Noisy Search with Comparative Feedback

TL;DR

This paper analyzes the query complexity of noisy search with feedback that varies with distance, showing it can find a target in O(log n) queries and revealing a surprising log log k speedup limit.

Contribution

It provides new theoretical bounds on query complexity in noisy, distance-dependent feedback search models, including a surprising logarithmic speedup limit.

Findings

Target can be found in O(log n) queries.

Speedup with k answers per query is limited to log log k.

Feedback noise depends on distance, affecting search efficiency.

Abstract

We present theoretical results in terms of lower and upper bounds on the query complexity of noisy search with comparative feedback. In this search model, the noise in the feedback depends on the distance between query points and the search target. Consequently, the error probability in the feedback is not fixed but varies for the queries posed by the search algorithm. Our results show that a target out of n items can be found in O(log n) queries. We also show the surprising result that for k possible answers per query, the speedup is not log k (as for k-ary search) but only log log k in some cases.