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Implementations of Reinforcement Learning and Planning algorithms

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A collection of Reinforcement Learning agents



pip install --user git+


Most experiments can be run from

  experiments evaluate   (--train|--test)
                                             [--episodes ]
                                             [--seed ]
  experiments benchmark  (--train|--test)
                                    [--processes ]
                                    [--episodes ]
                                    [--seed ]
  experiments -h | --help

Options: -h --help Show this screen. --analyze Automatically analyze the experiment results. --episodes Number of episodes [default: 5]. --processes Number of running processes [default: 4]. --seed Seed the environments and agents. --train Train the agent. --test Test the agent.


command allows to evaluate a given agent on a given environment. For instance,
# Train a DQN agent on the CartPole-v0 environment
$ python3 evaluate configs/CartPoleEnv/env.json configs/CartPoleEnv/DQNAgent.json --train --episodes=200

Every agent interacts with the environment following a standard interface:

action = agent.act(state)
next_state, reward, done, info = env.step(action)
agent.record(state, action, reward, next_state, done, info)

The environments are described by their gym

, and module for registration.
    "id": "CartPole-v0",
    "import_module": "gym"

And the agents by their class, and configuration dictionary.

    "__class__": "",
    "model": {
        "type": "MultiLayerPerceptron",
        "layers": [512, 512]
    "gamma": 0.99,
    "n_steps": 1,
    "batch_size": 32,
    "memory_capacity": 50000,
    "target_update": 1,
    "exploration": {
        "method": "EpsilonGreedy",
        "tau": 50000,
        "temperature": 1.0,
        "final_temperature": 0.1

If keys are missing from these configurations, values in

will be used instead.

Finally, a batch of experiments can be scheduled in a benchmark. All experiments are then executed in parallel on several processes.

# Run a benchmark of several agents interacting with environments
$ python3 benchmark cartpole_benchmark.json --test --processes=4

A benchmark configuration file contains a list of environment configurations and a list of agent configurations.

    "environments": ["envs/cartpole.json"],
    "agents": ["agents/dqn.json", "agents/mcts.json"]


There are several tools available to monitor the agent performances: * Run metadata: for the sake of reproducibility, the environment and agent configurations used for the run are merged and saved to a

file. * Gym Monitor: the main statistics (episode rewards, lengths, seeds) of each run are logged to an
file. They can be automatically visualised by running
* Logging: agents can send messages through the standard python logging library. By default, all messages with log level INFO are saved to a
file. Add the option
scripts/ --verbose
to save with log level DEBUG. * Tensorboard: by default, a tensoboard writer records information about useful scalars, images and model graphs to the run directory. It can be visualized by running:
tensorboard --logdir 


The following agents are currently implemented:


Value Iteration

Perform a Value Iteration to compute the state-action value, and acts greedily with respect to it.

Only compatible with finite-mdp environments, or environments that handle an

conversion method.

Reference: Dynamic Programming, Bellman R., Princeton University Press (1957).

Cross-Entropy Method

A sampling-based planning algorithm, in which sequences of actions are drawn from a prior gaussian distribution. This distribution is iteratively bootstraped by minimizing its cross-entropy to a target distribution approximated by the top-k candidates.

Only compatible with continuous action spaces. The environment is used as an oracle dynamics and reward model.

Reference: A Tutorial on the Cross-Entropy Method, De Boer P-T., Kroese D.P, Mannor S. and Rubinstein R.Y. (2005).

Monte-Carlo Tree Search

A world transition model is leveraged for trajectory search. A look-ahead tree is expanded so as to explore the trajectory space and quickly focus around the most promising moves.

References: * Efficient Selectivity and Backup Operators in Monte-Carlo Tree Search, Coulom R., 2006.

Upper Confidence bounds applied to Trees

The tree is traversed by iteratively applying an optimistic selection rule at each depth, and the value at leaves is estimated by sampling. Empirical evidence shows that this popular algorithms performs well in many applications, but it has been proved theoretically to achieve a much worse performance (doubly-exponential) than uniform planning in some problems.

References: * Bandit based Monte-Carlo Planning, Kocsis L., Szepesvári C. (2006). * Bandit Algorithms for Tree Search, Coquelin P-A., Munos R. (2007).

