USCO-Solver: Solving Undetermined Stochastic Combinatorial Optimization Problems

TL;DR

USCO-Solver introduces a universal approach for solving stochastic combinatorial optimization problems with unknown objectives, leveraging empirical data without explicit objective learning, and demonstrates promising results on synthetic and real datasets.

Contribution

The paper proposes a novel universal solver for undetermined stochastic combinatorial problems that avoids learning the objective function, supported by PAC-Bayesian analysis and empirical validation.

Findings

High-quality solutions achieved without explicit objective learning

Effective across multiple classic combinatorial problems

Promising results on both synthetic and real-world datasets

Abstract

Real-world decision-making systems are often subject to uncertainties that have to be resolved through observational data. Therefore, we are frequently confronted with combinatorial optimization problems of which the objective function is unknown and thus has to be debunked using empirical evidence. In contrast to the common practice that relies on a learning-and-optimization strategy, we consider the regression between combinatorial spaces, aiming to infer high-quality optimization solutions from samples of input-solution pairs -- without the need to learn the objective function. Our main deliverable is a universal solver that is able to handle abstract undetermined stochastic combinatorial optimization problems. For learning foundations, we present learning-error analysis under the PAC-Bayesian framework using a new margin-based analysis. In empirical studies, we demonstrate our design using proof-of-concept experiments, and compare it with other methods that are potentially applicable. Overall, we obtain highly encouraging experimental results for several classic combinatorial problems on both synthetic and real-world datasets.