ほぼ不連続な関数の汎化誤差を抑えた暗黙学習
Generalization Bounded Implicit Learning of Nearly Discontinuous Functions
脚式移動やマニピュレーションで現れる接触の切り替わりによる不連続関数に対し、陽的・暗黙的な学習定式化の汎化誤差限界を導出し、違反ベースの暗黙損失が急峻な勾配に頑健であることを示した理論研究。
著者: Bibit Bianchini, Mathew Halm, Nikolai Matni, Michael Posa
分類: cs.RO
原文アブストラクト
Inspired by recent strides in empirical efficacy of implicit learning in many robotics tasks, we seek to understand the theoretical benefits of implicit formulations in the face of nearly discontinuous functions, common characteristics for systems that make and break contact with the environment such as in legged locomotion and manipulation. We present and motivate three formulations for learning a function: one explicit and two implicit. We derive generalization bounds for each of these three approaches, exposing where explicit and implicit methods alike based on prediction error losses typically fail to produce tight bounds, in contrast to other implicit methods with violation-based loss definitions that can be fundamentally more robust to steep slopes. Furthermore, we demonstrate that this violation implicit loss can tightly bound graph distance, a quantity that often has physical roots and handles noise in inputs and outputs alike, instead of prediction losses which consider output noise only. Our insights into the generalizability and physical relevance of violation implicit formulations match evidence from prior works and are validated through a toy problem, inspired by rigid-contact models and referenced throughout our theoretical analysis.
