Bayesian Optimization Demo Game: Can you beat the 'computer'?

...an interactive matplotlib (GTK3) app served on the web.
app (not working properly on Chrome): [http://bayeisan-optimization.25800bfd.svc.dockerapp.io:8000/bo]
[https://github.com/majidaldo/GTK3webserver]

I recently made a notebook about Gaussian processes (GP). Now, Gaussian processes are used by Bayesian optimization. In Bayesian optimization, the goal is to optimize a function with as few (probably expensive) function evaluations as possible. Here's a good tutorial.

To see how it works, I implemented a basic optimizer following the mathematics introduced in the referenced tutorial (which wasn't as difficult as the math behind the GP!). I began from the code for the GP, to see how a Bayesian optimizer (BO) would optimize a toy 1-D problem.

But then, I wondered how the performance of a human would compare to the BO. So I made a game! In this game, the goal is to, of course, find the maximum of the function is as few tries as possible. Both players in each trial will attempt to find the maximum. A running average of the number of tries is kept.

After some experimentation playing the game, it seems there is a lower bound for the average number of tries needed. For the way I have my game set up (50 possible choices), the BO needed 10 point something +/-  point something tries. Furthermore, trying different so-called acquisition functions for the BO did not have much of an effect. This figure is based on thousands of trials (central limit theorem at work). And playing as the creator of my game, it was difficult for me to keep below 10 tries as an average. Of course, I can't play thousands of times.

These results imply that a human would not be able to optimize a function in three dimensions or more in less tries than a BO. There are simply too many variables to keep track of and it is very difficult if not impossible to visualize which is part of the point of using BOs.


Some features of the program:

• For aesthetic reasons, the y-axis has to be fixed based on the range of values of the function. But then the visual clue of having a point close to the top edge of the plot gives the human player an unfair advantage. The solution is to add some random margin between the maximum and the edge. So, if you happen to get a point that is close to the top edge, choose its neighbors!
• To generate a 'random' smooth function, I get some normally distributed points and sprinkle them on the domain. Then I use splines to connect them. It works surprisingly well!

Implementation notes:

The programming started in a functional style which is what you'd expect out of mathematical code and it's what I'm used to. However, once I got into matplotlib's GUI stuff, things started to get a little messy as a GUI requires reactive event-driven programming. Both styles of programming exist in my program and they intersect at while loops. You can run the game script with python on your desktop from the command line.

Now, the work involved in putting the game on the web, so that you, the reader, can easily engage in it, deserves its own post or two! Once I had the 'desktop' application running, I swam through oceans of technology until I got it to the form presented here. I should mention here that I came across a program similar to mine on Wolfram|Alpha but I can't find it anymore.

So here is the game served on the web. It's a Docker container managed for free, for now, by tutum.co but hosted almost for free on AWS for a few more months as of the date of this post. If you can spare 1GB of HD space and 100MB of memory to host my program, let me know!

Making My Near-Field Radiation Calculator Application for nanohub.org

I wanted to share a bit of my experience developing my python application for nanohub.org. For me, there were two main issues: One is configuring the nanohub computing environment to resemble my development environment (and you'll need to figure out the details of installing your tool by looking at other tools and some docs that can help). The other is using Rappture to implement the functionality I want for my application.

To set up my development environment in nanohub, I first delved into how I could make a self-contained python installation. This had me looking into pythonbrew and virtualenv with pythonbrew being more useful. But the admins at nanohub were willing to install the packages that I needed so I didn't have to mess with that too much. Nonetheless, these two projects are great for creating portable python projects.

After I took care of the development environment, I went ahead and started learning about Rappture. I needed some flexibility and what I call 'dynamic input'. Now I could have made a simple application but then it wouldn't be as useful. I had to bend the API to suit my needs. I ended up merging what should have been two simple applications into one more complicated application. That is: I had two sets of inputs for the same calculation. I'll list the issues I had with Rappture:

• Lacking documentation especially for the Python API. This is compensated for by looking at the API for the other languages and the many examples. I mainly figured out how Rappture works by example.
• Lack of computation status output as addressed by this page.
• Not all GUI elements are in the GUI GUI builder.
• Could not generate an authentic contour plot. I used the elements field and cloud to generate a contour plot. This probably wasn't the intended use of the of the elements but it worked...horribly. It struggled to display just a 50x50 grid calculation not to mention that I couldn't put axis labels. Also of general note, elements take strings to input numbers which is inefficient (but works). In my case, I wanted to be able to display at least 1000x1000 points. My solution was to ditch this GUI element and just use an image generated by matplotlib's contourf.
• 'Static' input. I wanted a user of my program to be able to change and check inputs in certain ways.
• I wanted the user to be able to add a selection to a drop-down list. Could not be done. Instead, I have the user reviewing a table of named text input so that the name can go into a text box which should have been a selection.
• Have an input value checked based on another input value. Can be done functionally by writing code that gets processed after hitting the 'Simulate' button. I don't know how I could hook into the GUI input elements so that they can be checked before the inputs are processed for simulation. For example, in my program I wanted to check that the value of 1.0 wasn't between two input values.
• Limited selection of units. (eg. no rad/s.) There should be functionality so that any unit can be input and can be converted to a compatible unit.

Despite these concerns, I believe Rappture is great for those simple (from an input/output point of view) programs that were originally designed for textual input and output. For more complicated programs, Rappture poses limitations. But then there are other developed and more sophisticated GUI APIs out there. So a better Rappture would be duplicating efforts of those other APIs.

Here's how it works:
First you get a page where you can enter named electric permittivity functions.

Then you input the simulation parameters and options.

Then you get various outputs. I'm showing the cool ones here:

The characteristic nearly monochromatic near-field radiation between SiC and SiC

The above graph is an integration over the y-axis of the following function in two variables.