Optimistic Planning for Deterministic systems

This algorithm is tailored for systems with deterministic dynamics and rewards. It exploits the reward structure to achieve a polynomial rate on regret, and behaves efficiently in numerical experiments with dense rewards.

Reference: Optimistic Planning for Deterministic Systems, Hren J., Munos R. (2008).

Open Loop Optimistic Planning

References: * Open Loop Optimistic Planning, Bubeck S., Munos R. (2010). * Practical Open-Loop Optimistic Planning, Leurent E., Maillard O.-A. (2019).


Reference: Blazing the trails before beating the path: Sample-efficient Monte-Carlo planning, Grill J. B., Valko M., Munos R. (2017).


Reference: Scale-free adaptive planning for deterministic dynamics & discounted rewards, Bartlett P., Gabillon V., Healey J., Valko M. (2019).

Safe planning

Robust Value Iteration

A list of possible finite-mdp models is provided in the agent configuration. The MDP ambiguity set is constrained to be rectangular: different models can be selected at every transition.The corresponding robust state-action value is computed so as to maximize the worst-case total reward.

References: * Robust Control of Markov Decision Processes with Uncertain Transition Matrices, Nilim A., El Ghaoui L. (2005). * Robust Dynamic Programming, Iyengar G. (2005). * Robust Markov Decision Processes, Wiesemann W. et al. (2012).

Discrete Robust Optimistic Planning

The MDP ambiguity set is assumed to be finite, and is constructed from a list of modifiers to the true environment. The corresponding robust value is approximately computed by Deterministic Optimistic Planning so as to maximize the worst-case total reward.

References: * Approximate Robust Control of Uncertain Dynamical Systems, Leurent E. et al. (2018).

Interval-based Robust Planning

We assume that the MDP is a parametrized dynamical system, whose parameter is uncertain and lies in a continuous ambiguity set. We use interval prediction to compute the set of states that can be reached at any time t, given that uncertainty, and leverage it to evaluate and improve a robust policy.

If the system is Linear Parameter-Varying (LPV) with polytopic uncertainty, an fast and stable interval predictor can be designed. Otherwise, sampling-based approaches can be used instead, with an increased computational load.

References: * Approximate Robust Control of Uncertain Dynamical Systems, Leurent E. et al. (2018). * Interval Prediction for Continuous-Time Systems with Parametric Uncertainties, Leurent E. et al (2019).


Deep Q-Network

A neural-network model is used to estimate the state-action value function and produce a greedy optimal policy.

Implemented variants: * Double DQN * Dueling architecture * N-step targets

References: * Playing Atari with Deep Reinforcement Learning, Mnih V. et al (2013). * Deep Reinforcement Learning with Double Q-learning, van Hasselt H. et al. (2015). * Dueling Network Architectures for Deep Reinforcement Learning, Wang Z. et al. (2015).


A Q-function model is trained by performing each step of Value Iteration as a supervised learning procedure applied to a batch of transitions covering most of the state-action space.

Reference: Tree-Based Batch Mode Reinforcement Learning, Ernst D. et al (2005).

Safe Value-based

Budgeted Fitted-Q

An adaptation of

in the budgeted setting: we maximise the expected reward r of a policy π under the constraint that an expected cost c remains under a given budget β. The policy π(a | s, _β)_ is conditioned on this cost budget β, which can be changed online.

To that end, the Q-function model is trained to predict both the expected reward Qr and the expected cost Qc of the optimal constrained policy π.

This agent can only be used with environments that provide a cost signal in their

field: ```

obs, reward, done, info = env.step(action) info {'cost': 1.0} ```

Reference: Budgeted Reinforcement Learning in Continuous State Space, Carrara N., Leurent E., Laroche R., Urvoy T., Maillard O-A., Pietquin O. (2019).


If you use this project in your work, please consider citing it with:

  author = {Leurent, Edouard},
  title = {rl-agents: Implementations of Reinforcement Learning algorithms},
  year = {2018},
  publisher = {GitHub},
  journal = {GitHub repository},
  howpublished = {\url{}},

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