Value Iteration

In [1]:

from behavior_generation_lecture_python.mdp.mdp import (
    MDP,
    GridMDP,
    expected_utility_of_action,
    derive_policy,
    value_iteration,
    GRID_MDP_DICT,
    HIGHWAY_MDP_DICT,
    LC_RIGHT_ACTION,
    STAY_IN_LANE_ACTION,
)
from behavior_generation_lecture_python.utils.grid_plotting import (
    make_plot_grid_step_function,
    make_plot_policy_step_function,
)

from behavior_generation_lecture_python.mdp.mdp import ( MDP, GridMDP, expected_utility_of_action, derive_policy, value_iteration, GRID_MDP_DICT, HIGHWAY_MDP_DICT, LC_RIGHT_ACTION, STAY_IN_LANE_ACTION, ) from behavior_generation_lecture_python.utils.grid_plotting import ( make_plot_grid_step_function, make_plot_policy_step_function, )

TOY EXAMPLE¶

In [2]:

grid_mdp = GridMDP(**GRID_MDP_DICT)

grid_mdp = GridMDP(**GRID_MDP_DICT)

In [3]:

computed_utility_history = value_iteration(
    mdp=grid_mdp, epsilon=0.001, max_iterations=30, return_history=True
)

computed_utility_history = value_iteration( mdp=grid_mdp, epsilon=0.001, max_iterations=30, return_history=True )

In [4]:

%matplotlib inline
plot_grid_step = make_plot_grid_step_function(
    columns=4, rows=3, U_over_time=computed_utility_history
)

%matplotlib inline plot_grid_step = make_plot_grid_step_function( columns=4, rows=3, U_over_time=computed_utility_history )

In [5]:

mkdocs_flag = False  # set to true if you are running the notebook locally
if mkdocs_flag:
    import ipywidgets
    from IPython.display import display

    iteration_slider = ipywidgets.IntSlider(
        min=0, max=len(computed_utility_history) - 1, step=1, value=0
    )
    w = ipywidgets.interactive(plot_grid_step, iteration=iteration_slider)
    display(w)

mkdocs_flag = False # set to true if you are running the notebook locally if mkdocs_flag: import ipywidgets from IPython.display import display iteration_slider = ipywidgets.IntSlider( min=0, max=len(computed_utility_history) - 1, step=1, value=0 ) w = ipywidgets.interactive(plot_grid_step, iteration=iteration_slider) display(w)

In [6]:

plot_grid_step(19)

plot_grid_step(19)

HIGHWAY EXAMPLE¶

In [7]:

if False:
    # we will change this to true later on, to see the effect
    HIGHWAY_MDP_DICT["transition_probabilities_per_action"][LC_RIGHT_ACTION] = [
        (0.4, LC_RIGHT_ACTION),
        (0.6, STAY_IN_LANE_ACTION),
    ]

if False: # we will change this to true later on, to see the effect HIGHWAY_MDP_DICT["transition_probabilities_per_action"][LC_RIGHT_ACTION] = [ (0.4, LC_RIGHT_ACTION), (0.6, STAY_IN_LANE_ACTION), ]

In [8]:

highway_mdp = GridMDP(**HIGHWAY_MDP_DICT)

highway_mdp = GridMDP(**HIGHWAY_MDP_DICT)

In [9]:

utility_history_highway = value_iteration(
    highway_mdp, epsilon=0.001, max_iterations=30, return_history=True
)

utility_history_highway = value_iteration( highway_mdp, epsilon=0.001, max_iterations=30, return_history=True )

In [10]:

plot_grid_step_highway = make_plot_grid_step_function(
    columns=10, rows=4, U_over_time=utility_history_highway
)

plot_grid_step_highway = make_plot_grid_step_function( columns=10, rows=4, U_over_time=utility_history_highway )

In [11]:

if mkdocs_flag:
    iteration_slider = ipywidgets.IntSlider(
        min=0, max=len(utility_history_highway) - 1, step=1, value=0
    )
    w = ipywidgets.interactive(plot_grid_step_highway, iteration=iteration_slider)
    display(w)

if mkdocs_flag: iteration_slider = ipywidgets.IntSlider( min=0, max=len(utility_history_highway) - 1, step=1, value=0 ) w = ipywidgets.interactive(plot_grid_step_highway, iteration=iteration_slider) display(w)

In [12]:

plot_grid_step_highway(10)

plot_grid_step_highway(10)

In [13]:

policy_array = [
    derive_policy(highway_mdp, utility) for utility in utility_history_highway
]

policy_array = [ derive_policy(highway_mdp, utility) for utility in utility_history_highway ]

In [14]:

plot_policy_step_highway = make_plot_policy_step_function(
    columns=10, rows=4, policy_over_time=policy_array
)

plot_policy_step_highway = make_plot_policy_step_function( columns=10, rows=4, policy_over_time=policy_array )

In [15]:

if mkdocs_flag:
    iteration_slider = ipywidgets.IntSlider(
        min=0, max=len(utility_history_highway) - 1, step=1, value=0
    )
    w = ipywidgets.interactive(plot_policy_step_highway, iteration=iteration_slider)
    display(w)

if mkdocs_flag: iteration_slider = ipywidgets.IntSlider( min=0, max=len(utility_history_highway) - 1, step=1, value=0 ) w = ipywidgets.interactive(plot_policy_step_highway, iteration=iteration_slider) display(w)

In [16]:

plot_policy_step_highway(10)

plot_policy_step_highway(10)