Deep Bayesian Quadrature Policy Optimization

Akella Ravi Tej¹, Kamyar Azizzadenesheli², Mohammad Ghavamzadeh³, Anima Anandkumar⁴, Yisong Yue^4
1Indian Institute of Technology Roorkee, ²Purdue University, ³Google Research, ⁴Caltech

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Preprint: arxiv.org/abs/2006.15637

Bayesian quadrature is an approach in probabilistic numerics for approximating a numerical integration. When estimating the policy gradient integral, replacing standard Monte-Carlo estimation with Bayesian quadrature provides

1. more accurate gradient estimates with a significantly lower variance
2. a consistent improvement in the sample complexity and average return for several policy gradient algorithms
3. a methodological way to quantify the uncertainty in gradient estimation.

This repository contains a computationally efficient implementation of BQ for estimating the policy gradient integral (gradient vector) and the estimation uncertainty (gradient covariance matrix). The source code is written in a modular fashion, currently supporting three policy gradient estimators and three policy gradient algorithms (9 combinations overall):

Policy Gradient Estimators :-

1. Monte-Carlo Estimation
2. Deep Bayesian Quadrature Policy Gradient (DBQPG)
3. Uncertainty Aware Policy Gradient (UAPG)

Policy Gradient Algorithms :-

1. Vanilla Policy Gradient
2. Natural Policy Gradient (NPG)
3. Trust-Region Policy Optimization (TRPO)

Project Setup

This codebase requires Python 3.6 (or higher). We recommend using Anaconda or Miniconda for setting up the virtual environment. Here's a walk through for the installation and project setup.

git clone https://github.com/Akella17/Deep-Bayesian-Quadrature-Policy-Optimization.git
cd Deep-Bayesian-Quadrature-Policy-Optimization
conda create -n DBQPG python=3.6
conda activate DBQPG
pip install -r requirements.txt

Supported Environments

1. Classic Control
2. MuJoCo
3. PyBullet
4. Roboschool
5. DeepMind Control Suite (via dm_control2gym)

Training

Modular implementation:

python agent.py --env-name <gym_environment_name> --pg_algorithm <VanillaPG/NPG/TRPO> --pg_estimator <MC/BQ> --UAPG_flag

All the experiments will run for 1000 policy updates and the logs get stored in session_logs/ folder. To reproduce the results in the paper, refer the following command:

# Running Monte-Carlo baselines
python agent.py --env-name <gym_environment_name> --pg_algorithm <VanillaPG/NPG/TRPO> --pg_estimator MC
# DBQPG as the policy gradient estimator
python agent.py --env-name <gym_environment_name> --pg_algorithm <VanillaPG/NPG/TRPO> --pg_estimator BQ
# UAPG as the policy gradient estimator
python agent.py --env-name <gym_environment_name> --pg_algorithm <VanillaPG/NPG/TRPO> --pg_estimator BQ --UAPG_flag

For more customization options, kindly take a look at the arguments.py.

Visualization

visualize.ipynb can be used to visualize the Tensorboard files stored in session_logs/ (requires jupyter and tensorboard installed).

Results

Vanilla Policy Gradient

Natural Policy Gradient

Trust Region Policy Optimization

Implementation References

• pytorch-trpo
  • TRPO and NPG implementation.
• GPyTorch library
  • Structured kernel interpolation (SKI) with Toeplitz method for RBF kernel.
  • Kernel learning with GPU acceleration.
• fbpca
  • Fast randomized singular value decomposition (SVD) through implicit matrix-vector multiplications.
• "A new trick for calculating Jacobian vector products"
  • Efficient Jvp computation through regular reverse-mode autodiff (more details in Appendix D of our paper).

Contributing

Contributions are very welcome. If you know how to make this code better, please open an issue. If you want to submit a pull request, please open an issue first. Also see the todo list below.

TODO

• Implement policy network for discrete action space and test on Arcade Learning Environment (ALE).
• Add other policy gradient algorithms.

Citation

If you find this work useful, please consider citing:

@article{ravi2020DBQPG,
    title={Deep Bayesian Quadrature Policy Optimization},
    author={Akella Ravi Tej and Kamyar Azizzadenesheli and Mohammad Ghavamzadeh and Anima Anandkumar and Yisong Yue},
    journal={arXiv preprint arXiv:2006.15637},
    year={2020}
}