# Dual-Mandate Patrols: Multi-Armed Bandits for Green Security

arXiv: https://arxiv.org/abs/2009.06560 · HTML: https://mlsanity.com/paper/2009.06560/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Sep 2020.

## Built on by (most cited first, 14 of 14)

- [Calibrated Stackelberg Games: Learning Optimal Commitments Against Calibrated Agents](https://mlsanity.com/paper/2306.02704/) (2023)
- [Optimistic Whittle Index Policy: Online Learning for Restless Bandits](https://mlsanity.com/paper/2205.15372/) (2022)
- [Artificial Replay: A Meta-Algorithm for Harnessing Historical Data in Bandits](https://mlsanity.com/paper/2210.00025/) (2022)
- [Robust Reinforcement Learning Under Minimax Regret for Green Security](https://mlsanity.com/paper/2106.08413/) (2021)
- [Composite Flow Matching for Reinforcement Learning with Shifted-Dynamics Data](https://mlsanity.com/paper/2505.23062/) (2025)
- [Selective Intervention Planning using Restless Multi-Armed Bandits to Improve Maternal and Child Health Outcomes](https://mlsanity.com/paper/2103.09052/) (2021)
- [Networked Restless Multi-Armed Bandits for Mobile Interventions](https://mlsanity.com/paper/2201.12408/) (2022)
- [Robust Optimization with Diffusion Models for Green Security](https://mlsanity.com/paper/2503.05730/) (2025)
- [Revisiting Matrix Sketching in Linear Bandits: Achieving Sublinear Regret via Dyadic Block Sketching](https://mlsanity.com/paper/2410.10258/) (2024)
- [Ranked Prioritization of Groups in Combinatorial Bandit Allocation](https://mlsanity.com/paper/2205.05659/) (2022)
- [Reflections from the Workshop on AI-Assisted Decision Making for Conservation](https://mlsanity.com/paper/2307.08774/) (2023)
- [Combining Diverse Information for Coordinated Action: Stochastic Bandit Algorithms for Heterogeneous Agents](https://mlsanity.com/paper/2408.03405/) (2024)
- [GINO-Q: Learning an Asymptotically Optimal Index Policy for Restless Multi-armed Bandits](https://mlsanity.com/paper/2408.09882/) (2024)
- [A Unified Online-Offline Framework for Co-Branding Campaign Recommendations](https://mlsanity.com/paper/2505.22254/) (2025)

## Abstract (arXiv)

Conservation efforts in green security domains to protect wildlife and forests are constrained by the limited availability of defenders (i.e., patrollers), who must patrol vast areas to protect from attackers (e.g., poachers or illegal loggers). Defenders must choose how much time to spend in each region of the protected area, balancing exploration of infrequently visited regions and exploitation of known hotspots. We formulate the problem as a stochastic multi-armed bandit, where each action represents a patrol strategy, enabling us to guarantee the rate of convergence of the patrolling policy. However, a naive bandit approach would compromise short-term performance for long-term optimality, resulting in animals poached and forests destroyed. To speed up performance, we leverage smoothness in the reward function and decomposability of actions. We show a synergy between Lipschitz-continuity and decomposition as each aids the convergence of the other. In doing so, we bridge the gap between combinatorial and Lipschitz bandits, presenting a no-regret approach that tightens existing guarantees while optimizing for short-term performance. We demonstrate that our algorithm, LIZARD, improves performance on real-world poaching data from Cambodia.