Markovian Pandora's box

TL;DR

This paper introduces the Markovian Pandora's Box problem, analyzing decision strategies in graph-structured, Markovian reward settings, and proposes algorithms with near-optimal performance and significant computational speedups.

Contribution

It extends Pandora's Box problem to Markovian reward dependencies within graph structures and develops new strategies with provable approximation guarantees.

Findings

Optimal fully adaptive strategies for forest-structured graphs

Near-optimal strategies with speedup over exact solutions

Significant computational improvements as graph size increases

Abstract

In this paper, we study the Markovian Pandora's Box Problem, where decisions are governed by both order constraints and Markovianly correlated rewards, structured within a shared directed acyclic graph. To the best of our knowledge, previous work has not incorporated Markovian dependencies in this setting. This framework is particularly relevant to applications such as data or computation driven algorithm design, where exploration of future models incurs cost. We present optimal fully adaptive strategies where the associated graph forms a forest. Under static transition, we introduce a strategy that achieves a near optimal expected payoff in multi line graphs and a 1/2 approximation in forest-structured graphs. Notably, this algorithm provides a significant speedup over the exact solution, with the improvement becoming more pronounced as the graph size increases. Our findings deepen the understanding of sequential exploration under Markovian correlations in graph-based decision-making.