Title: Quantifying Memory Use in Reinforcement Learning with Temporal Range
Primary area: reinforcement learning
Keywords: Reinforcement Learning, Sequential Decision Making

Abstract: How much does a trained RL policy actually use its past observations? We propose Temporal Range, a model-agnostic metric that treats first-order sensitivities of a final-step vector output to the input sequence as a temporal influence profile and summarizes it by the magnitude-weighted average lag. Temporal Range is computed via reverse-mode automatic differentiation from the Jacobian blocks $\partial y_T/\partial x_t\in\mathbb{R}^{c\times d}$ and is well-characterized in the linear setting by a small set of natural axioms.
Across diagnostic and control tasks (POPGym; flicker/occlusion; Copy-$k$) and architectures (MLPs, RNNs, SSMs), Temporal Range (i) remains small in fully observed control, (ii) scales with the task's ground-truth lag in Copy-$k$, and (iii) aligns with the minimum history window required for near-optimal return as confirmed by window ablations. We also report Temporal Range for a compact Long
Expressive Memory (LEM) policy trained on the task, using it as a proxy readout of task-level memory. Our axiomatic treatment draws on recent work on range measures, specialized here to temporal lag and extended to vector-valued outputs in the RL setting. Temporal Range thus offers a practical per-sequence readout of memory dependence for comparing agents and environments and for selecting the
shortest sufficient context.