USCO-Solver: Solving Undetermined Stochastic Combinatorial Optimization Problems
This addresses decision-making under uncertainty for real-world systems, but it appears incremental as it builds on regression between combinatorial spaces rather than introducing a new paradigm.
The paper tackles undetermined stochastic combinatorial optimization problems by proposing a universal solver that infers high-quality solutions directly from input-solution pairs without learning the objective function, achieving encouraging results on synthetic and real-world datasets.
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.