A Single Deep Preference-Conditioned Policy for Learning Pareto Coverage Sets

• URL: http://arxiv.org/abs/2605.08946v1
• Date: Sat, 09 May 2026 13:35:50 GMT
• Title: A Single Deep Preference-Conditioned Policy for Learning Pareto Coverage Sets
• Abstract summary: We study the uniqueness and continuity of the preference-to-solution correspondence under nonlinear scalarization.<n>We use smooth Tchebycheff scalarization as a monotone utility to solve the problem.<n>We show that each update is equivalent to solving a Kullback-Leibler-regularized MDP with the previous policy as reference.
• Score: 0.4369550829556578
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Preference-conditioned multi-objective reinforcement learning aims to learn a single policy that captures trade-offs across preferences, but under nonlinear scalarization the uniqueness and continuity of the preference-to-solution correspondence remain unclear. We study this problem in tabular multi-objective Markov decision processes (MDPs) using smooth Tchebycheff scalarization as a monotone utility. Under mild interior conditions on the preference set, we prove that each preference induces a unique Pareto-optimal return vector and that this vector depends Lipschitz-continuously on the preference, providing a principled foundation for preference sweeping toward dense Pareto-front coverage. To compute these targets, we formulate the problem over occupancy measures and derive Concave Mirror Descent Policy Iteration (CMDPI), which achieves an $O(1/k)$ objective-suboptimality rate. We further show that each update is equivalent to solving a Kullback-Leibler-regularized MDP with the previous policy as reference, yielding a policy-iteration interpretation and finite-iterate policy continuity across preferences. We instantiate the update as a deep actor-critic algorithm preserving previous-policy regularization. On eight MO-Gymnasium tasks, it achieves the best average hypervolume rank among recent baselines and strong expected-utility performance. Continuous-control experiments indicate gains beyond the discrete-action setting.

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