arXiv:2605.11908cs.LG2026-05

新算法让强化学习避开低效策略陷阱,加速收敛到最优解。

Delightful Gradients Accelerate Corner Escape

论文配图:Delightful Gradients Accelerate Corner Escape
图 1 · 摘自论文原文
  • 用优势与动作意外度乘积控制梯度,打破角落陷阱机制。
  • 在多臂老虎机中,逃出次优角落的时间对数级依赖初始概率比。
  • 适合解决初始策略不佳的强化学习问题,尤其在复杂网络中表现更优。

Softmax策略梯度以 $O(1/t)$ 收敛,但在单纯形的次优角落附近可能呈指数级缓慢。瓶颈在于自陷:负优势动作会强化角落策略,并可能将最优动作推向后退。我们研究了 extit{愉悦策略梯度}(DG),其通过优势与动作意外度的乘积来门控每项梯度。对于 $K$-臂老虎机,我们证明,在零温度极限下,DG 在任意次优角落附近的定量区域中消除了这一陷阱机制,实现首次退出时间对数级于初始概率比。在任意固定温度下,由于有害动作随稀有程度多项式抑制,该局部机制仍存在。关键洞察是:任何优于角落动作的动作都是 extit{盟友},其对逃离的贡献非负。结合角落不稳定性与单调值提升恒等式,我们证明在多臂老虎机和表格型马尔可夫决策过程(tabular MDPs)中,DG 全局收敛至最优策略,渐近速率保持 $O(1/t)$。然而,通过精确反例表明,该机制在共享函数逼近下可能失效。在使用共享参数神经网络的MNIST上下文老虎机任务中,尽管如此,DG 仍能比标准策略梯度更快从坏初始化恢复,暗示该反例标志的是理论边界而非实际限制。

原文摘要 · Abstract (English)

Softmax policy gradient converges at $O(1/t)$, but its transient behavior near sub-optimal corners of the simplex can be exponentially slow. The bottleneck is self-trapping: negative-advantage actions reinforce the corner policy and can initially push the optimal action backward. We study \emph{Delightful Policy Gradient} (DG), which gates each policy-gradient term by the product of advantage and action surprisal. For $K$-armed bandits, we prove that the zero-temperature limit of DG removes this corner-trapping mechanism on a quantitative sector near any sub-optimal corner, yielding a first-exit escape bound logarithmic in the initial probability ratio. At every fixed temperature, the same local mechanism persists because harmful actions are polynomially suppressed as they become rare. A key structural insight is that every action better than the corner action is an \emph{ally}: its contribution to escape is non-negative. Combining corner instability with a monotonic value improvement identity, we prove that DG converges globally to the optimal policy in both bandits and tabular MDPs at an asymptotic $O(1/t)$ rate. We also show, via an exact counterexample, that this tabular mechanism can fail under shared function approximation. In MNIST contextual bandits with a shared-parameter neural network, DG nevertheless recovers from bad initializations faster than standard policy gradient, suggesting that the counterexample marks a boundary of the theory rather than a practical prohibition.

强化学习策略梯度收敛加速多臂老虎机

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