On the Stability and Convergence of Entropy-Regularized Causal Decision Systems: The Kerimov-Alekberli Framework

Entropy-based accountability metrics for AI systems have recently been proposed to address the limitations of snapshot evaluation frameworks. However, the dynamical properties of such entropy-regularized decision systems remain poorly understood. In this paper, we analyze the stability and convergence properties of the Kerimov-Alekberli (KA) framework augmented with the Causal Entropic Responsibility (CER) metric. We formalize the resulting decision process as a nonlinear dynamical system over policy space and establish conditions under which the system admits stable xed points. Our contributions include: (1) dening the KATCR operator, a causal entropy-regularized policy update map; (2) proving a Lyapunov-style stability theorem showing monotonic entropy contraction under bounded regularization; (3) establishing convergence guarantees to xed-point policies under nite MDP assumptions; and (4) identifying a phase transition regime governed by the regularization coecient c. We complement our theoretical analysis with empirical observations in three benchmark environments and discuss limitations and future directions for continuous-state extensions.