Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Global-Order GFlowNets

Lluís Pastor-Pérez, Javier Alonso-Garcia, Lukas Mauch

TL;DR

This work addresses conflicts in multi-objective black-box optimization arising from local Pareto-ordering in Order-Preserving GFlowNets. It introduces Global-Order GFlowNets that impose a globally consistent ranking through two strategies—Global Rank and Nearest Neighbor Order—ensuring alignment with Pareto dominance. The authors evaluate the approach on DNA sequence generation, fragment-based molecule generation, and QM9, finding that global-order methods match or exceed prior OP- and PC-GFNs, with improved exploration and more non-dominated samples in several tasks. The results suggest that enforcing a global ordering is a promising direction for scalable, diverse Pareto-front sampling in MO problems, with Cheap-GR-GFNs offering computational efficiency advantages in high-dimensional settings.

Abstract

Order-Preserving (OP) GFlowNets have demonstrated remarkable success in tackling complex multi-objective (MOO) black-box optimization problems using stochastic optimization techniques. Specifically, they can be trained online to efficiently sample diverse candidates near the Pareto front. A key advantage of OP GFlowNets is their ability to impose a local order on training samples based on Pareto dominance, eliminating the need for scalarization - a common requirement in other approaches like Preference-Conditional GFlowNets. However, we identify an important limitation of OP GFlowNets: imposing a local order on training samples can lead to conflicting optimization objectives. To address this issue, we introduce Global-Order GFlowNets, which transform the local order into a global one, thereby resolving these conflicts. Our experimental evaluations on various benchmarks demonstrate the efficacy and promise of our proposed method.

Global-Order GFlowNets

TL;DR

This work addresses conflicts in multi-objective black-box optimization arising from local Pareto-ordering in Order-Preserving GFlowNets. It introduces Global-Order GFlowNets that impose a globally consistent ranking through two strategies—Global Rank and Nearest Neighbor Order—ensuring alignment with Pareto dominance. The authors evaluate the approach on DNA sequence generation, fragment-based molecule generation, and QM9, finding that global-order methods match or exceed prior OP- and PC-GFNs, with improved exploration and more non-dominated samples in several tasks. The results suggest that enforcing a global ordering is a promising direction for scalable, diverse Pareto-front sampling in MO problems, with Cheap-GR-GFNs offering computational efficiency advantages in high-dimensional settings.

Abstract

Order-Preserving (OP) GFlowNets have demonstrated remarkable success in tackling complex multi-objective (MOO) black-box optimization problems using stochastic optimization techniques. Specifically, they can be trained online to efficiently sample diverse candidates near the Pareto front. A key advantage of OP GFlowNets is their ability to impose a local order on training samples based on Pareto dominance, eliminating the need for scalarization - a common requirement in other approaches like Preference-Conditional GFlowNets. However, we identify an important limitation of OP GFlowNets: imposing a local order on training samples can lead to conflicting optimization objectives. To address this issue, we introduce Global-Order GFlowNets, which transform the local order into a global one, thereby resolving these conflicts. Our experimental evaluations on various benchmarks demonstrate the efficacy and promise of our proposed method.

Paper Structure

This paper contains 42 sections, 1 theorem, 9 equations, 13 figures, 7 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Multi-Objective Optimization
  4. Performance measures for Multi-Objective Optimization
  5. GFlowNets for multi-objective optimization
  6. Method
  7. Local Order Dilemma of OP GFNs
  8. Global Orders
  9. Global Rank
  10. Nearest Neighbor Order
  11. Experiments
  12. Replay Buffer and Cheap GFlowNets
  13. DNA Sequence Generation
  14. Results
  15. Fragment-Based Molecule Generation
  16. ...and 27 more sections

Key Result

Theorem 1

Let $\mathcal{X}$ be a set of samples with associated rewards $R_1, R_2, ..., R_d$, and let $\hat{R}: \mathcal{X} \to \mathbb{R}$ be a ranking function produced by the Global Rank algorithm. For any two samples $x_1, x_2 \in \mathcal{X}$, if $x_1$ Pareto dominates $x_2$, then $\hat{R}(x_1) > \hat{R}

Figures (13)

  • Figure 1: An example for the local order dilemma of OP GFNs. We can construct three different subsets $\mathcal{X}_1$, $\mathcal{X}_2$, $\mathcal{X}_3$, for which we can no longer construct $P(x;\theta)$ that is consistent with all conditionals.
  • Figure 2: $\hat{R}$ computed with Global Rank (left) and Nearest Neighbor (right) algorithms
  • Figure 3: The 1280 generated samples, with 18 unique samples for OP-GFNs compared to 356 of Cheap-GR-GFNs
  • Figure 4: Image of the different points in the $[0,1]\times [0,1]$. In orange, we find the Pareto front. In the first cases, we omit $r_1(x,y)=x$ for clarity.
  • Figure 5: Comparison of the algorithms Global Rank (left) and Nearest Neighbor Order (right) with different rewards
  • ...and 8 more figures

Theorems & Definitions (4)

  • Definition 1: MOO problem
  • Definition 2: Pareto Dominance and Pareto Set
  • Theorem 1: Consistency of Global Rank with Pareto Dominance
  • proof