Extending theoretical guarantees beyond smooth and fully observed settings

Extend the stability and descent-style guarantees of the bias–noise–alignment diagnostic-driven methods to settings involving non-smooth objectives, delayed feedback, or partially observed error signals.

Background

The theoretical analysis in the paper relies on standard smoothness and bounded-variance assumptions. These assumptions facilitate bounded updates and descent behavior but may not hold in many practical scenarios.

The authors explicitly identify the extension of guarantees to non-smooth, delayed-feedback, and partially observed error regimes as an open challenge, signaling the need for broader theoretical foundations.

References

Finally, the theoretical analysis in this work relies on standard smoothness and bounded-variance assumptions; extending guarantees to non-smooth objectives, delayed feedback, or partially observed error signals remains an open challenge.

— Adaptive Learning Guided by Bias-Noise-Alignment Diagnostics  (2512.24445 - Samanta et al., 30 Dec 2025) in Section 7: Unified Perspective, Implications, and Limitations