PhD Position: Riemannian Geometry in Reinforcement Learning – AI4I

PhD Position:iemannian Geometry in Reinforcement Learning – AI4I Deadline December 17th 2025 at 12 (noon – CET) Curriculum Hostile and Unstructured Environments (CODE 11660), Topic number 1 Hosting Institution AI4I – The Italian Institute of Artificial Intelligence Funding Scheme This doctorate grant is fully funded by The Italian institute of Artificial Intelligence (AI4I) in collaboration withUniversità degli Studi di Genova Position Description The Italian Institute of Artificial Intelligence (AI4I) , in collaboration with Università degli Studi di Genova , invites applications for a PhD position in Riemannian Geometry in Reinforcement Learning as part of the PhD Programme in Hostile and Unstructured Environments. Reinforcement learning (RL) methods have been applied in a broad range of application domains, and represent one of the most successful learning paradigms for fine-tuning modern foundational models. However, most of RL methods work under the assumption that the states, actions and policy belong to Euclidean spaces. This PhD thesis is aimed at exploring how non-Euclidean geometries can be leveraged into the representation of states and actions in RL algorithms, and how such geometries impact the policy learning formulation. The first objective is to relax the Euclidean assumption on the formulation of a general RL problem via a Riemannian perspective. Later, the thesis will explore how methods like policy gradient need to be reformulated accordingly, and which advantages and challenges this new perspective brings in. Moreover, from a top-down approach, the next objective will be to leverage the Riemannian geometry of the Wasserstein space to understand, analyze and formulation policy learning methods based on Riemannian gradient flows and Wasserstein metrics. The thesis will explore applications of the developed methods in the control of physical systems such as robots or quadrotors, as well as the fine-tuning of foundational models, among others. Requirements Must have skills: Excellent Master’s degree in computer science, physics, mathematics, electrical or mechatronics engineering, or a related field Strong background in machine learning and robotics Good programming skills in Python Fluent in spoken and written English A team player, but also can work autonomously Experience with scientific writing Good to have skills: Background on (applied) differential geometry Publication of peer-reviewed research papers References 3. G. Tennenholtz and S. Mannor, “Uncertainty Estimation Using Riemannian Model Dynamics for Offline Reinforcement Learning”, NeurIPS, 2022. Number of Positions Available 1 Application Documents One-page cover letter including a short (two-paragraph) research proposal related to the PhD topic and aligned with your professional interests. Bachelor’s and Master’s diplomas with transcripts and grades. Main Research Site AI4I – The Italian Institute of Artificial Intelligence for IndustryCorso Castelfidardo 22, 10129 Torino, Italy What We Offer Access to high-performance computing resources and advanced research infrastructure. Opportunities for international collaboration and contributions to high-impact publications. A dynamic and interdisciplinary research environment. Financial support for attending international conference and Winter/Summer schools. Start Date 1st March 2026 How to Apply Applications for this position are managed by Università degli Studi di Genova .Please apply via the university’s official PhD admissions portal: AI4I – The Italian Research Institute for Artificial Intelligence AI4I has been founded to perform transformative, application-oriented research in Artificial Intelligence. AI4I is set to engage and empower gifted, entrepreneurial, young researchers who commit to producing an impact at the intersection of science, innovation, and industrial transformation. Highly competitive pay, bonus incentives, access to dedicated high-performance computing, state-of-the-art laboratories, industrial collaborations, and an ecosystem tailored to support the initiation and growth of startups stand out as some of the distinctive features of AI4I, bringing together people in a dynamic international environment. AI4I is an Institute that aims to enhance scientific research, technological