On Greedy and Strategic Evaders in Sequential Interdiction Settings with Incomplete Information

TL;DR

This paper investigates strategic evasion in sequential network interdiction where the interdictor has incomplete information, proposing heuristics that outperform greedy policies and analyzing the complexity of evasion strategies.

Contribution

It introduces a heuristic for strategic evasion under greedy interdiction and analyzes the computational complexity of evasion policies with incomplete network information.

Findings

Heuristic outperforms greedy evasion policies on synthetic networks.

Optimal evasion policies have specific properties in two-epoch scenarios.

Evasion complexity varies with initial information and feedback noise.

Abstract

We consider a class of sequential network interdiction problem settings where the interdictor has incomplete initial information about the network while the evader has complete knowledge of the network including its structure and arc costs. In each decision epoch, the interdictor can block (for the duration of the epoch) at most $k$ arcs known to him/her. By observing the evader's actions, the interdictor learns about the network structure and costs and thus, can adjust his/her actions in subsequent decision epochs. It is known from the literature that if the evader is greedy (i.e., the shortest available path is used in each decision epoch), then under some assumptions the greedy interdiction policies that block $k$-most vital arcs in each epoch are efficient and have a finite regret. In this paper, we consider the evader's perspective and explore deterministic "strategic" evasion policies under the assumption that the interdictor is greedy. We first study the theoretical computational complexity of the evader's problem. Then we derive basic constructive properties of optimal evasion policies for two decision epochs when the interdictor has no initial information about the network structure. These properties are then exploited for the design of a heuristic algorithm for a strategic evader in a general setting with an arbitrary time horizon and any initial information available to the interdictor. Our computational experiments demonstrate that the proposed heuristic outperforms the greedy evasion policy on several classes of synthetic network instances under either perfect or noisy information feedback. Finally, some interesting insights from our theoretical and computational results conclude the paper.