The Learnability of an Unknown System From Input-Output Data

Abstract: Artificial intelligence is transforming how scientists build models, test ideas, and make predictions. Beneath these advances lies a fundamental question: from the data we collect, when is learning possible in principle, and when is it not? We cast inference as a game between a learner, who holds a pool of candidate models, and an adversary, who holds the unknown ground-truth system. The learner observes the system and selects a candidate model to achieve one of three goals: identify the system, predict its output, or verify an input. We analyze 81 cases that arise by varying these goals, the available observations from both ground truth and candidates, and whether systems are single- or multi-valued. For each case, we prove whether universal solvability is possible. By clarifying which observations make success achievable in principle, our results explain why certain data-driven problems are solvable and guide how to collect data and evaluate models.

Submission Type: Regular submission (no more than 12 pages of main content)

Previous TMLR Submission Url: https://openreview.net/forum?id=bDLWLmP3LM

Changes Since Last Submission: The paper was previously desk-rejected due to an incorrect font. The font has been corrected in this submission.

Assigned Action Editor: ~Gilles_Louppe1

Submission Number: 8567