Refactor description in app.py to improve readability

app.py

@@ -251,29 +251,72 @@ iface = gr.Interface(
         datatype=["number"] * len(example_result),
     ),
     description="""
-    `y1`, `y2`, `y3`, and `y4`, should all be minimized. `y1` and `y2` are
-    correlated, whereas `y1` and `y2` are both anticorrelated with `y3`. `y1`,
-    `y2`, and `y3` are stochastic (heteroskedastic, parameter-free noise),
-    whereas `y4` is deterministic, but still considered 'black-box'. In other
-    words, repeat calls with the same input arguments will result in different
-    values for `y1`, `y2`, and `y3`, but the same value for `y4`.
-
-    If `y1` is greater than 0.2, the result is considered "bad" no matter how good
-    the other values are. If `y2` is greater than 0.7, the result is considered
-    "bad" no matter how good the other values are. If `y3` is greater than 1800,
-    the result is considered "bad" no matter how good the other values are. If `y4`
-    is greater than 40e6, the result is considered "bad" no matter how good the
-    other values are.
-
-    `fidelity1` is a fidelity parameter. 0 is the lowest fidelity, and 1 is the
-    highest fidelity. The higher the fidelity, typically the more expensive the
-    evaluation. However, this also typically means higher quality and relevance
-    to the optimization campaign goals. `fidelity1` and `y3` are
-    correlated.
-
-    Constraints:
-    - `x19` should be less than `x20`.
-    - `x6` and `x15` should sum to no more than 1.0.
+    ## Objectives
+    
+    **Minimize `y1`, `y2`, `y3`, and `y4`**
+    
+    ### Correlations
+
+    - `y1` and `y2` are correlated
+    - `y1` is anticorrelated with `y3`
+    - `y2` is anticorrelated with `y3`
+    
+    ### Noise 
+    
+    `y1`, `y2`, and `y3` are stochastic with heteroskedastic, parameter-free
+    noise, whereas `y4` is deterministic, but still considered 'black-box'. In
+    other words, repeat calls with the same input arguments will result in
+    different values for `y1`, `y2`, and `y3`, but the same value for `y4`.
+
+    ### Objective thresholds
+    
+    If `y1` is greater than 0.2, the result is considered "bad" no matter how
+    good the other values are. If `y2` is greater than 0.7, the result is
+    considered "bad" no matter how good the other values are. If `y3` is greater
+    than 1800, the result is considered "bad" no matter how good the other
+    values are. If `y4` is greater than 40e6, the result is considered "bad" no
+    matter how good the other values are.
+
+    ## Search Space
+
+    ### Fidelity
+    
+    `fidelity1` is a fidelity parameter. The lowest fidelity is 0, and the
+    highest fidelity is 1. The higher the fidelity, the more expensive the
+    evaluation, and the higher the quality.
+    
+    NOTE: `fidelity1` and `y3` are correlated.
+
+    ### Constraints
+
+    - x<sub>19</sub> < x<sub>20</sub>
+    - x<sub>6</sub> + x<sub>15</sub> ≤ 1.0
+
+    ### Parameter bounds
+
+    - 0 ≤ x<sub>i</sub> ≤ 1 for i ∈ {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,
+      14, 15, 16, 17, 18, 19, 20}
+    - c<sub>1</sub> ∈ {c1_0, c1_1}
+    - c<sub>2</sub> ∈ {c2_0, c2_1}
+    - c<sub>3</sub> ∈ {c3_0, c3_1, c3_2}
+    - 0 ≤ fidelity1 ≤ 1
+
+    ## Notion of best
+
+    Thresholded Pareto front hypervolume vs. running cost for three different
+    budgets, and averaged over 10 search campaigns.
+
+    References:
+    
+    (1) Baird, S. G.; Liu, M.; Sparks, T. D. High-Dimensional Bayesian
+        Optimization of 23 Hyperparameters over 100 Iterations for an
+        Attention-Based Network to Predict Materials Property: A Case Study on
+        CrabNet Using Ax Platform and SAASBO. Computational Materials Science
+        2022, 211, 111505. https://doi.org/10.1016/j.commatsci.2022.111505.
+    (2) Baird, S. G.; Parikh, J. N.; Sparks, T. D. Materials Science
+        Optimization Benchmark Dataset for High-Dimensional, Multi-Objective,
+        Multi-Fidelity Optimization of CrabNet Hyperparameters. ChemRxiv March
+        7, 2023. https://doi.org/10.26434/chemrxiv-2023-9s6r7.
     """,
 )
 iface.launch()