Professor of Practice, SDA Bocconi School of Management, Bocconi University, Milan
ERC Principal Investigator · Researcher at Inria (on leave)
I work on guarantees for AI: statistical guarantees for learning at scale, certificates of optimality for non-convex problems, and machine-checked proofs for AI systems that reason and act.
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My work makes guarantees practical. I designed FALKON, which made kernel learning with optimal statistical guarantees practical on billions of points. With kernel sums-of-squares, non-convex optimization problems are transformed into equivalent high-dimensional convex ones, whose solutions come with a certificate of how close they are to the global optimum. My ERC project REAL develops learning methods that are reliable, with explicit bounds on their error, and cost-effective.
I now work on machine-checked guarantees for AI systems that reason and act. With Carlo Ciliberto and Enrico Tassi I introduced Proof Carrying Contracts (PC2), an open protocol that makes agreements between AI agents enforceable: before an action covered by the agreement runs, the agent must supply a machine-checkable proof that it preserves the agreed constraints. I also work on infrastructure for formalized mathematics at scale and on the confidential deployment of language models.
Before Bocconi I spent seven years at Inria and École Normale Supérieure in Paris, where I led a group of more than ten PhD students and postdocs. In industry I was VP of AI at Prem AI (until June 2026), a Swiss company building confidential AI infrastructure, and worked on machine learning with EliseAI, SNCF and LightOn. I studied computer science in Rome and worked as a software engineer before a PhD at the University of Genoa and IIT, with a visiting period at MIT, and a postdoc at IIT and MIT.
Open protocol · 2026–
Enforceable agreements between AI agents acting for different people and organisations. Before an action covered by the agreement runs, the agent must supply a machine-checkable proof that it preserves the agreed constraints, and an execution environment, the Airlock, checks the proof. Commitments are preserved when work is delegated to other agents.
AI for Math Fund · 2026–2028
An AI-first database for formalized mathematics. Lean-compatible formal artifacts live in one persistent, versioned and queryable corpus, so that theorem provers and autoformalization systems can find, reuse and build on each other's results.
ERC Starting Grant · 2021–2027
Learning methods that come with explicit bounds on their error and use the least computation needed to reach them: optimal kernel methods at billion scale, certified non-convex optimization, learning of dynamical systems.
AI agents increasingly act for different people and organisations: they buy services, exchange information and delegate work to one another. What an agent must respect is written as text, and text does not make it comply. Proof Carrying Contracts turn agreed constraints into conditions checked before each action, so that parties can rely on an agreement without having to trust one another's agents.
Proof-carrying contracts: commitments AI agents cannot break, arXiv 2026
Program: Proof Carrying Contracts (PC2).
A machine-checked proof is the strongest guarantee there is, and AI is making proofs cheaper to produce. I work on the infrastructure that lets AI systems produce, find and reuse formal proofs at scale.
Program: Searchable formalized mathematics at scale (2026–2028).
How to run large language models so that only the user can read prompts and answers, and what trusted execution environments, homomorphic encryption and multi-party computation can each guarantee today.
Privacy-preserving LLM inference in practice, Cryptology ePrint Archive, 2026.
When can approximations make learning cheaper without losing statistical accuracy? Nyström and random-feature methods with optimal rates led to FALKON, which trains kernel models on billions of points on GPUs.
Less is more: Nyström computational regularization, NeurIPS 2015, oral
Generalization properties of learning with random features, NeurIPS 2017, oral
FALKON: an optimal large scale kernel method, NeurIPS 2017
Kernel methods through the roof: handling billions of points efficiently, NeurIPS 2020, oral
Kernel sums-of-squares represent non-negative functions so that non-convex optimization problems are transformed into equivalent high-dimensional convex ones; the solution comes with a certificate of how close it is to the global optimum.
Finding global minima via kernel approximations, Mathematical Programming 2025
Non-convex optimization with certificates and fast rates through kernel sums of squares, COLT 2022
GloptiNets: scalable non-convex optimization with certificates, NeurIPS 2023, spotlight
Learning stochastic dynamics from data with rates of convergence, and exploring an unknown system without violating safety constraints.
Safely learning controlled stochastic dynamics, NeurIPS 2025
Non-parametric learning of stochastic differential equations with non-asymptotic fast rates, Foundations of Computational Mathematics 2026
Efficient sampling of stochastic differential equations with positive semi-definite models, NeurIPS 2023
A general theory for learning to predict structured objects, such as sequences, graphs and rankings, with consistency guarantees.
A consistent regularization approach for structured prediction, NeurIPS 2016
A general framework for consistent structured prediction with implicit loss embeddings, JMLR 2020
Localized structured prediction, NeurIPS 2019
Kernel learning with optimal statistical guarantees, made practical at scale: the method reaches optimal accuracy in O(n√n) time and O(n) memory, and its open-source multi-GPU library trains on billions of points. Library developed with Giacomo Meanti (lead developer), Luigi Carratino and Lorenzo Rosasco.
Used for model-independent searches for new physics in particle physics (Eur. Phys. J. C, 2022, and follow-ups at MIT, Geneva and ETH Zürich), for 3D surface reconstruction (Neural Splines, CVPR 2021) and for fast on-line learning on the iCub humanoid robot (IEEE Transactions on Robotics, 2022). A standard baseline for large-scale kernel solvers.
At Inria and École Normale Supérieure I co-supervised nine PhD students and four postdocs. Where they are now:
Current PhD students at Inria: Andrea Basteri (with Francis Bach) and Pierre Boudart (with Alexandre d'Aspremont and Pierre Gaillard).
Seven research and engineering positions on PC2 are being prepared, based in Milan (Bocconi, REAL) and Turin (AI4I, PRAXIS): see the positions.
Area chair for NeurIPS, ICML and COLT. Reviewer for the Journal of Machine Learning Research, the Annals of Statistics, Applied and Computational Harmonic Analysis and Inverse Problems.
alessandro.rudi@sdabocconi.it
SDA Bocconi School of Management, Via Sarfatti 10, 20136 Milan, Italy