This repository is deprecated. If you would like to use any of the algorithms for your own research please refer to the fragile framework.
It is only for educational purposes, and for providing code to the Fractal AI paper.
Once you start doubting, just like you’re supposed to doubt, you ask me if the science is true. You say no, we don’t know what’s true, we’re trying to find out and everything is possibly wrong.
–Richard P. Feynman, The Pleasure of Finding Things Out: The Best Short Works of Richard P. Feynman.
Fractal AI (arXiv#1, arXiv#2) is a theory for efficiently sampling state spaces. It allows one to derive new mathematical tools that could be useful for modeling information using cellular automaton-like structures instead of smooth functions.
In this repository we present Fractal Monte Carlo (FMC), a new planning algorithm derived from the first principles of Fractal AI theory. A FMC agent is capable of solving Atari-2600 games under the OpenAI Gym several orders of magnitude more efficiently than similar planning algorithms, such as Monte Carlo Tree Search (MCTS) [1].
We also present a more advanced Swarm Wave implementation, also derived from Fractal AI principles, that allows one to solve Markov decision processes under a perfect/informative model of the environment. This implementation is far more efficient than FMC, effectively "solving" a substantial number of Atari games.
The code provided under this repository exemplifies how it is now possible to beat some of the current state-of-the-art benchmarks on Atari games while generating a large set of top-performing examples with little computation required, turning Reinforcement Learning (RL) into a supervised problem.
These new algorithms propose a new approach to modeling the decision space, while maintaining control over any aspects of the agent's behavior. The algorithms can be applied to all combinations of discrete or continuous decision and state spaces.
To quickly understand the fundamentals of Fractal AI you can refer to the Introduction to FAI. The document provides a brief explanation of the algorithms here presented and their potential applications on the field of Reinforcement Learning.
To test how the Fractal Monte Carlo Agent performs on any Atari game you can refer to the FMC example notebook. This example allows us to run games using either the RAM content or the pixel render as observations.
To better understand how the Swarm Wave algorithm works in practice you can refer to the Swarm Wave example notebook.
Pleas note the authors are open to discuss the ideas and code here presented under the conceptual framework of Reinforcement Learning and its standard terminology.
The code provided aims to be both simple and self-explanatory. Requirements and instructions to set up the environment are provided below.
As a first step, install the dependencies as explained on the OpenAI gym documentation:
To install the full set of environments, you'll need to have some system packages installed. We'll build out the list here over time; please let us know what you end up installing on your platform. In case you want to run the notebook:
pip3 install jupyterOn OSX:
brew install cmake boost boost-python sdl2 swig wgetOn Ubuntu 14.04:
sudo apt-get install -y python-numpy python-dev cmake zlib1g-dev libjpeg-dev xvfb libav-tools xorg-dev python-opengl libboost-all-dev libsdl2-dev swig libav-tools
On the terminal, run:
git clone git@github.com:FragileTheory/FractalAI.git
cd FractalAI
sudo pip3 install -e .It doesn't matter how beautiful your theory is, it doesn't matter how smart you are.
If it doesn't agree with experiment, it's wrong.
–Richard P. Feynman
We used a standard set of 50 Atari-2600 games, common to all the planning algorithms articles found in the literature, to compare our implementation of the FMC algorithm against:
| FMC Wins | % | |
|---|---|---|
| FMC vs Standard Human | 49 / 50 | 98% |
| FMC vs World Human Record | 32 / 50 | 64% |
| FMC vs Planning SOtA (1) | 50 / 50 | 100% |
| FMC vs Hidden score limit | 16 / 50 | 32% |
(1) On average, the Swarm Wave version of FMC used 360 times fewer samples per action than the rest of planning algorithm, typically using 150k samples per action.
The following table depicts the Fractal Monte Carlo Agent performance on each tested game.
