## 4 Performance Evaluation: Results
### Discussion of Results  
Results presented in this section clearly show that the best choice on the algorithm to use strongly depends on the distribution of the rewards. Conservative algorithms that spend more time measuring/exploring, such as UCB1 and muUCB1, should be preferred when the different arms are characterized by similar rewards, while the MLI algorithm, more tilted towards _use_, should be the preferred choice when one arm is significantly better than others. Other aggressive algorithms such as POKER and \(\varepsilon\)-decreasing may potentially lead to an extremely low regret, but present a very high variability in final regret, and are thus characterized by a low reliability. Results also show that the proposed MLI and muUCB1 algorithms, which are capable of taking advantage of the measuring phase introduced in the muMAB model, consistently improve their performance as the \(T_{U}/T_{M}\) ratio increases. Transferring the above observations into real world cases, this means that the choice of which algorithm to use strongly depends on which network quality parameters are taken into account in network selection. As an example, a binary parameter such as the availability of a network can be modelled with a Bernoulli distribution [25], while a parameter such as the measured SNR in a channel affected by Rayleigh fading can be modelled as an exponential random variable [26]. In the considered scenario, where the final goal is to offer the final user the best performance in terms of perceived quality, the parameters of the networks we are interested on depend, in turn, on the type of application that the user wants to use, and therefore on the requested traffic type; models linking measurable network parameters to perceived quality have been indeed proposed in the literature (see, for example, [26]). Results also allow to observe that the variability of the selected network parameters may play a significant role in the selection of the network selection algorithm: if the reward obtained by the network parameters presents a large variance, some algorithms may incur in a large penalty in terms of regret. Figure 13: Performance in terms of regret of the six considered algorithms, with real captured data used as reward and \(T_{U}/T_{M}=10\). (**a**) linear conversion; (**b**) logarithmic conversion. An additional important consideration should be done on the considered time horizon: given the same reward distribution and the same \(T_{U}/T_{M}\) ratio, two different time horizons can require the selection of different algorithms in order to guarantee the lowest regret. As an a example, MLI during the very first steps only performs _measure_ actions, thus obtaining a null gain. It is, therefore, obvious that if the time horizon is very short, this algorithm should never be selected. In real world scenarios, where it can be expected that the considered time horizon is usually much longer, this initial period can be considered negligible; more details on this aspect can be found in [27]. Again, the definition of the time horizon will, however, depend on the selected network QoS/QoE parameters: if parameters change frequently, this will translate in a short available time horizon, which would call for an algorithm capable of accumulating gain in a shorter time. One last aspect worth mentioning regards computational complexity. Although a complete complexity analysis is not carried out in this work, the proposed algorithms were compared with existing ones by measuring the execution time assuming a ratio \(T_{U}/T_{M}=1\). Results are presented in Figure 14, showing the ratio between the execution time of each algorithm and the execution time of the \(\varepsilon\)-greedy algorithm, which proved to be the fastest one. Results show that \(\varepsilon\)-greedy, \(\varepsilon\)-decreasing and MLI algorithms require similar execution times.