  In this paper, we aim to utilize only offline trajectory data to train a
policy for multi-objective RL. We extend the offline policy-regularized method,
a widely-adopted approach for single-objective offline RL problems, into the
multi-objective setting in order to achieve the above goal. However, such
methods face a new challenge in offline MORL settings, namely the
preference-inconsistent demonstration problem. We propose two solutions to this
problem: 1) filtering out preference-inconsistent demonstrations via
approximating behavior preferences, and 2) adopting regularization techniques
with high policy expressiveness. Moreover, we integrate the
preference-conditioned scalarized update method into policy-regularized offline
RL, in order to simultaneously learn a set of policies using a single policy
network, thus reducing the computational cost induced by the training of a
large number of individual policies for various preferences. Finally, we
introduce Regularization Weight Adaptation to dynamically determine appropriate
regularization weights for arbitrary target preferences during deployment.
Empirical results on various multi-objective datasets demonstrate the
capability of our approach in solving offline MORL problems.
