Knothe-Rosenblatt Quantile Regression for Risk-sensitive Multi-objective Reinforcement Learning

In this work, we extend distributional reinforcement learning (RL) to develop a risk-sensitive multi-objective RL framework, with applications to domains such as finance and robotics. We achieve this by adopting vector-risk measures and approximating them via Knothe-Rosenblatt (KR) quantile regression. This approach directly extends the IQN framework to the multi-objective setting, aligns with the axiomatic definition of vector-risk measures, and guarantees that critics converge under the distributional Bellman operator. To mitigate the artificial ordering imposed by the KR map, we employ a transformer architecture without positional encoding, and introduce MO-TQC for training stability. We demonstrate improved performance on MO-Gymnasium benchmarks and use our framework to study risk-sensitive policies in multi-objective tasks.