Data Compression for Fast Online Stochastic Optimization

Irina Wang, Marta Fochesato, Bartolomeo Stellato
https://arxiv.org/abs/2504.08097 https://arxiv.org/pdf/2504.08097 https://arxiv.org/html/2504.08097

arXiv:2504.08097v1 Announce Type: new
Abstract: We propose an online data compression approach for efficiently solving distributionally robust optimization (DRO) problems with streaming data while maintaining out-of-sample performance guarantees. Our method dynamically constructs ambiguity sets using online clustering, allowing the clustered configuration to evolve over time for an accurate representation of the underlying distribution. We establish theoretical conditions for clustering algorithms to ensure robustness, and show that the performance gap between our online solution and the nominal DRO solution is controlled by the Wasserstein distance between the true and compressed distributions, which is approximated using empirical measures. We provide a regret analysis, proving that the upper bound on this performance gap converges sublinearly to a fixed clustering-dependent distance, even when nominal DRO has access, in hindsight, to the subsequent realization of the uncertainty. Numerical experiments in mixed-integer portfolio optimization demonstrate significant computational savings, with minimal loss in solution quality.

#introduction

I am a scientist at Meta AI in NYC and study machine learning and optimization, recently involving reinforcement learning, control, optimal transport, and geometry. On social media, I enjoy finding and boosting interesting content from the original authors on these topics

I made this small animation with my recent project on optimal transport that connects continuous structures in the world. The source code to reproduce this and other examples is online at https://github.com/facebookresearch/w2ot

I'm a professor & #ISYE dept chair at #uwmadison, #INFORMS President-Elect, and the author of the blog #PunkRockOR.

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my Mastodon #intro/#introduction

#introductions

Hi, I'm Pietro. I work in the Discrete Optimization and Operations Research Group at the Politecnico di Milano. My research interests are in nonconvex optimization (mixed integer and nonlinear), multiobjective optimization, and optimization under uncertainty.

I am the developer of Couenne, an open-source MINLP solver. I also worked in the dev. team of FICO Xpress.

Glad to switch to a social network with the same name as a heavy metal band 😛

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