https://github.com/blackhc/mdp
Make it easy to specify simple MDPs that are compatible with the OpenAI Gym.
https://github.com/blackhc/mdp
mdp openai-gym rl
Last synced: 6 months ago
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Make it easy to specify simple MDPs that are compatible with the OpenAI Gym.
- Host: GitHub
- URL: https://github.com/blackhc/mdp
- Owner: BlackHC
- License: apache-2.0
- Created: 2017-09-12T12:39:17.000Z (about 8 years ago)
- Default Branch: master
- Last Pushed: 2023-01-23T09:57:29.000Z (over 2 years ago)
- Last Synced: 2025-04-13T18:18:32.739Z (6 months ago)
- Topics: mdp, openai-gym, rl
- Language: Python
- Homepage:
- Size: 684 KB
- Stars: 40
- Watchers: 5
- Forks: 10
- Open Issues: 3
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# MDP environments for the OpenAI Gym
This Python framework makes it very easy to specify simple MDPs.
[](https://travis-ci.org/BlackHC/mdp)
## Installation
To install using pip, use:
```
pip install blackhc.mdp
```
To run the tests, use:
```
python setup.py test
```
## Whitepaper
A whitepaper is available at . Here is a BibTeX entry that you can use in publications (or download [CITE_ME.bib](CITE_ME.bib)):
```
@techreport{blackhc.mdp,
Author = {Andreas Kirsch},
Title = {MDP environments for the OpenAI Gym},
Year = {2017},
Url = {https://arxiv.org/abs/1709.09069}
}
```
## Introduction
In reinforcement learning, agents learn to maximize accumulated rewards from an environment that they can interact with by observing and taking actions. Usually, these environments satisfy a Markov property and are treated as *Markov Decision Processes* (*MDPs*).
The OpenAI Gym is a standardized and open framework that provides many different environments to train agents against through a simple API.
Even the simplest of these environments already has a level of complexity that is interesting for research but can make it hard to track down bugs. However, the gym provides four very simple environments that are useful for testing. The `gym.envs.debugging` package contains a one-round environment with deterministic rewards and one with non-deterministic rewards, and a two-round environment with deterministic rewards and another one with non-deterministic rewards.
The author has found these environments very useful for smoke-testing code changes.
This Python framework makes it very easy to specify simple MDPs like the ones described above in an extensible way. With it, one can validate that agents converge correctly as well as examine other properties.
## Specification of MDPs
MDPs are Markov processes that are augmented with a reward function and discount factor. An MDP can be fully specified by a tuple of:
* a finite set of states,
* a finite set of actions,
* a matrix that specifies probabilities of transitions to a new state for a given a state and action,
* a reward function that specifies the reward for a given action taken in a certain state, and
* a discount rate.
The reward function can be either deterministic, or it can be a probability distribution.
Within this framework, MDPs can be specified in Python using a simple *domain-specific language* (*DSL*).
For example, the one-round deterministic environment defined in `gym.envs.debugging.one_round_deterministic_reward` could be specified as follows:
```python
from blackhc.mdp import dsl
start = dsl.state()
end = dsl.terminal_state()
action_0 = dsl.action()
action_1 = dsl.action()
start & (action_0 | action_1) > end
start & action_1 > dsl.reward(1.)
```
The DSL is based on the following grammar (using EBNF[@ebnf]):
TRANSITION ::= STATE '&' ACTION '>' OUTCOME
OUTCOME ::= (REWARD | STATE) ['*' WEIGHT]
ALTERNATIVES ::= ALTERNATIVE ('|' ALTERNATIVE)*
See below for how alternatives work. Alternatives can be used in place of states, actions and outcomes, and comprise of states, actions and outcomes.
For a given state and action, outcomes can be specified. Outcomes are state transitions or rewards.
If multiple state transitions or rewards are specified for the same state and action, the MDP is non-deterministic and the state transition (or reward) are determined using a categorical distribution. By default, each outcome is weighted uniformly, except if specified otherwise by either having duplicate transitions or by using an explicit weight factor.
For example, to specify that a state receives a reward of +1 or -1 with equal probability and does not change states with probability 3/4 and only transitions to the next state with probability 1/4, we could write:
```python
state & action > dsl.reward(-1.) | dsl.reward(1.)
state & action > state * 3 | next_state
```
Alternatives are distributive with respect to both conjunctions (`&`) and outcome mappings (`>`), so:
(a | b) & (c | d) > (e | f) ===
(a & c > e) | (a & c > f) | (a & d > e) |
(a & d > f) | (b & c > e) | ...
Alternatives can consist of states, actions, outcomes, conjunctions or partial transitions. For example, the following are valid alternatives:
stateA & actionA | stateB & actionB
(actionA > stateC) | (actionB > stateD)
As the DSL is implemented within Python, operator overloading is used to implement the semantics. Operator precedence is favorable as `*` has higher precedence than `&`, which has higher precedence than `|`, which has higher precedence than `>`. This allows for a natural formulation of transitions.
## Conventional API
The framework also supports specifying an MDP using a conventional API as DSLs are not always preferred.
```python
from blackhc import mdp
spec = mdp.MDPSpec()
start = spec.state('start')
end = spec.state('end', terminal_state=True)
action_0 = spec.action()
action_1 = spec.action()
spec.transition(start, action_0, mdp.NextState(end))
spec.transition(start, action_1, mdp.NextState(end))
spec.transition(start, action_1, mdp.Reward(1))
```
## Visualization
To make debugging easier, MDPs can be converted to `networkx` graphs and rendered using `pydotplus` and `GraphViz`.
```python
from blackhc import mdp
from blackhc.mdp import example
spec = example.ONE_ROUND_DMDP
spec_graph = spec.to_graph()
spec_png = mdp.graph_to_png(spec_graph)
mdp.display_mdp(spec)
```
Figure 1: One round deterministic MDP
## Optimal values
The framework also contains a small module that can compute the optimal value functions using linear programming.
```python
from blackhc.mdp import lp
from blackhc.mdp import example
solver = lp.LinearProgramming(example.ONE_ROUND_DMDP)
print(solver.compute_q_table())
print(solver.compute_v_vector())
```
## Gym environment
An environment that is compatible with the OpenAI Gym can be created easily by using the `to_env()` method. It supports rendering into Jupyter notebooks, as RGB array for storing videos, and as png byte data.
```python
from blackhc import mdp
from blackhc.mdp import example
env = example.MULTI_ROUND_NMDP.to_env()
env.reset()
env.render()
is_done = False
while not is_done:
state, reward, is_done, _ = env.step(env.action_space.sample())
env.render()
```
Figure 2: env.render() of `example.MULTI_ROUND_NMDP`
# Examples
The `blackhc.mdp.example` package provides 5 MDPs. Four of them match the ones in `gym.envs.debugging`, and the fifth one is depicted in figure 2.