Adapting Critic Match Loss Landscape Visualization to Off-policy Reinforcement Learning

Abstract: This work extends an established critic match loss landscape visualization method from online to off-policy reinforcement learning (RL), aiming to reveal the optimization geometry behind critic learning. Off-policy RL differs from stepwise online actor-critic learning in its replay-based data flow and target computation. Based on these two structural differences, the critic match loss landscape visualization method is adapted to the Soft Actor-Critic (SAC) algorithm by aligning the loss evaluation with its batch-based data flow and target computation, using a fixed replay batch and precomputed critic targets from the selected policy. Critic parameters recorded during training are projected onto a principal component plane, where the critic match loss is evaluated to form a 3-D landscape with an overlaid 2-D optimization path. Applied to a spacecraft attitude control problem, the resulting landscapes are analyzed both qualitatively and quantitatively using sharpness, basin area, and local anisotropy metrics, together with temporal landscape snapshots. Comparisons between convergent SAC, divergent SAC, and divergent Action-Dependent Heuristic Dynamic Programming (ADHDP) cases reveal distinct geometric patterns and optimization behaviors under different algorithmic structures. The results demonstrate that the adapted critic match loss visualization framework serves as a geometric diagnostic tool for analyzing critic optimization dynamics in replay-based off-policy RL-based control problems.