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https://github.com/willieneis/bayesian-algorithm-execution

Bayesian algorithm execution (BAX)
https://github.com/willieneis/bayesian-algorithm-execution

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Bayesian algorithm execution (BAX)

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# Bayesian Algorithm Execution (BAX)



Code for the paper:



> [Bayesian Algorithm Execution: Estimating Computable Properties of Black-box Functions

> Using Mutual Information](https://arxiv.org/abs/2104.09460)\

> Willie Neiswanger, Ke Alexander Wang, Stefano Ermon\

> International Conference on Machine Learning (ICML), 2021\

> _arXiv:2104.09460_



See also the [BAX website](https://willieneis.github.io/bax-website/) for additional details

and animations.



### One-sentence summary



Extending Bayesian optimization from estimating global optima to

estimating other function properties defined by the output of algorithms.



### Abstract



In many real world problems, we want to infer some property of an expensive black-box

function f, given a budget of T function evaluations. One example is budget constrained

global optimization of f, for which Bayesian optimization is a popular method. Other

properties of interest include local optima, level sets, integrals, or graph-structured

information induced by f. Often, we can find an algorithm A to compute the desired

property, but it may require far more than T queries to execute. Given such an A, and a

prior distribution over f, we refer to the problem of inferring the output of A using T

evaluations as Bayesian Algorithm Execution (BAX).



To tackle this problem, we present a procedure, InfoBAX, that sequentially chooses

queries that maximize mutual information with respect to the algorithm's output.

Applying this to Dtra's algorithm, for instance, we infer shortest paths in synthetic

and real-world graphs with black-box edge costs.  Using evolution strategies, we yield

variants of Bayesian optimization that target local, rather than global, optima. On

these problems, InfoBAX uses up to 500 times fewer queries to f than required by the

original algorithm. Our method is closely connected to other Bayesian optimal

experimental design procedures such as entropy search methods and optimal sensor

placement using Gaussian processes.



## Installation



This repo requires Python 3.6+. To install Python dependencies, `cd` into this repo and

run:

```bash

$ pip install -r requirements/requirements.txt

$ pip install -r requirements/requirements_gpfs.txt

```

Note that this installs dependencies for

[GPflowSampling](https://github.com/j-wilson/GPflowSampling), which our implementation

uses to efficiently run algorithms on GP posterior function samples.



For some functionality, you'll also need to compile a [Stan](https://mc-stan.org/) model

by running:

```bash

$ python bax/models/stan/compile_models.py

```



## Examples



**[WIP]** More examples are in the process of being merged into this branch. Note that

the following API and functionality may undergo changes, as this library is still in the

early stages.



First make sure this repo directory is on the PYTHONPATH, e.g. by running:

```bash

$ source shell/add_pwd_to_pythonpath.sh

```



### Example 1: Estimating shortest paths in graphs



For a demo on a 10x10 grid graph, run:

```bash

$ python examples/dijkstra/bax_grid10_viz_simple_demo.py

```



To produce images for an animation on a 20x20 grid graph, run:

```bash

$ python examples/dijkstra/bax_grid20_animation.py

```





    




### Example 2: Bayesian local optimization



For a demo on a two-dimensional optimization problem, run:

```bash

$ python examples/branin/bax_viz2d_simple_demo.py

```





     

    




### Example 3: Top-k estimation



For a demo on a top-10 estimation task over a discrete set of points, run:

```bash

$ python examples/topk/bax_simple_demo.py

```





    




## Citation

Please cite [our paper](https://arxiv.org/abs/2104.09460) if you find this project

helpful:

```

@inproceedings{neiswanger2021bayesian,

  title         = {Bayesian Algorithm Execution: Estimating Computable Properties of Black-box Functions Using Mutual Information},

  author        = {Neiswanger, Willie and Wang, Ke Alexander and Ermon, Stefano},

  booktitle     = {International Conference on Machine Learning},

  year          = {2021},

  organization  = {PMLR}

}

```