Learning parities in the mistake-bound model

Learning Parities in the Mistake-Bound model

We study the problem of learning parity functions that depend on at most k variables (kparities) attribute-efficiently in the mistake-bound model. We design a simple, deterministic, polynomial-time algorithm for learning k-parities with mistake bound O(n1− 1 k ). This is the first polynomial-time algorithm to learn ω(1)-parities in the mistake-bound model with mistake bound o(n). Using the stan...

Expected Mistake Bound Model for On-Line Reinforcement Learning

We propose a model of eecient on-line reinforcement learning based on the expected mistake bound framework introduced by Haussler, Littlestone and Warmuth (1987). The measure of performance we use is the expected diierence between the total reward received by the learning agent and that received by an agent behaving optimally from the start. We call this expected diierence the cumulative mistak...

Separating Distribution-Free and Mistake-Bound Learning Models

Separating Distribution-Free and Mistake-Bound Learning Models over the Boolean Domain

Two of the most commonly used models in computational learning theory are the distribution-free model in which examples are chosen from a fixed but arbitrary distribution, and the absolute mistake-bound model in which examples are presented in an arbitrary order. Over the Boolean domain {0, 1}, it is known that if the learner is allowed unlimited computational resources then any concept class l...

Learning Parities with Structured Noise

In the learning parities with noise problem —well-studied in learning theory and cryptography— we have access to an oracle that, each time we press a button, returns a random vector a ∈ GF(2) together with a bit b ∈ GF(2) that was computed as a ·u+η, where u ∈ GF(2) is a secret vector, and η ∈ GF(2) is a noise bit that is 1 with some probability p. Say p = 1/3. The goal is to recover u. This ta...