Add gen_grid utility to build GridMDP grids of arbitrary size (#984)

Add gen_grid(n_rows, n_cols, terminals, main_reward, terminal_rewards,
block_coords) to mdp.py, which produces a list-of-lists grid in the format
GridMDP accepts, so larger grid worlds can be created without writing the
grid by hand. Based on the helper proposed and approved in #984, with a
modernized signature (tuple defaults instead of mutable list defaults).
The default reproduces the canonical 4x3 Figure 17.1 grid. Add a test.

Author: dmeoli

mdp.py

@@ -188,6 +188,24 @@ def to_arrows(self, policy):
         return self.to_grid({s: chars[a] for (s, a) in policy.items()})
 
 
+def gen_grid(n_rows=3, n_cols=4, terminals=((3, 2), (3, 1)), main_reward=-0.04,
+             terminal_rewards=(1, -1), block_coords=((1, 1),)):
+    """Generate a grid (list of lists of rewards) of arbitrary size in the format
+    accepted by GridMDP, e.g. GridMDP(gen_grid(...), terminals=[...]).
+    n_rows, n_cols: grid dimensions.
+    terminals: (x, y) coordinates of the terminal cells.
+    main_reward: reward for every non-terminal, non-blocked cell.
+    terminal_rewards: reward for each cell in terminals (paired by position).
+    block_coords: (x, y) coordinates of obstacles (set to None / unreachable)."""
+    grid = [[main_reward] * n_cols for _ in range(n_rows)]
+    for (x, y), reward in zip(terminals, terminal_rewards):
+        grid[y][x] = reward
+    for x, y in block_coords:
+        grid[y][x] = None
+    grid.reverse()  # row 0 at the bottom, matching GridMDP's convention
+    return grid
+
+
 # ______________________________________________________________________________
 
 

tests/test_mdp.py

@@ -22,6 +22,26 @@
                                             terminals=[(2, 2), (3, 2), (0, 4), (5, 0)])
 
 
+def test_gen_grid():
+    # the default reproduces the canonical 4x3 Figure 17.1 grid
+    assert gen_grid() == [[-0.04, -0.04, -0.04, 1],
+                          [-0.04, None, -0.04, -1],
+                          [-0.04, -0.04, -0.04, -0.04]]
+    # and feeds GridMDP to the same optimal policy as the shipped environment
+    generated = GridMDP(gen_grid(), terminals=[(3, 2), (3, 1)])
+    assert (best_policy(generated, value_iteration(generated, .001)) ==
+            best_policy(sequential_decision_environment,
+                        value_iteration(sequential_decision_environment, .001)))
+    # an arbitrary larger world places terminals and obstacles correctly
+    big = gen_grid(n_rows=5, n_cols=5, terminals=[(4, 3), (4, 2)], main_reward=0.04,
+                   terminal_rewards=[1, -1], block_coords=[(0, 3), (2, 3), (3, 1)])
+    assert big == [[0.04, 0.04, 0.04, 0.04, 0.04],
+                   [None, 0.04, None, 0.04, 1],
+                   [0.04, 0.04, 0.04, 0.04, -1],
+                   [0.04, 0.04, 0.04, None, 0.04],
+                   [0.04, 0.04, 0.04, 0.04, 0.04]]
+
+
 def test_value_iteration():
     # exact float equality on the value function is brittle across numpy/BLAS
     # versions (the values can differ in the last decimal), so compare with a