cs.AIMay 4, 2026

ANO: Robust Policy Optimization via Bounded, Redescending Gain Fields

Authors: Yiheng ZhangYiming WangKaiyan ZhaoZhenglin WanJiayu ChenLeong Hou U

Organizations: University of Macau · Wuhan University · National University of Singapore · University of Hong Kong

Abstract

Proximal Policy Optimization (PPO) dominates reinforcement learning and LLM alignment, yet its hard-clipping mechanism and unconstrained alternatives (e.g., SPO) sit at two extremes of a stability-efficiency dilemma. We argue that this dilemma is best understood dynamically: a surrogate objective is a feedback law on the probability ratio, and its clipping/penalty shape defines a gain field that drives the update dynamics. PPO's clip induces a dead zone (zero feedback outside the trust region), leaving the policy to drift open-loop under momentum; SPO's quadratic penalty induces an unbounded, linearly growing gain that stiffens the dynamics and destabilizes under aggressive step sizes. Guided by this view, we derive Anchored Neighborhood Optimization (ANO), which designs the gain field directly: a CC^\infty shaping kernel that anchors the identity map at r=1r{=}1, peaks exactly at a prescribed trust-region boundary 1+ε1{+}ε, bounds the push on severely off-policy samples by a tunable κ+κ_{+}, and exerts a bounded, redescending pull of tunable depth κκ_{-} on extreme outliers. The three hyperparameters have decoupled roles, and all internal constants are solved in closed form. Empirically, ANO ranks first on both Atari (40 games) and MuJoCo in IQM and Median of normalized scores. While the runner-up differs across domains (PAPO on Atari, SPO on MuJoCo), ANO is the only method consistently at the top. Under a learning-rate stress test (3×104 ⁣ ⁣1033\times10^{-4}\!\to\!10^{-3}), ANO degrades by only 0.9%0.9\% whereas PPO collapses by 54.5%54.5\%, and the stressed ANO still outperforms PPO and PAPO at their best-tuned learning rates.

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