Time-inconsistent behavior, such as procrastination or abandonment of long-term goals, arises when agents evaluate immediate outcomes disproportionately higher than future ones. This leads to globally suboptimal behavior, where plans are frequently revised or abandoned entirely. In the influential model of Kleinberg and Oren (2014) such behavior is modeled by a present-biased agent navigating a task graph toward a goal, making locally optimal decisions at each step based on discounted future costs. As a result, the agent may repeatedly deviate from initial plans. Recent work by Belova et al. (2024) introduced a two-agent extension of this model, where a fully-aware principal attempts to guide the present-biased agent through a specific set of critical tasks without causing abandonment. This captures a rich class of principal-agent dynamics in behavioral settings. In this paper, we provide a comprehensive algorithmic characterization of this problem. We analyze its computational complexity through the framework of parameterized algorithms, focusing on graph parameters that naturally emerge in this setting, such as treewidth, vertex cover, and feedback vertex set. Our main result is a fixed-parameter tractable algorithm when parameterized by the treewidth of the task graph and the number of distinct (v,t)-path costs. Our algorithm encaptures several input settings, such as bounded edge costs and restricted task graph structure. We demonstrate that our main result yields efficient algorithms for a number of such configurations. We complement this with tight hardness results, that highlight the extreme difficulty of the problem even on simplest graphs with bounded number of nodes and constant parameter values, and motivate our choice of parameters. We delineate tractable and intractable regions of the problem landscape, which include answers to open questions of Belova et al. (2024).

翻译：时间不一致行为（如拖延或放弃长期目标）源于智能体对即时结果的评估远高于未来结果。这导致全局次优行为，即计划频繁被修改或完全放弃。在Kleinberg与Oren（2014）提出的影响深远的模型中，此类行为被建模为一个现时偏好的智能体在任务图中向目标移动，基于折现的未来成本在每一步做出局部最优决策。因此，智能体可能反复偏离初始计划。Belova等人（2024）的最新研究提出了该模型的双智能体扩展，其中一个完全知情的主导者试图引导现时偏好智能体完成特定关键任务集合而不导致其放弃。这捕捉了行为场景中丰富的主导者-智能体动态关系。本文对该问题进行了全面的算法刻画。我们通过参数化算法框架分析其计算复杂度，重点关注该场景中自然涌现的图参数，如树宽、顶点覆盖和反馈顶点集。我们的核心成果是当以任务图的树宽和不同(v,t)路径成本数量为参数时，该问题存在固定参数可解算法。该算法涵盖多种输入场景，如有界边成本和受限任务图结构。我们证明了核心成果可为多种此类配置生成高效算法。我们进一步给出了紧致硬度结果，这些结果揭示了即使在节点数有界且参数值为常数的简单图上，该问题仍具有极端困难性，从而佐证了我们对参数的选择。我们划定了该问题版图中可解与不可解的区域，其中包含对Belova等人（2024）开放问题的解答。