Incrementally Learning Time-varying Half-planes

Part of Advances in Neural Information Processing Systems 4 (NIPS 1991)

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Anthony Kuh, Thomas Petsche, Ronald Rivest


We present a distribution-free model for incremental learning when concepts vary with time. Concepts are caused to change by an adversary while an incremental learning algorithm attempts to track the changing concepts by minimizing the error between the current target concept and the hypothesis. For a single half(cid:173) plane and the intersection of two half-planes, we show that the average mistake rate depends on the maximum rate at which an adversary can modify the concept. These theoretical predictions are verified with simulations of several learning algorithms including back propagation.