Mirror Descent Beyond Euclidean Stability: An Exponential Separation in Initialization Sensitivity
arXiv:2606.11431v1 Announce Type: new Abstract: Mirror Descent (MD) extends Gradient Descent (GD) beyond Euclidean geometry and has recently reappeared as a lens for KL-regularized policy optimization in reinforcement learning and LLM post-training. This raises a basic robustness question, crucial to reproducibility and reliability: how sensitive are MD dynamics to their inputs? We focus on initialization, often itself a pretrained or previously aligned model. Quadratic-regularized MD, including GD and Mahalanobis geometries, is well-known to be stable for convex smooth objectives. We show a s
The paper addresses a crucial robustness question for Mirror Descent, which has recently re-emerged as a fundamental technique in the rapidly advancing fields of reinforcement learning and large language model post-training.
Understanding the sensitivity of Mirror Descent dynamics to initialization is vital for the reproducibility, reliability, and safe deployment of advanced AI systems, particularly as they become more autonomous and critical.
This research reveals an exponential separation in initialization sensitivity for certain Mirror Descent applications beyond Euclidean stability, necessitating new considerations for model design and training in cutting-edge AI.
- · AI researchers focusing on robust optimization
- · Developers of AI safety and reliability tools
- · Organizations prioritizing dependable AI deployments
- · Developers neglecting robust initialization methods
- · AI systems with unaddressed initialization sensitivities
Increased focus on initial conditions and robustness in the development of advanced AI models.
Development of new initialization strategies or validation techniques to mitigate sensitivity issues in large language models and reinforcement learning.
Potential for new benchmarks and certification standards for AI model robustness, particularly concerning initialization sensitivity.
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