Offline Multi-Objective Optimization

TL;DR

This work introduces Off-MOO-Bench, the first benchmark for offline multi-objective optimization, spanning synthetic-to-real-world tasks with shared evaluation protocols and open-source implementations. It analyzes offline MOO through four lenses—data, architecture, learning, and search—and proposes two surrogate-based frameworks using DNNs or Gaussian processes to approximate objectives from static datasets. Empirical results show that offline MOO methods can outperform the best training data but no single approach consistently dominates across tasks, highlighting the need for improved data utilization, surrogate accuracy, and search strategies. The benchmark and findings provide a structured basis for evaluating offline MOO methods and chart clear directions for future research, including handling mixed search spaces, high dimensionality, constraints, noise, and few-shot scenarios.

Abstract

Offline optimization aims to maximize a black-box objective function with a static dataset and has wide applications. In addition to the objective function being black-box and expensive to evaluate, numerous complex real-world problems entail optimizing multiple conflicting objectives, i.e., multi-objective optimization (MOO). Nevertheless, offline MOO has not progressed as much as offline single-objective optimization (SOO), mainly due to the lack of benchmarks like Design-Bench for SOO. To bridge this gap, we propose a first benchmark for offline MOO, covering a range of problems from synthetic to real-world tasks. This benchmark provides tasks, datasets, and open-source examples, which can serve as a foundation for method comparisons and advancements in offline MOO. Furthermore, we analyze how the current related methods can be adapted to offline MOO from four fundamental perspectives, including data, model architecture, learning algorithm, and search algorithm. Empirical results show improvements over the best value of the training set, demonstrating the effectiveness of offline MOO methods. As no particular method stands out significantly, there is still an open challenge in further enhancing the effectiveness of offline MOO. We finally discuss future challenges for offline MOO, with the hope of shedding some light on this emerging field. Our code is available at \url{https://github.com/lamda-bbo/offline-moo}.

Figures (6)

• Figure 1: Benchmarks for offline MOO.
• Figure 2: Objective space visualization of Multi-Head model without (left column) and with (right column) data pruning on RE21, where the upper and bottom rows correspond to the surrogate objective space and real objective space, respectively. Each point denotes a solution in the search history, whose color gradually changes from yellow to blue based on the iteration rounds of the search algorithm.
• Figure 3: Elites loss changes (upper) and objective space visualizations of the final solution set (bottom), for Vanilla Multi-head model and Multi-head model with GradNorm on the two tasks, DTLZ1 and NAS-Bench-201-Test.
• Figure 4: (a) The average rank of MOBO with different number of initial data points on six tasks. (b) The performance of four search algorithms on seven tasks.
• Figure 5: Visualization of datasets in Off-MOO-Bench. Blue points represent the offline dataset, and red points represent the 256 best-non-dominated solutions over the dataset. Note that some red dots are not visible in the graph due to the plot perspective.

Theorems & Definitions (1)

• Definition 2.1