Rethinking Learnability in Offline Data-driven Optimization
A paper proposes algorithm-dependent learnability, which requires accuracy only on the optimizer's trajectory, and proves its value-query form is sufficient for greedy and local search in submodular maximization, while its first-order analogue is sufficient for projected gradient descent on convex minimization.
The paper addresses offline data-driven optimization, which seeks high-quality solutions using only a fixed set of previous evaluations. It notes that PAC learnability is insufficient because the optimal region may remain poorly learned. The authors introduce algorithm-dependent learnability and provide theoretical sufficiency results for representative discrete and continuous settings.
The proposed algorithm-dependent learnability relaxes the requirement of uniform accuracy over the entire domain, focusing only on points visited by the optimization algorithm. This could enable more sample-efficient offline optimization by aligning learning objectives with the optimizer's actual trajectory.
Offline data-driven optimization is relevant to industries where online evaluations are expensive or impossible, such as drug discovery, material design, and hardware tuning. A weaker learnability condition may lower data requirements and make offline optimization more practical.
If algorithm-dependent learnability reduces the amount of offline data needed for optimization, it could lower costs and accelerate design cycles in engineering and scientific applications.
Next signals include empirical validation of algorithm-dependent learnability on real-world offline optimization benchmarks, extension to stochastic or non-convex settings, and development of practical algorithms that exploit this weaker learnability condition.