  Solving multi-objective optimization problems is important in various
applications where users are interested in obtaining optimal policies subject
to multiple, yet often conflicting objectives. A typical approach to obtain
optimal policies is to first construct a loss function that is based on the
scalarization of individual objectives, and then find the optimal policy that
minimizes the loss. However, optimizing the scalarized (and weighted) loss does
not necessarily provide guarantee of high performance on each possibly
conflicting objective because it is challenging to assign the right weights
without knowing the relationship among these objectives. Moreover, the
effectiveness of these gradient descent algorithms is limited by the agent's
ability to explain their decisions and actions to human users. The purpose of
this study is two-fold. First, we propose a vector value function based
multi-objective reinforcement learning (V2f-MORL) approach that seeks to
quantify the inter-objective relationship via reinforcement learning (RL) when
the impact of one objective on others is unknown a prior. In particular, we
construct one actor and multiple critics that can co-learn the policy and
inter-objective relationship matrix (IORM), quantifying the impact of
objectives on each other, in an iterative way. Second, we provide a semantic
representation that can uncover the trade-off of decision policies made by
users to reconcile conflicting objectives based on the proposed V2f-MORL
approach for the explainability of the generated behaviors subject to given
optimization objectives. We demonstrate the effectiveness of the proposed
approach via a MuJoCo based robotics case study.
