
* The results seem promising for both algorithms in terms of key metrics and especially the diversity of the generated candidate.
* The results and comparisons with other methods are well explained. (e.g. why in some cases other baselines have higher scores on some of the metrics)

Weaknesses
* I believe the novelty is limited in terms of new ideas as the main technical contribution of the paper is the adaptation of the previously derived method to MOO setting. 

Minor issues and questions
* To make the paper self-consistent can you add how \alpha function in the Active Learning section combines a reward with an epistemic uncertainty?
* It is unclear to me from the paper how \alpha function map a set of rewards and their epistemic uncertainties to a single objective in each round of the Active Learning pipeline. Or is the \alpha function defined externally for each round and can be considered as a hyperparameter? 
* Do you retrain GFlowNet from scratch for each round of Active Learning?
clarity,_quality,_novelty_and_reproducibility: The technical novelty of the paper is how to apply and generalize the previously derived method to the MOO problem. I believe this technical novelty is solid. However, the novelty in terms of new ideas seems incremental to me. The paper is well-written with some exceptions that I mentioned. I believe the results are reproducible.
summary_of_the_review: In general, I believe the novelty of the paper is incremental as it is a straightforward adaptation of  GFlowNets to MOO settings. However, this adaptation may possess a solid technical contribution.
review_title: null

final_score: rating: 3: reject, not good enough
review_content: summary_of_the_paper: This paper extends the GFlowNets proposed for single-objective optimization to multi-objective optimization, namely MOGFNs. Experiments are conducted on molecule generation and sequence generation to study the effectiveness of the proposed method.
strength_and_weaknesses: Strengths
1.	This paper extends the GFlowNets proposed for single-objective optimization to multi-objective optimization. 
2.	Analyses are conducted to study the main components of MOGFNs. 

Weaknesses
1.	The goal of the research in this paper is not clear. How is diversity defined if it is not to cover the Pareto front of a multi-objective optimization problem?
2.	The proposed algorithm is mainly based on the assumption that a multi-objective optimization problem can be viewed as a family of single-objective problems defined by non-negative weighted vectors. This might be inappropriate when the Pareto front is not convex. 
3.	Similar to this paper, decomposition-based multi-objective evolutionary algorithms such as MOEA/D solve multi-objective optimization problems by considering a set of single-objective sub-problems. The advantages of the proposed method over such methods need to be discussed and evaluated.

clarity,_quality,_novelty_and_reproducibility: This paper is not well-organized. The problem to be solved is unclear and the novelty of the proposed method needs more discussions.
summary_of_the_review: This paper proposes a new method for multi-objective optimization. However, the advantages and effectiveness of the proposed method are not well described and evaluated.
review_title: null

Meta-review: metareview:_summary,_strengths_and_weaknesses: This paper proposes a new method for sampling points on the Pareto frontier and for performing multi-objective optimization with expensive-to-evaluate objectives. In addition to the standard criteria for these problems, the method aims to generate Pareto-optimal inputs that are different from each other (in the input space), with applications in drug discovery.

The paper is based closely on GFlowNets, recently proposed by Bengio et al. 2021b. This is a method for sampling inputs x approximately proportionally to their reward distribution.

The method in this paper, MOGFN-PC, for generating diverse inputs on the Pareto frontier works as follows:
1. choose a scalarization of the multiple objectives, which depends on a "preference" parameter omega
2. train a GFlowNet to sample inputs x proportionally to this scalarized reward, given the preference parameter
3. To sample candidates, draw the preference parameter at random (the paper proposes using a Dirichlet distribution), then sample from the GFlowNet

The second method in this paper, MOGFN-AL, for doing multi-objective optimization of expensive functions works as follows:
1. Choose a multi-objective BayesOpt acquisition function (the paper proposed expected hypervolume improvement, from Daulton et al., 2022)
2. Use GFlowNets to sample inputs proportional to this acquisition function
3. Evaluate the objective function at these candidates
4. Repeat, supplying these evaluations as input to the BayesOpt method

These methods are designed to work in complex discrete design spaces, such as those arising in molecular discovery.

3 reviewers provided reviews with two reviewers rating the paper a 3 and one rating it an 8. Given this substantial diversity in opinions, I spent additional time reviewing the paper myself. 

Strengths
1. Diversity is an important characteristic in drug discovery --- if one candidate compound turns out to be poor as a drug because of some unanticipated constraint, it is useful to have other compounds that are different and thus likely to not also fail this same constraint.
2. The proposed methods outperform baselines in an interesting set of experiments with complex high-dimensional inputs 

Weaknesses
1. Lack of novelty. The first proposed method, MOGFN-PC, combines GFlowNets and scalarizations in a straightforward way. The second proposed method, MOGFN-AL, combines GFlowNets and (MOO) Bayesian in a straightforward way. The second method is also close to GFlowNet-AL (Jain et al., 2022).

2. Given how well-studied the space of MOO for expensive functions is, the evaluations leave out many strong baselines. The paper mentions that MORBO (Daulton et al., 2022) and LaMOO (Zhao et al., 2022) are left out because they are designed for continuous spaces, but as the paper describes, there are now-standard methods for embedding molecular spaces into the continuum that could be used (e.g., Gómez-Bombarelli et al. 2018). Given that hypervolume is the quality measure used to measure optimization performance (Fig 2) in this setting, it seems important to include as baselines more BayesOpt methods that explicitly seek to optimize hypervolume. 

3. The quality of the results are sensitive to the scalarization chosen and the parameter beta that governs the concentration of the reward density. For the hypervolume, there is a factor of 3 difference between the best and worst out of the 3 values evaluated for beta, and a factor of 4 for the scalarization. Similarly, there is roughly a factor of 2 difference for the reward and R_2 metrics. Moreover, there does not seem to be a principled or robust way to choose these parameters.

4. Lack of clarity. Despite the conceptual simplicity of its approach, the paper is difficult to read.


Gómez-Bombarelli, Rafael, et al. "Automatic chemical design using a data-driven continuous representation of molecules." ACS central science 4.2 (2018): 268-276. 
justification_for_why_not_higher_score: - Insufficient novelty
- Evaluations leave out important baselines
- Sensitivity of the method's performance to its input parameters without a clear way to choose these
- Lack of clarity
Decision: Reject