Q_t(a) is the true mean, then we have Q_t(a) \le \hat Q_t(a) + \hat U_t(a). For arm a, \hat Q_t(a) is the sample mean, \hat U_t(a) is the upper confidence bound.In Bayesian bandit, the expected reward is measured as random variable. The expected reward \mu_k is treated as a fixed value, not a random variable. Notice UCB method is a classic statistic method.It can be iterpreted as the probability that a realized confidence bound include the ture estimate. It describe the property of a method to come up a confidence bound in individual trails. Confidence bound also called confidence interval, both the lower bound and upper bound are random variables. It is NOT the probability of certain outcome fall between the lower bound and upper bound (confidence interval). Confidence bound is usually misunderstood by it's name.For example, if the optimal arm is selected in the beginning, this algorithm will achieve better performance If the worst arm is selected in the beginning, it will stuck in getting the least reward. In each round, switch to a random arm with probability \epsilon, otherwise stick on the current optimal arm.Each step, you select one classifier uniform randomly and calculate the reward.This is what we do in the supervised training,.
In this algorithm, we basically evaluate all arms in every round, pretended we are in god's angle and know the underline distribution of each arm.But it doesn't heart that we evaluate this scenario as a benchmark for other algorithms. This doesn't apply to the real setting, because in the real bandit problem you can only play one arm at each round.T: total rounds K: number of arms G_t(k): reward (gain) obtained by play the k-th arm at the t-th round R_t(k): regret (loss) incurr by play the k-th arm at the t-th round \mu^*: the optimal expected payoff for the best arm (action) Brute force algorithm ¶ action is equivalent to arm, action i means play the i-th arm.Greedy (\epsilon\epsilon-Greedy) algorithm.Contextual Multi-Armed Bandit Contextual Multi-Armed Bandit Table of contents.Applied Scrum for Agile Project Management.Functional Programming Principles in Scala.
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