Learning to optimize with guarantees: a complete characterization of linearly convergent algorithms
arXiv:2508.00775v2 Announce Type: replace-cross Abstract: The design of many classical optimization algorithms is driven by the certification of linear convergence rates over classes of optimization problems. In this paper, we consider the problem of improving the average-case performance of an algorithm over a specific distribution of problem instances. While this task can be tackled by embedding trainable components into the algorithm updates, a key challenge is to preserve worst-case guarantees across the entire problem class. For classes of composite optimization problems, we show that all
This research, published in 2026, represents a significant theoretical advancement in the field of artificial intelligence by addressing crucial aspects of algorithm optimization and reliability.
A strategic reader should care because improving the certifiable performance of AI algorithms, particularly in convergence and robustness, underpins more reliable and deployable AI systems across various industries.
This paper offers a complete characterization of linearly convergent algorithms, providing a foundational understanding that can lead to the design of more efficient and trustworthy AI, especially for critical applications in optimization problems.
- · AI algorithm developers
- · Optimization software providers
- · Industries relying on AI for critical decision-making
- · Academic researchers in machine learning
- · Developers of inefficient or uncertifiable algorithms
- · Sectors using black-box optimization without guarantees
The immediate effect is a more rigorous and theoretically grounded approach to designing robust AI optimization algorithms.
This could lead to a new generation of AI applications with higher certifiable performance, particularly in fields requiring strong guarantees.
Over time, this enhanced reliability might accelerate AI adoption in highly regulated or safety-critical domains where current AI solutions are deemed too unpredictable.
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Read at arXiv cs.LG