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Implementations of selected inverse reinforcement learning algorithms. !
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# Inverse Reinforcement Learning Implements selected inverse reinforcement learning (IRL) algorithms as part of COMP3710, supervised by Dr Mayank Daswani and Dr Marcus Hutter. My final report is available here and describes the implemented algorithms.

If you use this code in your work, you can cite it as follows:

```bibtex
@misc{alger16,
author       = {Matthew Alger},
title        = {Inverse Reinforcement Learning},
year         = 2016,
doi          = {10.5281/zenodo.555999},
url          = {https://doi.org/10.5281/zenodo.555999}
}
```

## Algorithms implemented

• Linear programming IRL. From Ng & Russell, 2000. Small state space and large state space linear programming IRL.
• Maximum entropy IRL. From Ziebart et al., 2008.
• Deep maximum entropy IRL. From Wulfmeier et al., 2015; original derivation.

Additionally, the following MDP domains are implemented: - Gridworld (Sutton, 1998) - Objectworld (Levine et al., 2011)

## Requirements

• NumPy
• SciPy
• CVXOPT
• Theano
• MatPlotLib (for examples)

## Module documentation

Following is a brief list of functions and classes exported by modules. Full documentation is included in the docstrings of each function or class; only functions and classes intended for use outside the module are documented here.

### linear_irl

Implements linear programming inverse reinforcement learning (Ng & Russell, 2000).

Functions:

• `irl(n_states, n_actions, transition_probability, policy, discount, Rmax, l1)`
: Find a reward function with inverse RL.
• `large_inverseRL(value, transition_probability, feature_matrix, n_states, n_actions, policy)`
: Find the reward in a large state space.

### maxent

Implements maximum entropy inverse reinforcement learning (Ziebart et al., 2008).

Functions:

• `irl(feature_matrix, n_actions, discount, transition_probability, trajectories, epochs, learning_rate)`
: Find the reward function for the given trajectories.
• `find_svf(feature_matrix, n_actions, discount, transition_probability, trajectories, epochs, learning_rate)`
: Find the state visitation frequency from trajectories.
• `find_feature_expectations(feature_matrix, trajectories)`
: Find the feature expectations for the given trajectories. This is the average path feature vector.
• `find_expected_svf(n_states, r, n_actions, discount, transition_probability, trajectories)`
: Find the expected state visitation frequencies using algorithm 1 from Ziebart et al. 2008.
• `expected_value_difference(n_states, n_actions, transition_probability, reward, discount, p_start_state, optimal_value, true_reward)`
: Calculate the expected value difference, which is a proxy to how good a recovered reward function is.

### deep_maxent

Implements deep maximum entropy inverse reinforcement learning based on Ziebart et al., 2008 and Wulfmeier et al., 2015, using symbolic methods with Theano.

Functions:

• `irl(structure, feature_matrix, n_actions, discount, transition_probability, trajectories, epochs, learning_rate, initialisation="normal", l1=0.1, l2=0.1)`
: Find the reward function for the given trajectories.
• `find_svf(n_states, trajectories)`
: Find the state vistiation frequency from trajectories.
• `find_expected_svf(n_states, r, n_actions, discount, transition_probability, trajectories)`
: Find the expected state visitation frequencies using algorithm 1 from Ziebart et al. 2008.

### value_iteration

Find the value function associated with a policy. Based on Sutton & Barto, 1998.

Functions:

• `value(policy, n_states, transition_probabilities, reward, discount, threshold=1e-2)`
: Find the value function associated with a policy.
• `optimal_value(n_states, n_actions, transition_probabilities, reward, discount, threshold=1e-2)`
: Find the optimal value function.
• `find_policy(n_states, n_actions, transition_probabilities, reward, discount, threshold=1e-2, v=None, stochastic=True)`
: Find the optimal policy.

### mdp

#### gridworld

Implements the gridworld MDP.

Classes, instance attributes, methods:

• `Gridworld(grid_size, wind, discount)`
: Gridworld MDP.
• `actions`
: Tuple of (dx, dy) actions.
• `n_actions`
: Number of actions. int.
• `n_states`
: Number of states. int.
• `grid_size`
: Size of grid. int.
• `wind`
: Chance of moving randomly. float.
• `discount`
: MDP discount factor. float.
• `transition_probability`
: NumPy array with shape (nstates, nactions, nstates) where `transitionprobability[si, a, sk]` is the probability of transitioning from state si to state sk under action a.
• `feature_vector(i, feature_map="ident")`
: Get the feature vector associated with a state integer.
• `feature_matrix(feature_map="ident")`
: Get the feature matrix for this gridworld.
• `int_to_point(i)`
: Convert a state int into the corresponding coordinate.
• `point_to_int(p)`
: Convert a coordinate into the corresponding state int.
• `neighbouring(i, k)`
: Get whether two points neighbour each other. Also returns true if they are the same point.
• `reward(state_int)`
: Reward for being in state state_int.
• `average_reward(n_trajectories, trajectory_length, policy)`
: Calculate the average total reward obtained by following a given policy over n_paths paths.
• `optimal_policy(state_int)`
: The optimal policy for this gridworld.
• `optimal_policy_deterministic(state_int)`
: Deterministic version of the optimal policy for this gridworld.
• `generate_trajectories(n_trajectories, trajectory_length, policy, random_start=False)`
: Generate ntrajectories trajectories with length trajectorylength, following the given policy.

#### objectworld

Implements the objectworld MDP described in Levine et al. 2011.

Classes, instance attributes, methods:

• `OWObject(inner_colour, outer_colour)`
: Object in objectworld.
• `inner_colour`
: Inner colour of object. int.
• `outer_colour`
: Outer colour of object. int.
• `Objectworld(grid_size, n_objects, n_colours, wind, discount)`
: Objectworld MDP.
• `actions`
: Tuple of (dx, dy) actions.
• `n_actions`
: Number of actions. int.
• `n_states`
: Number of states. int.
• `grid_size`
: Size of grid. int.
• `n_objects`
: Number of objects in the world. int.
• `n_colours`
: Number of colours to colour objects with. int.
• `wind`
: Chance of moving randomly. float.
• `discount`
: MDP discount factor. float.
• `objects`
: Set of objects in the world.
• `transition_probability`
: NumPy array with shape (nstates, nactions, nstates) where `transitionprobability[si, a, sk]` is the probability of transitioning from state si to state sk under action a.
• `feature_vector(i, discrete=True)`
: Get the feature vector associated with a state integer.
• `feature_matrix(discrete=True)`
: Get the feature matrix for this gridworld.
• `int_to_point(i)`
: Convert a state int into the corresponding coordinate.
• `point_to_int(p)`
: Convert a coordinate into the corresponding state int.
• `neighbouring(i, k)`
: Get whether two points neighbour each other. Also returns true if they are the same point.
• `reward(state_int)`
: Reward for being in state state_int.
• `average_reward(n_trajectories, trajectory_length, policy)`
: Calculate the average total reward obtained by following a given policy over n_paths paths.
• `generate_trajectories(n_trajectories, trajectory_length, policy)`
: Generate ntrajectories trajectories with length trajectorylength, following the given policy.