CS 264 : Beyond Worst - Case Analysis Lecture # 19 : Self - Improving Algorithms ∗

The last several lectures discussed several interpolations between worst-case analysis and average-case analysis designed to identify robust algorithms in the face of strong impossibility results for worst-case guarantees. This lecture gives another analysis framework that blends aspects of worstand average-case analysis. In today’s model of self-improving algorithms, an adversary picks an input distribution, and then nature picks a sequence of i.i.d. samples from this distribution. This model is relatively close to traditional average-case analysis, but with the twist that the algorithm has to learn the input distribution (or a sufficient summary of it) from samples. It is not hard to think of real-world applications where there is enough data to learn over time an accurate distribution of future inputs (e.g., click-throughs on a major Internet platform). The model and results are by Ailon, Chazelle, Comandar, and Liu [1].