Abstract: 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.