Second-Order State Tracking to Stabilize Convergence in RCL

Develop a second-order optimizer state for Reflective Context Learning (RCL) in which the optimizer explicitly reasons about the trajectory and interactions of its own past playbook edits—not just the current batch-level diagnostics—and determine whether such trajectory-aware state further stabilizes convergence and reduces oscillatory updates.

Background

RCL maintains an optimizer state document to summarize recent edits, hypotheses, and assessments, which helps reduce oscillation and forgetting in context-space learning. The authors find that stabilization mechanisms provide significant gains, especially through optimizer state and related primitives.

They explicitly identify second-order state tracking—reasoning about edit trajectories over time—as an open direction to further stabilize convergence beyond the first-order state used in their experiments.