Tree Search Techniques for Minimizing Detectability and Maximizing Visibility

TL;DR

This paper formulates a game-theoretic approach to planning agent trajectories that balance visibility and detectability, introducing pruning techniques to efficiently compute optimal strategies in adversarial scouting scenarios.

Contribution

It models the visibility and detection trade-off as a two-player zero-sum game and proposes pruning methods to significantly reduce computational complexity while maintaining optimality.

Findings

Pruning reduces search nodes by approximately three orders of magnitude.

The approach effectively balances visibility and detectability in simulated scenarios.

Optimal policies can be computed more efficiently with the proposed techniques.

Abstract

We introduce and study the problem of planning a trajectory for an agent to carry out a scouting mission while avoiding being detected by an adversarial guard. This introduces an adversarial version of classical visibility-based planning problems such as the Watchman Route Problem. The agent receives a positive reward for increasing its visibility and a negative penalty when it is detected by the guard. The objective is to find a finite-horizon path for the agent that balances the trade-off maximizing visibility and minimizing detectability. We model this problem as a sequential two-player zero-sum discrete game. A minimax tree search can give the optimal policy for the agent but requires an exponential-time computation and space. We propose several pruning techniques to reduce the computational cost while still preserving optimality guarantees. Simulation results show that the proposed strategy prunes approximately three orders of magnitude nodes as compared to the brute-force strategy.