Incentivized Exploration with Stochastic Covariates

√T and √d show up; √K does not

The proof's learning term has the closed-form rate, but the measured arm dependence is too steep.

K cubed is exact; "linear in d" is not in the paper's regime

Theorem 1 gives exact K^3, inverse-quadratic budget, and phi0^-1 scaling. At sigma=0.05, dimension barely changes N.

Literal N(epsilon) also makes the cold start longer than every reported experiment: 1.5x to 3.7 million x the horizon.

The mechanism structure reproduces

Fourteen checks on Algorithms 1-2 passed: MPASC to RASC cold start, organic pulls excluded from sample counts, every arm saturated before Stage 2, and IPGS is a valid probability kernel.

Larger epsilon buys shorter cold starts

Setting 3 reproduces the predicted direction: relaxing the incentive budget lowers N, shortens the cold-start period, and lowers regret, while DBIC satisfaction becomes less exact.

This is the paper's real tradeoff: incentives are bought with exploration rounds, not obtained for free.

Warfarin error rate is close; weighted score is not

The full 5528-patient grid reproduces broad error rates but not the headline RCB weighted risk score. With actual prevalences the physician baseline is 0.224; using the paper's rounded prevalence gives 0.200.

Independent CPU-scale reproduction bundle

• 19 executable theorem checks, 14 mechanism checks, 150 regret simulations, and 90 warfarin runs.
• One HF CPU Job smoke check: Theorem 1 exponents K=3.000, d=0.079, epsilon=-2.000.
• No official code was released; implementation follows the paper pseudocode and appendices.