update docs

README.md

@@ -1,3 +1,46 @@
 # mud-games
 
-control systems with MUD points
+control systems with MUD points
+
+# installation
+
+```bash
+pip install -r requirements.txt
+```
+
+
+# usage
+
+A `data.pkl` file is provided for your convenience with input / output samples.
+
+The inputs are the parameters to a `4x1` matrix which is multiplied against the observations of the state in order to make a decision for the next action (push left or right). The output of the vector inner-product is binarized by comparison to zero as a threshold value.
+
+The parameter space is standard normal.
+There is no assumed error in observations, so the "data variance" is designed to reflect the acceptable ranges for the parameters:
+
+From [gym](https://www.gymlibrary.ml/pages/environments/classic_control/cart_pole):
+- The cart x-position (index 0) can be take values between (-4.8, 4.8), but the episode terminates if the cart leaves the (-2.4, 2.4) range.
+- The pole angle can be observed between (-.418, .418) radians (or ±24°), but the episode terminates if the pole angle is not in the range (-.2095, .2095) (or ±12°)
+
+
+The target "signal" is zero for all four dimensions of the observation space. The presumed "data variance" should actually correspond to the acceptable bands of signal (WIP).
+
+```bash
+python main.py
+```
+
+# generate data
+
+You can generate your own data with:
+```bash
+python data.py
+```
+
+Note: if you change the presumed sample space in `data.py`, you should make the corresponding changes to the initial distribution in `main.py`.
+
+
+# improvements
+
+Using the following presumptions, we can establish better values for the "data variance":
+The angular momentum of the pole is the most important thing to stabilize.
+