DRMDP with empathetic relationships: a social learning approach for cost reduction and decision stability

The Markov decision process (MDP) provides a framework for sequential decision optimization under uncertainty and serves as a foundation for dynamic programming problems. However, current robust optimization approaches often overlook the social attributes of decision-makers (DMs), while behavioral models that do account for social factors often treat them as external constraints rather than integrating them into a distributionally robust optimization (DRO) framework. To address these challenges, we construct a distributionally robust Markov decision process (DRMDP) that integrates empathetic relationships, aiming to minimize the system's total cost while also improving decision-making stability. First, we model DM profiles and the dynamic evolution of a group trust network to capture the effects of subjective performance evaluation. Next, we establish a principled learning process to generate a global empathetic weight matrix. Then, we construct a psychological cost mechanism that quantifies deviations from group consensus and trades off economic objectives against social alignment. Subsequently, we design an improved DRO process to analyze the stability of the MDP under empathetic relationships. Finally, experiments reveal a synergistic effect: the empathetic mechanism mitigates the conservatism of pure robust strategies, leading to a substantial reduction in both average total cost and cost dispersion. These findings demonstrate that high-quality group consensus can complement the data-derived robustness enhancing both economic efficiency and decision stability.