Divide and Learn: Multi-Objective Combinatorial Optimization at Scale

2026-02-11

AI Summary

This work proposes an online learning framework based on decomposed decision spaces for multi-objective combinatorial optimization over exponentially large discrete spaces. By reformulating the problem as a sequential construction task and incorporating an adaptive expert-guided strategy, the approach solves a multi-armed bandit subproblem at each position. It is the first to integrate decomposition-based search with online learning, achieving a regret bound that depends only on the subproblem dimensionality rather than the size of the combinatorial space, thereby significantly improving scalability. On standard benchmarks, the method attains 80–98% of the performance of specialized solvers while being two to three orders of magnitude more sample- and computation-efficient than Bayesian optimization. In real-world applications such as AI accelerator co-design, it consistently outperforms existing methods under fixed evaluation budgets, with performance gains amplifying as problem scale and objective count increase.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Online Learning & Bandits
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

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.

Problem

• multi-objective combinatorial optimization
• Pareto-optimal solutions
• scalability
• discrete optimization
• online learning

Innovation

• multi-objective combinatorial optimization
• decomposed decision space
• online learning
• bandit optimization
• regret bounds