| Game | Human Record | Planning SOtA | FMC |
|---|---|---|---|
| Alien | 251916 | 38951 | 479940 |
| Amidar | 155339 | 3122 | 5779 |
| Assault | 8647 | 1970 | 14472 |
| Asterix (*) | 335500 | 319667 | 999500 |
| Asteroids | 10004100 | 68345 | 12575000 |
| Atlantis | 7352737 | 198510 | 10000100 |
| Bank Heist | 199978 | 1171 | 3139 |
| Battle Zone (*) | 863000 | 330880 | 999000 |
| Bean Rider (*) | 999999 | 12243 | 999999 |
| Berzerk | 1057940 | 2096 | 17610 |
| Bowling | 300 | 69 | 180 |
| Boxing | 100 | 100 | 100 |
| Breakout | 752 | 772 | 864 |
| Centipede | 1301709 | 193799 | 1351000 |
| Chopper Command (*) | 999900 | 34097 | 999900 |
| Crazy Climber | 447000 | 141840 | 2254100 |
| Demon Attack (*) | 999970 | 34405 | 999970 |
| Double Dunk | 24 | 24 | 24 |
| Enduro | 3617.9 | 788 | 5279 |
| Fishing Derby | 71 | 42 | 63 |
| Freeway | 34 | 32 | 33 |
| Frostbyte (*) | 552590 | 6427 | 999960 |
| Gopher (*) | 120000 | 26297 | 999980 |
| Gravitar | 1673950 | 6520 | 14050 |
| Hero | 1000000 | 15280 | 43255 |
| Ice Hockey | 36 | 62 | 64 |
| Jamesbond | 45550 | 23070 | 152950 |
| Kangaroo | 1436500 | 8760 | 10800 |
| Krull | 1006680 | 15788 | 426534 |
| Kung fu master | 1000000 | 86290 | 172600 |
| Montezuma's Revenge | 1219200 | 500 | 5600 |
| Ms. Pacman (*) | 290090 | 30785 | 999990 |
| Name this Game | 25220 | 15410 | 53010 |
| Pong | 21 | 21 | 21 |
| Private Eye | 103100 | 2544 | 41760 |
| QBert () | 999975 | 44876 | 999975 |
| River Raid | 194940 | 15410 | 18510 |
| Road Runner (*) | 999900 | 120923 | 999900 |
| Robotank | 74 | 75 | 94 |
| Seaquest (*) | 527160 | 35009 | 999999 |
| Space Invaders | 621535 | 3974 | 17970 |
| Star Gunner (*) | 77400 | 14193 | 999800 |
| Tennis | 24 | 24 | 24 |
| Time Pilot | 66500 | 65213 | 90000 |
| Tutankham | 3493 | 226 | 342 |
| Up and Down (*) | 168830 | 120200 | 999999 |
| Venture | 31900 | 1200 | 1500 |
| Video Pinball (*) | 999999 | 471859 | 999999 |
| Wizard of Wor (*) | 99900 | 161640 | 99900 |
| Zaxxon | 100000 | 39687 | 92100 |
(*) Games with the "1 Million bug" where max. score is hard-limited.
We provide a more detailed Google Docs spreadsheet where the performance of the Fractal Monte Carlo Agent is logged relative to the current alternatives. In the spreadsheet we also provide the parameters used in each of the runs.
If you find any outdated benchmarks or for some reason you are unable to replicate some of our results, please open an issue and we will update the document accordingly.
Fractal AI: A Fragile Theory of Intelligence: This document explains the fundamental principles of the Fractal AI theory in which our Agent is based. We worked all the fundamental principles completely from scratch to build our own solution. We try to be consistent with existing terminology, and this document should contain everything you need to understand the theory. Comments on how to better explain the content are appreciated.
Solving Atari Games Using Fractals And Entropy: A short version of the article written by Spiros Baxevanakis and submitted -under very high uncertaintly- to NIPS2018.
EntropicAI, Sergio Hernández Cerezo's blog: Here you can find the evolution of the research process for developing this algorithm, documented and explained, as well as experiments which aim to apply the theory to other fields of research.
Fractal AI playlist: In the Youtube playlist you can find videos of the accomplishments over the years. Besides the recordings Atari games using the Agent, you can find videos recorded using a custom library that allows one to create different tasks in continuous control environments, as well as visualizations of how the Agent samples the state space.
GAS paper [9]: A manuscript describing an application of the Fractal AI theory on general optimization problems. There are certainly better ways to apply the theory such problems, yet it illustrates why code is better than maths to explain the theory. When trying to formalize it, things can get really non-intuitive.
Causal Entropic Forces by Alexander Wissner-Gross [10]: The fundamental concepts behind this paper inspired the present research. We develop our theory aiming to calculate future entropy more quickly and being able to leverage the information contained in the Entropy of any state space, together with any potential function.
@misc{1803.05049,
Author = {Sergio Hernández Cerezo and Guillem Duran Ballester},
Title = {Fractal AI: A fragile theory of intelligence},
Year = {2018},
Eprint = {arXiv:1803.05049},
}As questions regarding the research and methodology we will address them under the FAQ.
You can refer to the FAQ document.
Authors:
The authors have developed the theory as personal side projects driven purely by intellectual curiosity. Guillem worked on it while attending college, and Sergio while working as a programmer. The authors are not part of academia, have no corporate affiliation and no formal track record.
All the time and resources involved came from the authors themselves, besides the support from:
We currently do not have the resources to further carry our research. We will gladly accept contributions or sponsorships that allow us to continue working with what is our passion.
Special thanks: We want to thank all the people who has believed in us along the years. Their patience, understanding and support made possible for this project to evolve to this point.
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