Unsupervised reinforcement learning via state entropy maximization

Reinforcement Learning (RL) provides a powerful framework to address sequential decision-making problems in which the transition dynamics is unknown or too complex to be represented. The RL approach is based on speculating what is the best decision to make given sample estimates obtained from previous interactions, a recipe that led to several breakthroughs in various domains, ranging from game playing to robotics. Despite their success, current RL methods hardly generalize from one task to another, and achieving the kind of generalization obtained through unsupervised pre-training in non-sequential problems seems unthinkable. Unsupervised RL has recently emerged as a way to improve generalization of RL methods. Just as its non-sequential counterpart, the unsupervised RL framework comprises two phases: An unsupervised pre-training phase, in which the agent interacts with the environment without external feedback, and a supervised fine-tuning phase, in which the agent aims to efficiently solve a task in the same environment by exploiting the knowledge acquired during pre-training. In this thesis, we study unsupervised RL via state entropy maximization, in which the agent makes use of the unsupervised interactions to pre-train a policy that maximizes the entropy of its induced state distribution. First, we provide a theoretical characterization of the learning problem by considering a convex RL formulation that subsumes state entropy maximization. Our analysis shows that maximizing the state entropy in finite trials is inherently harder than RL. Then, we study the state entropy maximization problem from an optimization perspective. Especially, we show that the primal formulation of the corresponding optimization problem can be (approximately) addressed through tractable linear programs. Finally, we provide the first practical methodologies for state entropy maximization in complex domains, both when the pre-training takes place in a single environment as well as multiple environments.

Essays on risk-taking in corporate finance

This thesis consists of three independent essays on risk-taking in corporate finance. The first essay explores how community-level social capital (CSC), framed as a cultural characteristic of individuals born in different provinces of Italy, affects investment behavior in equity crowdfunding. Results show that investors born in high-CSC provinces invest more money in ventures characterized by an enhanced risk profile. Observed risk-taking is theoretically linked to higher generalized trust endowed to people born in high-CSC areas. The second essay focuses on how convexity of Chief Financial Officers’ stock options affects their hedging decisions in the oil and gas industry. Highly convex CFOs hedge less commodity price risk, even if the Chief Executive Officer’s incentives are consistent with a more conservative hedging strategy. Finally, the third essay is a systematic literature review on how different sources of compensation-based risk-taking incentives of Chief Executive Officers affect decision-making in corporate finance.

Poset associahedra as sections of graph associahedra

Poset associahedra are a family of convex polytopes recently introduced by Pavel Galashin in 2021. The associahedron An is an (n-2)-dimensional convex polytope whose facial structure encodes the ways of parenthesizing an n-letter word (among several equivalent combinatorial objects). Associahedra are deeply studied polytopes that appear naturally in many areas of mathematics: algebra, combinatorics, geometry, topology... They have many presentations and generalizations. One of their incarnations is as a compactification of the configuration space of n points on a line. Similarly, the P-associahedron of a poset P is a compactification of the configuration space of order preserving maps from P to R. Galashin presents poset associahedra as combinatorial objects and shows that they can be realized as convex polytopes. However, his proof is not constructive, in the sense that no explicit coordinates are provided. The main goal of this thesis is to provide an explicit construction of poset associahedra as sections of graph associahedra, thus solving the open problem stated in Remark 1.5 of Galashin's paper.

AGV Safety Areas Obstacle Detection and Interaction with Point Cloud Derived Map

This thesis project aims to the development of an algorithm for the obstacle detection and the interaction between the safety areas of an Automated Guided Vehicles (AGV) and a Point Cloud derived map inside the context of a CAD software. The first part of the project focuses on the implementation of an algorithm for the clipping of general polygons, with which has been possible to: construct the safety areas polygon, derive the sweep of this areas along the navigation path performing a union and detect the intersections with line or polygon representing the obstacles. The second part is about the construction of a map in terms of geometric entities (lines and polygons) starting from a point cloud given by the 3D scan of the environment. The point cloud is processed using: filters, clustering algorithms and concave/convex hull derived algorithms in order to extract line and polygon entities representing obstacles. Finally, the last part aims to use the a priori knowledge of possible obstacle detections on a given segment, to predict the behavior of the AGV and use this prediction to optimize the choice of the vehicle's assigned velocity in that segment, minimizing the travel time.