# Table: Performance Metrics Comparison (Learn-only, Act-only, Learn & Act) This table presents quantitative performance comparisons across three approaches for the G0, G1, and G2 cases. | Metric | Definition | Learn-only (fix q) | Act-only (fix β) | Learn & Act | |--------|------------|-------------------|------------------|-------------| | **Prescription Profitability** | Expected cost savings E[Cost]_baseline - E[Cost]_algorithm | | | | | G0 | Linear case | 0 | EC at q=1/2 | EC at q=1/2 | | G1 | Symmetric sigmoid (βr=βc=1) | 0 | EC at ln(3/2) | EC at ln(3/2) | | G2 | Asymmetric (βr<<βc) | 0 | EC at ln(3/2) | EC at ln(4) | | **Prediction Accuracy** | 1 - |β_estimated - β_true|/β_true | | | | | G0 | Linear case | 100% | 0% | 100% | | G1 | Symmetric sigmoid | 100% | 0% | 100% | | G2 | Asymmetric | 100% | 0% | 50% | | **Prediction Effectiveness** | 1 / (|q* - q_t| × |β_t - β_0|) | | | | | G0 | Linear case | 0 | ∞ | ∞ | | G1 | Symmetric sigmoid | ln(4) × 4.5 = 2.73 | ∞ | ∞ | | G2 | Asymmetric | 4.5 × ln(4) | ∞ | ∞ | | **Update Efficiency** | (E[Cost]_0 - E[Cost]_t) / (|q_t - q_0| + |β_t - β_0|) | | | | | G0 | Linear case | 0 | Saved/moved | Saved/moved | | G1 | Symmetric sigmoid | 0 | EC savings/ln(3/2) | EC savings/(ln(3/2)+4) | | G2 | Asymmetric | 0 | EC savings/ln(3/2) | EC savings/(ln(4)+1) | Key insights: - Learn-only approach (🟩D1.1): High accuracy but zero profitability (never optimizes quality) - Act-only approach (🟩D1.2): Immediate profitability but zero learning (infinite effectiveness) - Integrated approach (🟥C1/C2): Balances accuracy, profitability, and efficiency