PhD Position on Riemannian Geometry in Reinforcement Learning
AI4I – The Italian Institute of Artificial Intelligence and Università degli Studi di Genova invite applications for a PhD position in Riemannian Geometry in Reinforcement Learning as part of the PhD Programme in Hostile and Unstructured Environments.
Deadline
December 17th 2025 at 12 (noon – CET)
Hosting Institution
AI4I – The Italian Institute of Artificial Intelligence
Department
PHI Lab
Funding Scheme
This doctorate grant is fully funded by AI4I in collaboration with Università degli Studi di Genova.
Position Description
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.
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.

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
Please apply via the university’s official PhD admissions portal :
Details
Primary Hosting Institution: AI4I – The Italian Institute of Artificial Intelligence for Industry
About AI4I
AI4I – The Italian Research Institute for Artificial Intelligence 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.
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