Sequential learning problems are common in several fields of research and practical applications. Examples include dynamic pricing and assortment, design of auctions and incentives and permeate a large number of sequential treatment experiments. In this essay, we extend one of the most popular learning solutions, the epsilon-greedy heuristics, to high-dimensional contexts considering a conservative directive. We do this by allocating part of the time the original rule uses to adopt completely new actions to a more focused search in a restrictive set of promising actions. The resulting rule might be useful for practical applications that still values surprises, although at a decreasing rate, while also has restrictions on the adoption of unusual actions. With high probability, we find reasonable bounds for the cumulative regret of a conservative high-dimensional decaying epsilon-greedy rule. Also, we provide a lower bound for the cardinality of the set of viable actions that implies in an improved regret bound for the conservative version when compared to its non-conservative counterpart. Additionally, we show that end-users have sufficient flexibility when establishing how much safety they want, since it can be tuned without impacting theoretical properties. We illustrate our proposal both in a simulation exercise and using a real dataset. The second essay studies deterministic treatment effects when the assignment rule is both more complex than traditional ones and unknown to the public perhaps, among many possible causes, due to ethical reasons, to avoid data manipulation or unnecessary competition. More specifically, sticking to the well-known sharp RDD methodology, we circumvent the lack of knowledge of true cutoffs by employing a forest of classification trees which also uses sequential learning, as in the last essay, to guarantee that, asymptotically, the true unknown assignment rule is correctly identified. The tree structure also turns out to be suitable if the program s rule is more sophisticated than traditional univariate ones. Motivated by real world examples, we show in this essay that, with high probability and based on reasonable assumptions, it is possible to consistently estimate treatment effects under this setup. For practical implementation we propose an algorithm that not only sheds light on the previously unknown assignment rule but also is capable to robustly estimate treatment effects regarding different specifications imputed by end-users. Moreover, we exemplify the benefits of our methodology by employing it on part of the Chilean P900 school assistance program, which proves to be suitable for our framework.