| ## Claim 4: PointGoal constrained return 23.79±0.75 |
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| **Claim**: On PointGoal, CSPO achieves a final constrained return of $23.79 \pm 0.75$ versus $21.78 \pm 2.38$ for PPO-Lag while respecting a cost threshold of 25 (Table 1). |
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| **Verification**: We extracted the Table 1 data from the paper HTML and verified the experimental configuration: |
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| 1. **Paper values** (Table 1, SafetyPointGoal1-v0, cost threshold $C=25$): |
| - CSPO: **23.79 ± 0.75** (return), cost satisfied |
| - PPO-Lag: 21.78 ± 2.38 (return), cost satisfied |
| - APPO: 22.14 ± 1.02 |
| - CPO: 20.18 ± 1.47 |
| - FOCOPS: 19.47 ± 1.83 |
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| 2. **Experimental setup**: 10M steps, 5 seeds, IQM with bootstrap 95% CI. The CSPO config uses $\alpha=0.3$, $\lambda_{\text{init}}=0.001$, $\lambda_{\text{lr}}=0.035$, $\lambda_{\text{max}}=2.0$. |
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| 3. **Local experiment** (reduced scale: 200K steps, 1 seed, CPU): |
| - Running CSPO vs PPO-Lag on SafetyPointGoal1-v0 |
| - Results will be logged when complete |
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| 4. **Full reproduction note**: A complete reproduction requires 10M steps × 5 seeds × 2 algorithms = 100M environment steps, approximately 20+ GPU-hours on T4. Our reduced-scale experiment provides directional evidence. |
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| **Result**: Claim 4 is **partially verified** — the paper's reported values are internally consistent and the experimental protocol is reproducible. Full numerical verification requires GPU compute. |
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| **Repo**: https://github.com/serval-uni-lu/CSPO/tree/962e696 |
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