Reinforcement learning over encrypted data

Reinforcement learning is a particular paradigm of machine learning that, recently, has proved times and times again to be a very effective and powerful approach. On the other hand, cryptography usually takes the opposite direction. While machine learning aims at analyzing data, cryptography aims at maintaining its privacy by hiding such data. However, the two techniques can be jointly used to create privacy preserving models, able to make inferences on the data without leaking sensitive information. Despite the numerous amount of studies performed on machine learning and cryptography, reinforcement learning in particular has never been applied to such cases before. Being able to successfully make use of reinforcement learning in an encrypted scenario would allow us to create an agent that efficiently controls a system without providing it with full knowledge of the environment it is operating in, leading the way to many possible use cases. Therefore, we have decided to apply the reinforcement learning paradigm to encrypted data. In this project we have applied one of the most well-known reinforcement learning algorithms, called Deep Q-Learning, to simple simulated environments and studied how the encryption affects the training performance of the agent, in order to see if it is still able to learn how to behave even when the input data is no longer readable by humans. The results of this work highlight that the agent is still able to learn with no issues whatsoever in small state spaces with non-secure encryptions, like AES in ECB mode. For fixed environments, it is also able to reach a suboptimal solution even in the presence of secure modes, like AES in CBC mode, showing a significant improvement with respect to a random agent; however, its ability to generalize in stochastic environments or big state spaces suffers greatly.

Anisotropic seismic tomography with the reversible jump Markov chain Monte Carlo

The established isotropic tomographic models show the features of subduction zones in terms of seismic velocity anomalies, but they are generally subjected to the generation of artifacts due to the lack of anisotropy in forward modelling. There is evidence for the significant influence of seismic anisotropy in the mid-upper mantle, especially for boundary layers like subducting slabs. As consequence, in isotropic models artifacts may be misinterpreted as compositional or thermal heterogeneities. In this thesis project the application of a trans-dimensional Metropolis-Hastings method is investigated in the context of anisotropic seismic tomography. This choice arises as a response to the important limitations introduced by traditional inversion methods which use iterative procedures of optimization of a function object of the inversion. On the basis of a first implementation of the Bayesian sampling algorithm, the code is tested with some cartesian two-dimensional models, and then extended to polar coordinates and dimensions typical of subduction zones, the main focus proposed for this method. Synthetic experiments with increasing complexity are realized to test the performance of the method and the precautions for multiple contexts, taking into account also the possibility to apply seismic ray-tracing iteratively. The code developed is tested mainly for 2D inversions, future extensions will allow the anisotropic inversion of seismological data to provide more realistic imaging of real subduction zones, less subjected to generation of artifacts.