polish noise notebook (minor)

notebooks/notebook-usecases-noise.ipynb

@@ -54,7 +54,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Sanity check without noise."
+    "We start by a sanity check without noise."
    ]
   },
   {
@@ -103,7 +103,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "CMA-ES without noise handling in the Rosenbrock function with additive uniform noise."
+    "Next, we run CMA-ES _without_ noise handling on the Rosenbrock function with additive uniform noise."
    ]
   },
   {
@@ -297,7 +297,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "With noise handling, the CMA-ES does not get stuck and keeps searching with a somewhat constant variance (which will never converge). The step-size (green line) systematically increases, the smallest standard deviation (magenta line) does never drop far below $10^{-2}$."
+    "With noise handling, the CMA-ES does not get stuck and keeps searching with a somewhat constant variance (which will never converge). The step-size (green line in the upper left figure) systematically increases, the smallest standard deviation (lower magenta line) does never drop far below $10^{-2}$."
    ]
   },
   {
@@ -324,7 +324,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "All entries in `xfavorite` get consistently close-ish to 1. We could probably estimate a notably better solution by averaging the mean over some past iterations where the $f$-value was stagnating."
+    "All entries in `xfavorite` get consistently close-ish to 1. We could probably estimate a notably better solution by averaging the mean over some past iterations when the $f$-value was stagnating."
    ]
   },
   {
@@ -364,7 +364,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "We increase the population size by a factor of four."
+    "Now, we increase the population size by a factor of four."
    ]
   },
   {
@@ -722,11 +722,8 @@
   }
  ],
  "metadata": {
-  "interpreter": {
-   "hash": "d63c44124e99970b36478bac7366f7234ff1cfabe1191de4da3d5c25c8ed9e11"
-  },
   "kernelspec": {
-   "display_name": "Python 3.7.6 64-bit ('base': conda)",
+   "display_name": "py312",
    "language": "python",
    "name": "python3"
   },
@@ -740,7 +737,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.12.0"
+   "version": "3.12.2"
   },
   "orig_nbformat": 4
  },