mabalgs 0.4.4

Multi-armed bandit algorithms

Multi-Armed Bandit Algorithms

Multi-Armed Bandit (MAB) is a problem in which a fixed limited set of resources must be allocated between competing (alternative) choices in a way that maximizes their expected gain, when each choice's properties are only partially known at the time of allocation, and may become better understood as time passes or by allocating resources to the choice.

In the problem, each machine provides a random reward from a probability distribution specific to that machine. The objective of the gambler is to maximize the sum of rewards earned through a sequence of lever pulls. The crucial tradeoff the gambler faces at each trial is between "exploitation" of the machine that has the highest expected payoff and "exploration" to get more information about the expected payoffs of the other machines. The trade-off between exploration and exploitation is also faced in machine learning.

The main problems that the MAB help to solve is the split of the population in online experiments.

Installing

pip install mabalgs

Algorithms (Bandit strategies)

UCB1 (Upper Confidence Bound)

Is an algorithm for the multi-armed bandit that achieves regret that grows only logarithmically with the number of actions taken, with no prior knowledge of the reward distribution required.

Get a selected arm

from mab import algs

#Constructor receives number of arms.
ucb_with_two_arms = algs.UCB1(2)
ucb_with_two_arms.select()

Reward an arm

from mab import algs

#Constructor receives number of arms.
ucb_with_two_arms = algs.UCB1(2)
my_arm = ucb_with_two_arms.select()
ucb_with_two_arms.reward(my_arm)

UCB-Tuned (Upper Confidence Bound Tuned)

A strict improvement over both UCB solutions can be made by tuning the upper-bound parameter in UCB1’s decision rule. UCB-Tuned empirically outperforms UCB1 and UCB2 in terms of frequency of picking the best arm. Further, indicate that UCB-Tuned is “not very” sensitive to the variance of the arms.

Get a selected arm

from mab import algs

#Constructor receives number of arms.
ucbt_with_two_arms = algs.UCBTuned(2)
ucbt_with_two_arms.select()

Reward an arm

from mab import algs

#Constructor receives number of arms.
ucbt_with_two_arms = algs.UCBTuned(2)
my_arm = ucbt_with_two_arms.select()
ucbt_with_two_arms.reward(my_arm)

Thompson Sampling

Thompson Sampling is fully Bayesian: it generates a bandit configuration (i.e. a vector of expected rewards) from a posterior distribution, and then acts as if this was the true configuration (i.e. it pulls the lever with the highest expected reward).

“On the likelihood that one unknown probability exceeds another in view of the evidence of two samples” produced the first paper on an equivalent problem to the multi-armed bandit in which a solution to the Bernoulli distribution bandit problem now referred to as Thompson sampling is presented.

Get a selected arm

from mab import algs

#Constructor receives number of arms.
thomp_with_two_arms = algs.ThompsomSampling(2)
thomp_with_two_arms.select()

Reward an arm

from mab import algs

#Constructor receives number of arms.
thomp_with_two_arms = algs.ThompsomSampling(2)
my_arm = thomp_with_two_arms.select()
thomp_with_two_arms.reward(my_arm)

#Thompsom Sampling has a penalty function. It could be used in a onDestroy() event from a banner, for example. The arm was selected, showed to the user, but no interation was realized until the end of the arm cycle.
thomp_with_two_arms.penalty(my_arm)

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References

• Wikipedia MAB
• A Survey of Online Experiment Design with the Stochastic Multi-Armed Bandit
• Finite-time Analysis of the Multiarmed Bandit Problem
• Solving multiarmed bandits: A comparison of epsilon-greedy and Thompson sampling