Compositional Online Learning for Multi-Objective System Co-Design

TL;DR

This paper introduces an efficient online decision-making framework for multi-objective system co-design, using optimistic evaluators and elimination algorithms to identify optimal trade-offs with fewer evaluations.

Contribution

It develops a novel elimination-based algorithm with theoretical guarantees, applicable to compositional co-design problems modeled by multigraphs, improving sample efficiency.

Findings

Substantial sample-efficiency gains over existing methods.

Effective propagation of optimistic certificates in multigraph models.

Validated on multi-robot, mobility systems, and synthetic benchmarks.

Abstract

Many engineered systems must balance competing objectives, such as performance and safety, cost and reliability, or efficiency and sustainability, and are naturally modeled as compositions of interacting subsystems. We study online multi-objective decision-making in monotone co-design, where functionalities and resources are partially ordered, and the goal is to identify the target-feasible antichain of non-dominated trade-offs using few expensive evaluations. We introduce optimistic evaluators: history-dependent bounds on functionality and resource mappings that enable safe elimination of implementations before full evaluation. Based on these evaluators, we develop an elimination-based rejection-sampling algorithm, prove its soundness, and show that the admissible region shrinks monotonically as information accumulates. We instantiate the framework under monotonicity, Lipschitz continuity, and linear-parametric structure. For compositional co-design problems modeled by multigraphs, we show how local optimistic certificates propagate through the tractable remainder of the graph to yield system-level optimistic feasibility and resource bounds. Experiments on multi-robot fleet design, intermodal mobility systems, and synthetic monotone and Lipschitz benchmarks show substantial sample-efficiency gains over uniform sampling, Bayesian optimization, and multi-objective evolutionary algorithms.