SlowGuess/NeurIPS_2023_OCR huggingface dataset:
However, if we look at the problem in a bigger picture, the time costs for model training are likely negligible compared to those of evaluating molecular candidates in real-world applications. Therefore, we argue that the high quality of the candidates (the performance of the MOBO algorithm) is more essential than having a lower training cost.
C.1 Sampled molecules in MOBO experiments
We give some examples of sampled molecules from the Pareto front by HN-GFN in the GSK3 $\beta$  + JNK3 + QED + SA optimization setting (Figure 4). The numbers below each molecule refer to GSK3 $\beta$ , JNK3, QED, and SA scores respectively.
Figure 4: Sampled molecules from the approximate Pareto front by HN-GFN.
C.2 Synthetic scenario
As illustrated in Figure 5, the distribution of Top-100 GSK3 $\beta$  scores shows a consistent trend in preference-specific GFlowNet and our proposed HN-GFN, although the trend is not as significant as the JNK3 property.
Figure 5: Comparison of the distribution of Top-100 GSK3 $\beta$  scores sampled by different preference vectors using preference-specific GFlowNets and HN-GFN.
C.3 Effect of Surrogate models
We conduct ablation experiments to study the effectiveness of different surrogate models. We consider the following three surrogate models: evidential regression [1], Deep Ensembles [39], and GP based on the Tanimoto kernel [59]. As shown in Table 5, we can observe that evidential regression leads to better optimization performance than Deep Ensembles. While the HV of evidential regression and GP is comparable, evidential regression can propose more diverse candidates. Furthermore, we argue that GP is less flexible over discrete spaces than evidential regression and Deep Ensembles, as different kernels need to be designed according to the data structures.
GSK3β + JNK3	GSK3β + JNK3 + QED + SA
HV	Div	HV	Div
N-GFN (Evidential)	0.669 ± 0.061	0.793 ± 0.007	0.416 ± 0.023	0.738 ± 0.009
N-GFN (Ensemble)	0.583 ± 0.103	0.797 ± 0.004	0.355 ± 0.048	0.761 ± 0.012
N-GFN (GP)	0.662 ± 0.054	0.739 ± 0.008	0.421 ± 0.037	0.683 ± 0.018
Table 5: Evaluation of different surrogate models in MOBO scenarios
D Comparison with parallel work
While the concept of Pareto GFlowNet was theoretically discussed in Bengio et al. [7], we are among the first to study and instantiate this concept for MOO, and we address practical challenges that are not discussed thoroughly in the original theoretical exposition to potentially make sample-efficient molecular optimization a reality. We extensively study the impact of the conditioning mechanism (Section 5.1) and surrogate models (Appendix C.3). Moreover, we delicately propose a hindsight-like off-policy strategy (Section 4.3) which is rarely studied for MOO (in both the RL and GFlowNet literature).
We note that there is a parallel work introduced in Jain et al. [29], which shares the idea of using GFlowNets for MOO. In Jain et al. [29], they propose two variants MOGFN-PC and MOGFN-AL for MOO in the single-round scenario and Bayesian optimization (BO) scenario, respectively. Indeed, when HN-GFN is used as a stand-alone optimizer outside of MOBO (Section 5.1), it is similar to MOGFN-PC except for using different conditioning mechanisms. As for MOBO, MOGFN-AL is a vanilla GFlowNet whose reward function is defined as a multi-objective acquisition function (NEHVI [13]). In addition to extending GFlowNet, we delicately propose a hindsight-like off-policy strategy (Section 4.3) which is rarely studied for MOO (in both the RL and GFlowNet literature).