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Optimization over probability measures has become a cornerstone of modern machine learning and artificial intelligence. Traditional optimization techniques work with fixed datasets or parameters, but Anna Korba’s project goes further: it develops tools that operate directly on entire probability distributions, including very large or even infinite-dimensional spaces.

This framework has powerful implications for sampling tasks, generating representative examples from a distribution or model, which are critical in fields such as:

• Bayesian machine learning, where sampling helps quantify uncertainty in model predictions

• Generative modeling, where it enables creating realistic new data, such as images or complex biological structures

However, existing sampling and optimization techniques often face significant limitations: they can be computationally expensive, difficult to evaluate, and poorly suited to high-dimensional or complex data. Moreover, current models are mainly designed for vectorial data and struggle with more sophisticated infinite-dimensional structures.

OptInfinite aims to overcome these challenges by creating a unified theoretical and practical framework. Leveraging tools from optimal transport and information geometry, the project will:

• develop more efficient and adaptable sampling algorithms

• design robust evaluation methods to assess the quality of generated samples

• deliver an open-source software toolkit to make these techniques widely accessible

The methods developed through OptInfinite will be tested on real-world applications, including large-scale AI models, Bayesian inference, biological systems modeling, and beyond.