Finite-sample guarantees for data-driven forward-backward operator methods
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Abstract (arXiv)
We establish finite sample certificates on the quality of solutions produced by data-based forward-backward (FB) operator splitting schemes. As frequently happens in stochastic regimes, we consider the problem of finding a zero of the sum of two operators, where one is either unavailable in closed form or computationally expensive to evaluate, and shall therefore be approximated using a finite number of noisy oracle samples. Under the lens of algorithmic stability, we then derive probabilistic bounds on the distance between a true zero and the FB output without making specific assumptions about the underlying data distribution. We show that under weaker conditions ensuring the convergence of FB schemes, stability bounds grow proportionally to the number of iterations. Conversely, stronger assumptions yield stability guarantees that are independent of the iteration count. We then specialize our results to a popular FB stochastic Nash equilibrium seeking algorithm and validate our theoretical bounds on a control problem for smart grids, where the energy price uncertainty is approximated by means of historical data.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 22 of its 57 references that are in the map. First posted on arXiv 22 Dec 2025.
Builds on
22 of 57 references.
References · 22
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- 2013The Scenario Approach for Stochastic Model Predictive Control with Bounds on Closed-Loop Constraint Violationscited by 19
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Citing papers per year: 2026: 1.
1 paper.