add fidelities calculator for staged iteration optimizers (#123)

Signed-off-by: Grossberger Lukas (CR/AIR2.2) <[email protected]>

docs/index.md

@@ -26,6 +26,49 @@ implementation.
 BOHB is provided as a cleaner replacement of the former implementation in
 [HpBandSter](https://github.com/automl/HpBandSter).
 
+#### Fidelities for BOHB & Hyperband
+
+You can calculate the fidelity schedule resulting from these parameters:
+
+<script>
+function calculateFidelitiesBOHB() {
+    const min_fidelity = document.getElementById('minFidelityBOHB').value;
+    const max_fidelity = document.getElementById('maxFidelityBOHB').value;
+    const eta = document.getElementById('etaBOHB').value;
+
+    const max_num_stages = 1 + Math.floor(
+        Math.log(max_fidelity / min_fidelity) / Math.log(eta)
+    );
+    const num_configs_first_stage = Math.ceil(Math.pow(eta, max_num_stages - 1));
+    const num_configs_per_stage = Array.from({ length: max_num_stages }, (_, i) =>
+        Math.floor(num_configs_first_stage / Math.pow(eta, i))
+    );
+    const fidelities_per_stage = Array.from({ length: max_num_stages }, (_, i) =>
+        max_fidelity / Math.pow(eta, max_num_stages - 1 - i)
+    );
+
+    document.getElementById('fidelitiesBOHB').innerHTML = `Fidelities: ${fidelities_per_stage}`;
+}
+</script>
+<table>
+    <tr>
+        <td>min_fidelity</td>
+        <td><input type="text" id="minFidelityBOHB"></td>
+    </tr>
+    <tr>
+        <td>max_fidelity</td>
+        <td><input type="text" id="maxFidelityBOHB"></td>
+    </tr>
+    <tr>
+        <td>eta</td>
+        <td><input type="text" id="etaBOHB"></td>
+    </tr>
+    <tr>
+        <td></td><td><button onclick="calculateFidelitiesBOHB();">Submit</button></td>
+    </tr>
+</table>
+<p id="fidelitiesBOHB"></p>
+
 ### Optimization Loops
 
 As part of the `blackboxopt.optimization_loops` module compatible implementations for