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<main class="poster" data-measure-role="poster">
  <header class="header" data-measure-role="header">
    <div class="tag">ICML 2026 Reproduction</div>
    <div class="title">
      <h1>Incentivized Exploration with Stochastic Covariates</h1>
      <p>A two-stage RCB mechanism: executable theory checks, synthetic bandits, and warfarin dosing</p>
    </div>
    <div class="right-note">OpenReview LTHHiPNbrs<br>arXiv 2406.04374</div>
  </header>

  <section class="body" data-measure-role="body">
    <div class="column" data-measure-role="column">
      <article class="card" data-measure-role="card" data-logbook-target="claim-1-rcb-regret-is-o-sqrt-kdt" data-logbook-label="Claim 1: regret rate">
        <span class="verdict fail">Claim 1 falsified</span>
        <h2>√T and √d show up; √K does not</h2>
        <p>The proof's learning term has the closed-form rate, but the measured arm dependence is too steep.</p>
        <table>
          <tr><th>Rate / check</th><th>Measured</th><th>Claim</th></tr>
          <tr><td>T exponent</td><td>0.450-0.570</td><td>0.500</td></tr>
          <tr><td>d exponent</td><td>0.396</td><td>0.500</td></tr>
          <tr><td>K exponent</td><td>1.322 raw, 0.819 normalized</td><td>0.500</td></tr>
          <tr><td>Eq. E.30 bound</td><td>150/150 points satisfied</td><td>upper bound</td></tr>
        </table>
      </article>

      <article class="card" data-measure-role="card" data-logbook-target="claim-2-epsilon-dbic-requires-cold-start-size-scaling-as-k-cubed-times-d" data-logbook-label="Claim 2: epsilon DBIC">
        <span class="verdict fail">Claim 2 partly falsified</span>
        <h2>K cubed is exact; "linear in d" is not in the paper's regime</h2>
        <p>Theorem 1 gives exact K^3, inverse-quadratic budget, and phi0^-1 scaling. At sigma=0.05, dimension barely changes N.</p>
        <table>
          <tr><th>Dependency</th><th>Measured exponent</th></tr>
          <tr><td>K</td><td>3.000</td></tr>
          <tr><td>d over 2-200</td><td>0.079</td></tr>
          <tr><td>tau + epsilon</td><td>-2.000</td></tr>
          <tr><td>phi0</td><td>-1.000</td></tr>
        </table>
        <p>Literal N(epsilon) also makes the cold start longer than every reported experiment: 1.5x to 3.7 million x the horizon.</p>
      </article>

      <article class="card" data-measure-role="card" data-logbook-target="claim-3-two-stage-cold-start-exploitation-mechanism-with-ipgs" data-logbook-label="Claim 3: two-stage mechanism">
        <span class="verdict pass">Claim 3 verified</span>
        <h2>The mechanism structure reproduces</h2>
        <p>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.</p>
        <div class="metric-row">
          <div class="metric"><b>14/14</b><span>structure checks</span></div>
          <div class="metric"><b>0.1226</b><span>RASC frequency vs 0.125</span></div>
          <div class="metric"><b>1.042</b><span>cold-start K exponent</span></div>
        </div>
      </article>
    </div>

    <div class="column" data-measure-role="column">
      <article class="card" data-measure-role="card" data-logbook-target="claim-4-epsilon-budget-trades-off-cold-start-size-and-regret" data-logbook-label="Claim 4: epsilon tradeoff">
        <span class="verdict pass">Claim 4 verified</span>
        <h2>Larger epsilon buys shorter cold starts</h2>
        <p>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.</p>
        <p>This is the paper's real tradeoff: incentives are bought with exploration rounds, not obtained for free.</p>
        <table>
          <tr><th>epsilon</th><th>N</th><th>T_cold</th><th>Regret</th><th>DBIC frac.</th></tr>
          <tr><td>0.01</td><td>1582</td><td>50000</td><td>11188</td><td>1.000</td></tr>
          <tr><td>0.03</td><td>396</td><td>40962</td><td>5302</td><td>0.988</td></tr>
          <tr><td>0.05</td><td>176</td><td>11756</td><td>1714</td><td>0.956</td></tr>
        </table>
      </article>

      <article class="card" data-measure-role="card" data-logbook-target="claim-5-warfarin-simulations-reproduce-reported-risk-and-error-rates" data-logbook-label="Claim 5: warfarin">
        <span class="verdict fail">Claim 5 falsified on score</span>
        <h2>Warfarin error rate is close; weighted score is not</h2>
        <p>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.</p>
        <table>
          <tr><th>Policy</th><th>Error</th><th>Weighted score</th></tr>
          <tr><td>Physician</td><td>0.388</td><td>0.224 actual / 0.200 rounded</td></tr>
          <tr><td>RCB eps=0.025</td><td>0.384</td><td>0.232</td></tr>
          <tr><td>RCB eps=0.035</td><td>0.378</td><td>0.245</td></tr>
          <tr><td>RCB eps=0.045</td><td>0.377</td><td>0.245</td></tr>
          <tr><td>Offline oracle</td><td>0.324</td><td>0.352</td></tr>
        </table>
      </article>

      <article class="card" data-measure-role="card" data-logbook-target="conclusion" data-logbook-label="Bundle and rerun">
        <span class="verdict mixed">Scope and cost</span>
        <h2>Independent CPU-scale reproduction bundle</h2>
        <ul>
          <li>19 executable theorem checks, 14 mechanism checks, 150 regret simulations, and 90 warfarin runs.</li>
          <li>One HF CPU Job smoke check: Theorem 1 exponents K=3.000, d=0.079, epsilon=-2.000.</li>
          <li>No official code was released; implementation follows the paper pseudocode and appendices.</li>
        </ul>
      </article>
    </div>
  </section>

  <footer class="footer" data-measure-role="footer">
    <div><b>Outcome:</b> Claims 1, 2, and 5 fail in important quantified ways; Claim 3 and Claim 4 reproduce. All scripts, logs, data, and figures are bundled for rerun.</div>
    <div><b>Cost:</b> local CPU, about 5 minutes of logged runs in this session plus one cpu-basic HF Job smoke check.</div>
  </footer>
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