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14 changes: 12 additions & 2 deletions README.md
Original file line number Diff line number Diff line change
Expand Up @@ -273,13 +273,23 @@ Calculates advantage values $A^\pi(\mathbf{o}_t, \mathbf{a}_t)$ from offline tra

#### 1. Post-Training (N-Step Lookahead)

* **Formula:** $$A^\pi(\mathbf{o}_t, \mathbf{a}_t) = \sum_{t'=t}^{t+N-1} r'_{t'} + V^\pi(\mathbf{o}_{t+N}) - V^\pi(\mathbf{o}_t)$$
**Formula:**

```math
A^\pi(\mathbf{o}_t, \mathbf{a}_t) = \sum_{t'=t}^{t+N-1} r'_{t'} + V^\pi(\mathbf{o}_{t+N}) - V^\pi(\mathbf{o}_t)
```

* **Configuration:** $N = 50$
* **Execution:** Sum rewards over the $N$-step window, add the future value $V^\pi(\mathbf{o}_{t+N})$, and subtract the current value $V^\pi(\mathbf{o}_t)$.

#### 2. Pre-Training (Full Episode)

* **Formula:** $$A^\pi(\mathbf{o}_t, \mathbf{a}_t) = \sum_{t'=t}^{T} r'_{t'} - V^\pi(\mathbf{o}_t)$$
**Formula:**

```math
A^\pi(\mathbf{o}_t, \mathbf{a}_t) = \sum_{t'=t}^{T} r'_{t'} - V^\pi(\mathbf{o}_t)
```

* **Configuration:** $N = T$ (where $T$ is the terminal episode step)
* **Execution:** Calculate the empirical return from step $t$ to the episode's end, then subtract the baseline $V^\pi(\mathbf{o}_t)$.

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