arXiv:2601.12604cs.LG2026-01被引 2

用f-softargmax替代softmax,加速强化学习收敛并降低样本需求。

Beyond Softmax and Entropy: Convergence Rates of Policy Gradients with f-SoftArgmax Parameterization & Coupled Regularization

  • 以f-softargmax替代传统softmax,改善优化地形
  • 结合对应f散度正则化,实现多项式样本复杂度
  • 无需预处理即可保证收敛,适合高维策略优化

策略梯度方法对策略参数化方式高度敏感。常用的softmax参数化会引发病态优化地形,导致收敛速度指数级变慢。尽管可通过预处理缓解,但计算开销大。本文提出用广义f-softargmax替代softmax,并耦合同源f散度正则化,使优化地形更优,且保证正则化目标满足Polyak-Łojasiewicz不等式。基于此结构,首次在无预处理条件下,为随机策略梯度方法在有限马尔可夫决策过程上建立了明确的非渐近最后迭代收敛性。同时推导了无正则化问题的样本复杂度界,表明采用Tsallis散度的f-PG可实现多项式样本复杂度,而标准softmax参数化则为指数级复杂度。

原文摘要 · Abstract (English)

Policy gradient methods are known to be highly sensitive to the choice of policy parameterization. In particular, the widely used softmax parameterization can induce ill-conditioned optimization landscapes and lead to exponentially slow convergence. Although this can be mitigated by preconditioning, this solution is often computationally expensive. Instead, we propose replacing the softmax with an alternative family of policy parameterizations based on the generalized f-softargmax. We further advocate coupling this parameterization with a regularizer induced by the same f-divergence, which improves the optimization landscape and ensures that the resulting regularized objective satisfies a Polyak-Lojasiewicz inequality. Leveraging this structure, we establish the first explicit non-asymptotic last-iterate convergence guarantees for stochastic policy gradient methods for finite MDPs without any form of preconditioning. We also derive sample-complexity bounds for the unregularized problem and show that f-PG, with Tsallis divergences achieves polynomial sample complexity in contrast to the exponential complexity incurred by the standard softmax parameterization.

强化学习策略梯度优化理论样本效率

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