softmax

A softmax algorithm for multi-armed bandit problems

This implementation is based on Bandit Algorithms for Website Optimization and related empirical research in "Algorithms for the multi-armed bandit problem". In addition, this module conforms to the BanditLab/2.0 specification.

Get started

Prerequisites

• Node.js 6.x+ (LTS track)
• npm

Installing

Install with npm (or yarn):

npm install softmax --save

Caveat emptor

This implementation often encounters extended floating point numbers. Arm selection is therefore subject to JavaScript's floating point precision limitations. For general information about floating point issues see the floating point guide.

Usage

1. Create an optimizer with 3 arms and default annealing:

   const Algorithm = require('softmax');
   
   const algorithm = new Algorithm({
     arms: 3
   });

2. Select an arm (exploits or explores, determined by the algorithm):

   algorithm.select().then((arm) => {
     // do something based on the chosen arm
   });

3. Report the reward earned from a chosen arm:

   algorithm.reward(arm, value);

API

Algorithm(config)

Create a new optimization algorithm.

Arguments

• config (Object): algorithm instance parameters

The config object supports three optional parameters:

• arms (Number, Integer): The number of arms over which the optimization will operate; defaults to 2
• gamma (Number, Float, 0 to Infinity): Annealing factor, higher leads to less exploration; defaults to 1e-7 (0.0000001)
• tau (Number, Float, 0 to Infinity): Fixed temperature, higher leads to more exploration

By default, gamma is set to 1e-7 which causes the algorithm to reduce exploration as more information is received. That is, the "temperature cools" slightly with each iteration. In contrast, tau represents a "constant temperature" wherein the influence of random search is fixed across all iterations. If tau is provided then gamma is ignored.

Alternatively, the state object resolved from Algorithm#serialize can be passed as config.

Returns

An instance of the softmax optimization algorithm.

Example

const Algorithm = require('softmax');
const algorithm = new Algorithm();

assert.equal(algorithm.arms, 3);
assert.equal(algorithm.gamma, 0.0000001);

Or, with a passed config:

const Algorithm = require('softmax');
const algorithm = new Algorithm({ arms: 4, tau: 0.000005 });

assert.equal(algorithm.arms, 4);
assert.equal(algorithm.tau, 0.000005);

Algorithm#select()

Choose an arm to play, according to the optimization algorithm.

Arguments

None

Returns

A Promise that resolves to a Number corresponding to the associated arm index.

Example

const Algorithm = require('softmax');
const algorithm = new Algorithm();

algorithm.select().then(arm => console.log(arm));

Algorithm#reward(arm, reward)

Inform the algorithm about the payoff from a given arm.

Arguments

• arm (Number, Integer): the arm index (provided from Algorithm#select())
• reward (Number): the observed reward value (which can be 0 to indicate no reward)

Returns

A Promise that resolves to an updated instance of the algorithm. (The original instance is mutated as well.)

Example

const Algorithm = require('softmax');
const algorithm = new Algorithm();

algorithm.reward(0, 1).then(updatedAlgorithm => console.log(updatedAlgorithm));

Algorithm#serialize()

Obtain a plain object representing the internal state of the algorithm.

Arguments

None

Returns

A Promise that resolves to a stringify-able Object with parameters needed to reconstruct algorithm state.

Example

const Algorithm = require('softmax');
const algorithm = new Algorithm();

algorithm.serialize().then(state => console.log(state));

Development

Contribute

PRs are welcome! For bugs, please include a failing test which passes when your PR is applied. Travis CI provides on-demand testing for commits and pull requests.

Workflow

1. Feature development and bug fixing should occur on a non-master branch.
2. Changes should be submitted to master via a Pull Request.
3. Pull Requests should be merged via a merge commit. Local "in-process" commits may be squashed prior to pushing to the remote feature branch.

To enable a git hook that runs npm test prior to pushing, cd into the local repo and run:

touch .git/hooks/pre-push
chmod +x .git/hooks/pre-push
echo "npm test" > .git/hooks/pre-push

Tests

To run the unit test suite:

npm test

Or, to run the test suite and view test coverage:

npm run coverage

Note: Tests against stochastic methods (e.g. Algorithm#select) are inherently tricky to test with deterministic assertions. The approach here is to iterate across a semi-random set of conditions to verify that each run produces valid output. As a result, each test suite run encounters slightly different execution state. In the future, the test suite should be expanded to include a more robust test of the distribution's properties – though because of the number of runs required, should be triggered with an optional flag.