One of the core problems in reinforcement learning is the multi-armed bandit problem. This problem has been well studied and is commonly used to explore the tradeoff between exploration and exploitation integral to reinforcement learning.
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What is the multi-armed bandit problem?
Given a number of options to choose between, the multi-armed bandit problem describes how to choose the best option when you don’t know much about any of them.
You are faced repeatedly with n choices, of which you must choose one. After your choice, you are again faced with n choices of which you must choose one, and so on.
After each choice, you receive a numerical reward chosen from a probability distribution that corresponds to your choice. You don’t know what the probability distribution is for that choice before choosing it, but after you have picked it a few times you will start to get an idea of its underlying probability distribution (unless it follows an extreme value distribution, I guess).
The aim is to maximise your total reward over a given number of selections.
One analogy for this problem is this: you are placed in a room with a number of slot machines, and each slot machine when played will spit out a reward sampled from its probability distribution. Your aim is to maximise your total reward.
If you like, here are three more explanations of the multi-armed bandit problem:
- This article comes in two parts. The first part describes the problem and the second part describes a Bayesian solution.
- The Wikipedia explanation
- A more mathematical introduction
There are many strategies for solving the multi-armed bandit problem.
One class of strategies is known as semi-uniform strategies. These strategies always choose the best slot machine except for a set percentage of the time, where they choose a random slot machine.
Three of these strategies can be easily explored with the aid of the simulation:
Epsilon-greedy strategy: The best slot machine is chosen 1-ε percent of the time, and a random slot machine is chosen ε percent of the time. Implement this by leaving the epsilon slider in one place during a simulation run.
Epsilon-first strategy: Choose randomly for the first k trials, and then after that choose only the best slot machine. To implement this start the simulation with the epsilon slider at 1, then drag it to 0 at some point during the simulation.
Epsilon-decreasing strategy: The chance to choose a slot machine randomly ε decreases over the course of the simulation. Implement this by slowly dragging the epsilon slider towards 0 while the simulation is being run. You can use the arrow keys to decrement it by constant amounts.
There also exist other classes of strategy to solve the multi-armed bandit problem, such as probability matching strategies, pricing strategies and particular strategies that depend on the domain of the application. Also existing are different variants of the multi-armed bandit problem, including non-stationary variants and contextual variants.
I hope you find the simulation useful. Happy banditing!