## 3 Results
### Adaptive Learning Integration with ABMS
Still, extensive simulation times constrain the

Figure 10: Base case mean and confidence intervals of the epidemic curves. number of trials to perform in a reasonable time and with limited computing resources. Consequently, a \(2^{k}\) factorial design is chosen, where \(k\) is the number of factors to analyze. Specifically, \(k=3\) factors are considered according to parameters \(\alpha\), \(\gamma\), and \(\epsilon\). Table 8 presents the figures selected as the low and high levels for each experimental factor. The factors' levels were selected intuitively following their effects. Namely, \(\alpha\) was assigned a 0.1 low level, as smaller values will likely lead to imperceptible corrections and a 0.25 high level as larger figures could potentially head to oscillatory behavior. Similar arguments were examined while choosing the bounds of the remaining parameters. Table 9 describes the proposed \(2^{3}\) factorial design. The experiments were repeated six times, as previously stated, to capture the variability of the model's outcomes up to a 10% confidence interval deviation from the mean. Remarkably, results show that agents are absolutely capable of learning to avoid crowds on campus, thus, validating the hypothesis that the suggested RL-based approach is suitable for implementing the adaptive learning mechanism. As expected, maximum weekly densities reduce progressively while agents accumulate experiences in their daily activities. Figure 11 exhibits the mentioned behavior. Figure 11: Comparison of maximum weekly densities. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Factor** & **Low Level (\(-\))** & **High Level (\(+\))** \\ \hline Learning rate (\(\alpha\)) & 0.1 & 0.25 \\ Exploration probability (\(\epsilon\)) & 0.1 & 0.25 \\ Discount factor (\(\gamma\)) & 0.8 & 0.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Experimental factor levels. Figure 11 contrasts the base scenario with the eight experiments. What is striking about the outcomes is that all parameter settings significantly reduce maximum weekly densities with respect to the base case. Notwithstanding, some scenarios provide better results than others. For example, Experiment 2 affords the greatest decline in supreme densities and ends up in a situation where on-campus gatherings are, on average, below the 0.40 mark (10 points below the recommended social distancing policy). Extraordinarily, all experiments render a behavioral shift that positions the community in a sweet spot regarding compliance with the minimum physical distancing measures. Table 10 displays some relevant density figures for each one of the scenarios. What stands out in Table 10 is that the experiments with the highest relative reduction in the maximum weekly densities (Experiments 2 and 6) share the same parameter values for \(\epsilon\) and \(\gamma\). All in all, evidence suggests that the second setup is a local optimum with respect to the chosen experimental space. Nevertheless, the aforementioned settings are not guaranteed to be a globally optimal selection of learning parameters. Undoubtedly, a more in-depth optimization procedure is required to establish the Pareto set of learning factors to procure the maximum decline in density figures. Having said that, the obtained density reductions represent ideal learning configurations, meaning that these figures do not necessarily reflect actual human behavior. In contrast, those values portray fanciful conditions that could lead to the lowest attainable crowding level on campus. Results show that a significant drop in density values is plausible through a well-calibrated learning mechanism. However, an essential question is: do these improvements have a meaningful impact on the epidemic? The answer is not straightforward. We will start the analysis by visually inspecting the outcomes. Figure 12 contrasts the experiments' active cases curves against the reference scenario.