Tight Bounds for Blind Search on the Integers
Martin Dietzfelbinger, Jonathan E. Rowe, Ingo Wegener, Philipp Woelfel

TL;DR
This paper establishes tight bounds on the expected time for a random process to reach zero in a bounded interval, using optimal probability distributions, with implications for blind optimization strategies.
Contribution
It introduces a novel potential function method to derive tight bounds for the expected hitting time in a blind search process on integers.
Findings
Expected time is Θ((log n)^2) for optimal distribution.
Introduces a new potential function technique for analysis.
Results inform blind optimization of continuous functions.
Abstract
We analyze a simple random process in which a token is moved in the interval A=\{0,...,n\: Fix a probability distribution over \{1,...,n\. Initially, the token is placed in a random position in . In round , a random value is chosen according to . If the token is in position , then it is moved to position . Otherwise it stays put. Let be the number of rounds until the token reaches position 0. We show tight bounds for the expectation of for the optimal distribution . More precisely, we show that . For the proof, a novel potential function argument is introduced. The research is motivated by the problem of approximating the minimum of a continuous function over with a ``blind'' optimization strategy.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
