Optimal Mistake Bound Learning Is Hard

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...

Separating Distribution-Free and Mistake-Bound Learning Models

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...

Optimal Pricing Is Hard

We show that computing the revenue-optimal deterministic auction in unit-demand single-buyer Bayesian settings, i.e. the optimal itempricing, is computationally hard even in single-item settings where the buyer’s value distribution is a sum of independently distributed attributes, or multi-item settings where the buyer’s values for the items are independent. We also show that it is intractable ...

Learning Convex Bodies is Hard

We show that learning a convex body in R, given random samples from the body, requires 2 √