Divide and Learn: Multi-Objective Combinatorial Optimization at Scale

TL;DR

This paper introduces a scalable online learning approach for multi-objective combinatorial optimization, achieving high efficiency and competitive performance on benchmarks and real-world problems by reformulating the task as position-wise bandit subproblems.

Contribution

It presents a novel reformulation of multi-objective combinatorial optimization as an online learning problem with regret guarantees, enabling scalable and efficient solutions.

Findings

Achieves 80-98% of specialized solvers' performance on benchmarks.

Provides 2-3 orders of magnitude improvement in sample and computational efficiency.

Outperforms competing methods in real-world hardware-software co-design tasks.

Abstract

Multi-objective combinatorial optimization seeks Pareto-optimal solutions over exponentially large discrete spaces, yet existing methods sacrifice generality, scalability, or theoretical guarantees. We reformulate it as an online learning problem over a decomposed decision space, solving position-wise bandit subproblems via adaptive expert-guided sequential construction. This formulation admits regret bounds of $O(d\sqrt{T \log T})$ depending on subproblem dimensionality \(d\) rather than combinatorial space size. On standard benchmarks, our method achieves 80--98\% of specialized solvers performance while achieving two to three orders of magnitude improvement in sample and computational efficiency over Bayesian optimization methods. On real-world hardware-software co-design for AI accelerators with expensive simulations, we outperform competing methods under fixed evaluation budgets. The advantage grows with problem scale and objective count, establishing bandit optimization over decomposed decision spaces as a principled alternative to surrogate modeling or offline training for multi-objective optimization.