![]() Also, our priors have large intersections, as the model is not very certain about its weights. We see that in the first rounds our output probabilities have very large uncertainty and no clear direction. This way, it is very simple to use Thompson Sampling: we perform an OLR for each bandit, take a sample of the posterior of $\beta$, get the sampled output and choose the bandit with the highest prediction! Let us check one simulation: At the right-hand side, we can observe how the uncertainty in our coefficient translates to uncertainty in the prediction. The plot at the left-hand side shows the Normal posterior of the coefficient after fitting the model to some data. The following plot shows the Online Logistic Regression estimate for a simple linear model. m # weights are expected values of posteriorsĮlse : raise Exception ( 'mode not recognized!' ) # calculating probabilities w # weights are samples of posteriorsĮlif mode = 'expected' : w = self. get_weights () # using weight depending on mode dot ( X ** 2 ) # probability output method, using weights sampleĭef predict_proba ( self, X, mode = 'sample' ): # adding intercept to X Thus, we’re going to suppose that the probabilty of reward now is of the form\[\theta_k(x) = \frac). Therefore, we add the notion of context or state to support our decision. ![]() The Contextual Bandit is just like the Multi-Armed bandit problem but now the true expected reward parameter $\theta_k$ depends on external variables. This scenario is known as the Contextual bandit. In this post, we expand our Multi-Armed Bandit setting such that the expected rewards $\theta$ can depend on an external variable. All the code can be found on my GitHub page here. In this series of posts, I’ll introduce some applications of Thompson Sampling in simple examples, trying to show some cool visuals along the way. Thompson Sampling is a very simple yet effective method to addressing the exploration-exploitation dilemma in reinforcement/online learning.
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