# Data assimilation and online optimization with performance guarantees

## TL;DR

This paper introduces the ONDA Algorithm for real-time stochastic optimization that adaptively incorporates streaming data, ensuring high-probability performance guarantees and convergence under controlled data rates.

## Contribution

The paper presents a novel online data assimilation algorithm within a distributionally robust framework that guarantees performance and convergence in streaming data scenarios.

## Key findings

- Guarantees high-probability out-of-sample performance
- Converges with sufficiently slow data streaming rate
- Provides criteria for algorithm termination

## Abstract

This paper considers a class of real-time stochastic optimization problems dependent on an unknown probability distribution. In the considered scenario, data is streaming frequently while trying to reach a decision. Thus, we aim to devise a procedure that incorporates samples (data) of the distribution sequentially and adjusts decisions accordingly. We approach this problem in a distributionally robust optimization framework and propose a novel Online Data Assimilation Algorithm (ONDA Algorithm) for this purpose. This algorithm guarantees out-of-sample performance of decisions with high probability, and gradually improves the quality of the decisions by incorporating the streaming data. We show that the ONDA Algorithm converges under a sufficiently slow data streaming rate, and provide a criteria for its termination after certain number of data have been collected. Simulations illustrate the results.