By Rong Zheng, Cunqing Hua
This publication lays out the theoretical origin of the so-called multi-armed bandit (MAB) difficulties and places it within the context of source administration in instant networks. half I of the booklet offers the formulations, algorithms and function of 3 different types of MAB difficulties, particularly, stochastic, Markov and antagonistic. protecting all 3 sorts of MAB difficulties makes this booklet exact within the box. half II of the e-book presents special discussions of consultant functions of the sequential studying framework in cognitive radio networks, instant LANs and instant mesh networks.
Both contributors in and people within the instant learn neighborhood will make the most of this entire and well timed remedy of those subject matters. Advanced-level scholars learning communications engineering and networks also will locate the content material useful and accessible.
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Extra info for Sequential Learning and Decision-Making in Wireless Resource Management
However, DSEE utilizes a deterministic epoch structure whereas ε-greedy randomizes the arm to explore. The geometrically growing length of the exploration and exploitation epochs allows unbiased estimation of the sample means. 4 (Regret bound for DSEE [LLZ13]) Assume all arms are finite-state, irreducible, aperiodic Markov chains whose transition probability matrices have irreducible multiplicative symmetrizations. All rewards are nonnegative. Let L = 2 30rmax √ . Assume the best arm has a distinctive reward mean.
Do for i = 1, . . , K do w Set pi,t = (1 − γ ) K i,t + Kγ ; j=1 w j,t Draw action It randomly according to the probabilities p1,t , . . , p K ,t ; Play action It and receive reward X It ,t ; for j = 1, . . 10) γ Xˆ j,t K . EXP3 algorithm is an extension of the Hedge algorithm for the adversarial MAB problem with partial information as shown in Fig. 1b [Aue+02], that is, only the reward of the selected action can be observed. 2, EXP3 selects an action It according to the distribution Pt in each time step t, which is a mixture of the probability Pt defined in the Hedge algorithm and the uniform distribution to ensure that all actions are tried and the reward for each action is estimated.
Now, the optimal policy switches arms if the reward is 1 and stays otherwise. Example 1 and 2 also show that the optimal policy is not necessarily a singleaction policy. The regret incurred with respect to the optimal single-action policy is often called weak regret; on the other hand, strong regret is defined as the difference between the rewards attainable by the optimal policy with complete information and the policy under consideration. Furthermore, we observe from the example, the transition probabilities of the underlying Markov processes (as opposed to mean statistics) play an important role in determining the optimal policy.