Repeated Deceptive Path Planning against Learnable Observer

We study the problem of deceptive path planning (DPP), where an agent aims to conceal its true destination from external observers. While existing work assumes static, non-learning observers, real-world adversaries-such as in critical goods transportation or military operations-can adapt by learning from historical trajectories. To address this gap, we introduce Repeated Deceptive Path Planning (RDPP), a new formulation that explicitly models learnable observers. We show that existing DPP methods fail under this setting, as they cannot adapt to evolving adversarial predictions. While incorporating observer previous predictions into updates enables some adaptation, such incremental updates cause accumulative lag that degrades deception. To this end, we propose Deceptive Meta Planning (DeMP), a two-level optimization framework that combines episode-level adaptation, which enables short-term policy adjustment to counter updated observer, and meta-level updates, which leverage cross-episode feedback to capture how observers update their models and accelerate adaptation in future episodes. In this way, DeMP mitigates the accumulation of adaptation lag, enabling sustained deception against a learning observer. Experiments across environments demonstrate that DeMP significantly outperforms existing approaches in RDPP while maintaining competitive path cost. Our results highlight the importance of modeling repeated interactions with learnable adversaries, providing new insights into deception and privacy in multi-agent systems.