Natural Policy Gradient as Doubly Smoothed Policy Iteration: A Bellman-Operator Framework

• URL: http://arxiv.org/abs/2605.10671v1
• Date: Mon, 11 May 2026 14:53:03 GMT
• Title: Natural Policy Gradient as Doubly Smoothed Policy Iteration: A Bellman-Operator Framework
• Abstract summary: We show that natural policy gradient admits an exact formulation as a smoothed and averaged form of policy iteration.<n>We introduce doubly smoothed policy iteration (DSPI), a Bellman-operator framework in which each policy is obtained by applying a regularized greedy step to a weighted average of past $Q$-functions.
• Score: 3.950802208390739
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this work, we show that natural policy gradient, a core algorithm in reinforcement learning, admits an exact formulation as a smoothed and averaged form of policy iteration. Specifically, we introduce doubly smoothed policy iteration (DSPI), a Bellman-operator framework in which each policy is obtained by applying a regularized greedy step to a weighted average of past $Q$-functions. DSPI includes policy iteration, dual-averaged policy iteration, natural policy gradient, and more general policy dual averaging methods as special cases. Using only monotonicity and contraction of smoothed Bellman operators, we prove distribution-free global geometric convergence of DSPI. Consequently, standard natural policy gradient and policy dual averaging achieve an iteration complexity of $\mathcal{O}((1-γ)^{-1}\log((1-γ)^{-1}ε^{-1}))$ for computing an $ε$-optimal policy, without modifying the MDP, adding regularization beyond the mirror map inherent in the update, or using adaptive, trajectory-dependent stepsizes. For the unregularized greedy case, corresponding to dual-averaged policy iteration, we also prove finite termination. The same Bellman-operator framework further extends to discounted MDPs with linear function approximation and stochastic shortest path problems.

Related papers

• Stochastic MeanFlow Policies: One-Step Generative Control with Entropic Mirror Descent [53.828537014796574]
  Online off-policy reinforcement learning (RL) is shaped by two choices: the policy class and the update rule.<n>We propose MeanFlow Policies, a one-step generative policy class that maps noise to actions through a MeanFlow transformation.<n>Across seven MuJoCo benchmarks, S improves over Gaussian and generative baselines while retaining single-step inference efficiency.
  arXiv  Detail & Related papers  (2026-05-20T15:14:14Z)
• Achieve Performatively Optimal Policy for Performative Reinforcement Learning [55.983627302691424]
  This work proposes a zeroth-order FrankWolfe- (0FW) algorithm with a gradient of performative policy in the framework.<n> Experimental results demonstrate that our 0FW is more effective than the existing approximation in finding the desired PO policy.
  arXiv  Detail & Related papers  (2025-10-06T01:56:31Z)
• Last-Iterate Convergent Policy Gradient Primal-Dual Methods for Constrained MDPs [107.28031292946774]
  We study the problem of computing an optimal policy of an infinite-horizon discounted Markov decision process (constrained MDP) We develop two single-time-scale policy-based primal-dual algorithms with non-asymptotic convergence of their policy iterates to an optimal constrained policy. To the best of our knowledge, this work appears to be the first non-asymptotic policy last-iterate convergence result for single-time-scale algorithms in constrained MDPs.
  arXiv  Detail & Related papers  (2023-06-20T17:27:31Z)
• Linear Convergence of Natural Policy Gradient Methods with Log-Linear Policies [115.86431674214282]
  We consider infinite-horizon discounted Markov decision processes and study the convergence rates of the natural policy gradient (NPG) and the Q-NPG methods with the log-linear policy class. We show that both methods attain linear convergence rates and $mathcalO (1/epsilon2)$ sample complexities using a simple, non-adaptive geometrically increasing step size.
  arXiv  Detail & Related papers  (2022-10-04T06:17:52Z)
• First-order Policy Optimization for Robust Markov Decision Process [40.2022466644885]
  We consider the problem of solving robust Markov decision process (MDP) MDP involves a set of discounted, finite state, finite action space MDPs with uncertain transition kernels. For $(mathbfs,mathbfa)$-rectangular uncertainty sets, we establish several structural observations on the robust objective.
  arXiv  Detail & Related papers  (2022-09-21T18:10:28Z)
• Sample Complexity of Policy-Based Methods under Off-Policy Sampling and Linear Function Approximation [8.465228064780748]
  off-policy sampling and linear function approximation are employed for policy evaluation. Various policy update rules, including natural policy gradient (NPG), are considered for policy update. We establish for the first time an overall $mathcalO(epsilon-2)$ sample complexity for finding an optimal policy.
  arXiv  Detail & Related papers  (2022-08-05T15:59:05Z)
• Efficient Policy Iteration for Robust Markov Decision Processes via Regularization [49.05403412954533]
  Robust decision processes (MDPs) provide a framework to model decision problems where the system dynamics are changing or only partially known. Recent work established the equivalence between texttts rectangular $L_p$ robust MDPs and regularized MDPs, and derived a regularized policy iteration scheme that enjoys the same level of efficiency as standard MDPs. In this work, we focus on the policy improvement step and derive concrete forms for the greedy policy and the optimal robust Bellman operators.
  arXiv  Detail & Related papers  (2022-05-28T04:05:20Z)
• Bregman Gradient Policy Optimization [97.73041344738117]
  We design a Bregman gradient policy optimization for reinforcement learning based on Bregman divergences and momentum techniques. VR-BGPO reaches the best complexity $tilde(epsilon-3)$ for finding an $epsilon$stationary point only requiring one trajectory at each iteration.
  arXiv  Detail & Related papers  (2021-06-23T01:08:54Z)
• On the Convergence and Sample Efficiency of Variance-Reduced Policy Gradient Method [38.34416337932712]
  Policy gives rise to a rich class of reinforcement learning (RL) methods, for example the REINFORCE. Yet the best known sample complexity result for such methods to find an $epsilon$-optimal policy is $mathcalO(epsilon-3)$, which is suboptimal. We study the fundamental convergence properties and sample efficiency of first-order policy optimization method.
  arXiv  Detail & Related papers  (2021-02-17T07:06:19Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.