Adjustable Coins

TL;DR

This paper explores optimal strategies for selecting among multiple algorithms with success probabilities and costs to minimize expected total cost, considering various problem variants and their computational complexity.

Contribution

It introduces a framework for adaptive algorithm selection with probabilistic success and costs, analyzing different variants and establishing hardness results.

Findings

Optimal strategies for algorithm selection are characterized.

Certain variants are proven to be computationally hard.

Solution approaches for specific cases are proposed.

Abstract

In this paper we consider a scenario where there are several algorithms for solving a given problem. Each algorithm is associated with a probability of success and a cost, and there is also a penalty for failing to solve the problem. The user may run one algorithm at a time for the specified cost, or give up and pay the penalty. The probability of success may be implied by randomization in the algorithm, or by assuming a probability distribution on the input space, which lead to different variants of the problem. The goal is to minimize the expected cost of the process under the assumption that the algorithms are independent. We study several variants of this problem, and present possible solution strategies and a hardness result.