# Table: Effectiveness Comparison (When Can Each Approach Reach q*?) This table shows the binary effectiveness metric - whether each approach can theoretically reach the global optimal quality q* under different conditions. | Case | Learn-only (fix q) | Act-only (fix β) | Learn & Act | | --------------------------- | ------------------------------------------------ | --------------------------- | ---------------------- | | **Can reach q*?** | Only if costs/rewards stable (q* doesn't change) | Only if β parameters stable | Always ✓ | | **G0: Linear** | ✗ (q fixed at 0) | ✓ (reaches q*=1/2) | ✓ (reaches q*=1/2) | | **G1: Symmetric (βr=βc=1)** | ✗ (q fixed at 0) | ✓ (reaches q*=ln(3/2)) | ✓ (reaches q*=ln(3/2)) | | **G2: Asymmetric (βr<<βc)** | ✗ (q fixed at 0) | ✗ (wrong q*=ln(3/2)) | ✓ (reaches q*=ln(4)) | **Conditions for Effectiveness:** - **Learn-only (🟩D1.1)**: Requires stable cost ratio (Cu/(Cu+Co+V)) so that learning β doesn't change optimal q - **Act-only (🟩D1.2)**: Requires stable β parameters so initial assumption remains valid - **Learn & Act (🟥C1)**: No conditions - always converges to true optimum **Key Insight**: Only the integrated approach can handle both parameter uncertainty AND cost volatility.