← 研踪 PaperTrailarXiv:2601.07524 · v3
Stagewise Reinforcement Learning and the Geometry of the Regret Landscape
首次提交 2026-01-12 21:25
版本更新 2026-11-07 05:03
雷达观测 2026-11-10 10:11
摘要
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.
作者备注：48 pages, 10 figures
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v3 · 2026-11-07 05:03 · 最新观测版本
Stagewise Reinforcement Learning and the Geometry of the Regret Landscape
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.
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