Learning Implicitly with Noisy Data in Linear Arithmetic
This work addresses robust learning for AI systems dealing with real-world noisy data, representing an incremental extension of existing theoretical frameworks.
The paper tackles robust learning in linear arithmetic with noisy data by extending implicit learning in PAC-Semantics to handle intervals and threshold uncertainty, proving polynomial-time complexity and empirically showing it outperforms explicit approaches on benchmark problems.
Robust learning in expressive languages with real-world data continues to be a challenging task. Numerous conventional methods appeal to heuristics without any assurances of robustness. While probably approximately correct (PAC) Semantics offers strong guarantees, learning explicit representations is not tractable, even in propositional logic. However, recent work on so-called "implicit" learning has shown tremendous promise in terms of obtaining polynomial-time results for fragments of first-order logic. In this work, we extend implicit learning in PAC-Semantics to handle noisy data in the form of intervals and threshold uncertainty in the language of linear arithmetic. We prove that our extended framework keeps the existing polynomial-time complexity guarantees. Furthermore, we provide the first empirical investigation of this hitherto purely theoretical framework. Using benchmark problems, we show that our implicit approach to learning optimal linear programming objective constraints significantly outperforms an explicit approach in practice.