Computationally-Optimal Real-Resource Strategies

TL;DR

This paper develops a pseudopolynomial-time algorithm for constructing computationally optimal strategies to manage uncertain resource costs in problem-solving, addressing the complexity of combining multiple methods.

Contribution

It introduces an algorithm for generating optimal strategies considering uncertain costs and proves the problem's NP-completeness, applying Bellman's principle for efficiency.

Findings

Algorithm efficiently constructs optimal strategies.

Proves the problem is NP-complete.

Demonstrates applicability to multiple methods.

Abstract

This paper focuses on managing the cost of deliberation before action. In many problems, the overall quality of the solution reflects costs incurred and resources consumed in deliberation as well as the cost and benefit of execution, when both the resource consumption in deliberation phase, and the costs in deliberation and execution are uncertain and may be described by probability distribution functions. A feasible (in terms of resource consumption) strategy that minimizes the expected total cost is termed computationally-optimal. For a situation with several independent, uninterruptible methods to solve the problem, we develop a pseudopolynomial-time algorithm to construct generate-and-test computationally optimal strategy. We show this strategy-construction problem to be NP-complete, and apply Bellman's Optimality Principle to solve it efficiently.