On the "Causality" Step in Policy Gradient Derivations: A Pedagogical Reconciliation of Full Return and Reward-to-Go
In introductory presentations of policy gradients, one often derives the REINFORCE estimator using the full trajectory return and then states, by ``causality,'' that the full return may be replaced by the reward-to-go. Although this statement is correct, it is frequently presented at a level of rigor that leaves unclear where the past-reward terms disappear. This short paper isolates that step and gives a mathematically explicit derivation based on prefix trajectory distributions and the score-function identity. The resulting account does not change the estimator. Its contribution is conceptual: instead of presenting reward-to-go as a post hoc unbiased replacement for full return, it show...
| Authors | Nima H. Siboni |
|---|---|
| Primary category | cs.AI |
| Published | 6 April 2026 |
| Last updated at source | 6 April 2026 |
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