Quantifying Memory Use in Reinforcement Learning with Temporal Range
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 multiple vector outputs across a temporal window 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 ∂ ys/∂ xt∈Rc× d averaged over final timesteps s∈\t+1,…,T\ 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.
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