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[2601.07524] Stagewise Reinforcement Learning and the Geometry of the Regret Landscape
Summary
This paper explores Stagewise Reinforcement Learning (SRL) and its relation to the geometry of the regret landscape, demonstrating how learning transitions from simple to complex policies as training progresses.
Why It Matters
Understanding the dynamics of reinforcement learning through the lens of regret geometry can enhance the development of more efficient learning algorithms. This research provides insights into policy evolution, which is crucial for improving AI training methodologies and applications.
Key Takeaways
- The study extends singular learning theory to reinforcement learning.
- Local learning coefficients govern the concentration of policies in SRL.
- Empirical results show a clear phase transition in policy complexity during training.
Computer Science > Machine Learning arXiv:2601.07524 (cs) [Submitted on 12 Jan 2026 (v1), last revised 25 Feb 2026 (this version, v2)] Title:Stagewise Reinforcement Learning and the Geometry of the Regret Landscape Authors:Chris Elliott, Einar Urdshals, David Quarel, Matthew Farrugia-Roberts, Daniel Murfet View a PDF of the paper titled Stagewise Reinforcement Learning and the Geometry of the Regret Landscape, by Chris Elliott and 4 other authors View PDF HTML (experimental) Abstract:Singular learning theory characterizes Bayesian learning as an evolving tradeoff between accuracy and complexity, with transitions between qualitatively different solutions as sample size increases. We extend this theory to reinforcement learning, proving that the concentration of a generalized posterior over policies is governed by the local learning coefficient (LLC), an invariant of the geometry of the regret function. This theory predicts that deep reinforcement learning with SGD should proceed from simple policies with high regret to complex policies with low regret. We verify this prediction empirically in a gridworld environment exhibiting stagewise policy development: phase transitions over training manifest as "opposing staircases" where regret decreases sharply while the LLC increases. Comments: Subjects: Machine Learning (cs.LG) Cite as: arXiv:2601.07524 [cs.LG] (or arXiv:2601.07524v2 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2601.07524 Focus to learn more arXiv-i...
