Implementation of Point-Based Value Iteration

Point-based value iteration (PBVI) is an approximate method for solving partially observable Markov decision processes (POMDPs). I'm implementing the algorithm from:

Joelle Pineau, Geoffrey Gordon, Sebastian Thrun. Point-based value iteration: An anytime algorithm for POMDPs. In IJCAI, 2003.

Usage

For trying out piglet_pbvi I recommend downloading the Tiger (Tigger?) POMDP and converting it to JSON.

# Prerequisites – See README of pomdp2json for details.
$ git clone https://github.com/rmoehn/pomdp2json
$ cd pomdp2json
$ ./build.sh
$ mkdir ../pomdp_defs
$ wget --directory-prefix=../pomdp_defs http://www.pomdp.org/examples/tiger.95.POMDP
$ python2.7 pomdp2json.py ../pomdp_defs/tiger.95.POMDP ../pomdp_defs/tiger.95.POMDP.json
$ cd ..

$ git clone https://github.com/rmoehn/piglet_pbvi
$ cd piglet_pbvi
$ python2.7 piglet_pbvi/json_pomdp.py ../pomdp_defs/tiger.95.POMDP.json

You can do the last step in Python as well:

# Let Python know where to find the module, because I haven't made an
# installable package.
import sys
sys.path.insert(0, <path to piglet_pbvi repo clone>)

from piglet_pbvi import json_pomdp

pbvi_gen = json_pomdp.load_pomdp("<path to tiger.95.POMDP.json>")
for __ in xrange(10):
    print next(pbvi_gen)
    # Outputs current value function estimate and optimal policy for that value
    # function.

You might also have a look at pomdp_play.py. It's messy, but it runs piglet_pbvi and naive piglet_pbvi on an adaptation of the POMDP defined in AIMA.

I will add more documentation after I've made sure that piglet_pbvi works correctly.

Disclaimer

The implementation is far from mature. It probably has bugs and consists mostly of undocumented NumPy oatmeal that I don't completely understand, even though I've written it. It might not work for anything but the Tiger and AIMA POMDPs mentioned above.

Done

• Implement PBVI.
• Implement a naive version that is slower, but easier to read.
• Test them on a two-state problem from AIMA. Compare value function with AIMA. – Looks good.
• Test it on the Tiger95 POMDP. Compare value function with the result of pomdp-solve. – Looks okay. pomdp-solve returns a value function with more segments, but the policy is the same, I think.
• Make a tool to convert from Anthony Cassandra's POMDP file format to JSON.

To do

• Maybe find out why my implementation returns a value function with fewer segments than pomdp-solve on Tiger95.
• Make an OpenAI Gym environment that can run most POMDPs specified in Anthony Cassandra's POMDP file format converted to JSON. ‘Most’ means that the reward function will be limited to depend on the action and the state before taking the action.
• Maybe make it easier to obtain converted POMDP files.
• Run my implementation on the Hallway and Hallway2 POMDPs and compare the resulting rewards with those from the PBVI paper. This might turn up defects in my implementation or performance problems.
• Fix any defects or performance problems.
• Turn this into a Python package and upload to PyPi.
  • Convert README to reStructuredText.

Why?

• Why is the package called piglet_pbvi? Because I want to avoid name clashes with other people's PBVI implementations. ‘PBVI’ is also used as a generic term for point-based POMDP solution methods. So I took the first letters of the family names of the authors of the paper that describes the PBVI that I'm implementing and added an i and an l and an e to aid your memory.

License

See LICENSE.txt.