Why Policy Gradient Algorithms Work for Undiscounted Total-Reward MDPs

• URL: http://arxiv.org/abs/2510.18340v1
• Date: Tue, 21 Oct 2025 06:46:21 GMT
• Title: Why Policy Gradient Algorithms Work for Undiscounted Total-Reward MDPs
• Authors: Jongmin Lee, Ernest K. Ryu,
• Abstract summary: The classical policy gradient method is the theoretical and conceptual foundation of modern policy-based reinforcement learning algorithms.<n>A recent line of work on policy-based RL for large language models uses the undiscounted total-reward setting with $gamma = 1$, rendering much of the existing theory inapplicable.
• Score: 28.213334434903775
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The classical policy gradient method is the theoretical and conceptual foundation of modern policy-based reinforcement learning (RL) algorithms. Most rigorous analyses of such methods, particularly those establishing convergence guarantees, assume a discount factor $\gamma < 1$. In contrast, however, a recent line of work on policy-based RL for large language models uses the undiscounted total-reward setting with $\gamma = 1$, rendering much of the existing theory inapplicable. In this paper, we provide analyses of the policy gradient method for undiscounted expected total-reward infinite-horizon MDPs based on two key insights: (i) the classification of the MDP states into recurrent and transient states is invariant over the set of policies that assign strictly positive probability to every action (as is typical in deep RL models employing a softmax output layer) and (ii) the classical state visitation measure (which may be ill-defined when $\gamma = 1$) can be replaced with a new object that we call the transient visitation measure.

Related papers

• Random Policy Valuation is Enough for LLM Reasoning with Verifiable Rewards [47.557539197058496]
  We introduce Random Policy Valuation for Diverse Reasoning (ROVER)<n>ROVER is a minimalist yet highly effective RL method that samples actions from a softmax over uniform-policy Q-values.<n>It demonstrates superior performance in both textbfquality (textbf+8.2 on pass@1, textbf+16.8 on pass@256) and textbfdiversity (textbf+17.6%)
  arXiv  Detail & Related papers  (2025-09-29T16:09:07Z)
• Convergence and Sample Complexity of First-Order Methods for Agnostic Reinforcement Learning [66.4260157478436]
  We study reinforcement learning in the policy learning setting.<n>The goal is to find a policy whose performance is competitive with the best policy in a given class of interest.
  arXiv  Detail & Related papers  (2025-07-06T14:40:05Z)
• Convergence of Policy Mirror Descent Beyond Compatible Function Approximation [66.4260157478436]
  We develop theoretical PMD general policy classes where we strictly assume a weaker variational dominance and obtain convergence to the best-in-class policy.<n>Our main notion leverages a novel notion induced by the local norm induced by the occupancy- gradient measure.
  arXiv  Detail & Related papers  (2025-02-16T08:05:46Z)
• Achieving $\widetilde{\mathcal{O}}(\sqrt{T})$ Regret in Average-Reward POMDPs with Known Observation Models [69.1820058966619]
  We tackle average-reward infinite-horizon POMDPs with an unknown transition model.<n>We present a novel and simple estimator that overcomes this barrier.
  arXiv  Detail & Related papers  (2025-01-30T22:29:41Z)
• Multilinear Tensor Low-Rank Approximation for Policy-Gradient Methods in Reinforcement Learning [27.868175900131313]
  Reinforcement learning (RL) aims to estimate the action to take given a (time-varying) state.<n>This paper postulates multi-linear mappings to efficiently estimate the parameters of the RL policy.<n>We leverage the PARAFAC decomposition to design tensor low-rank policies.
  arXiv  Detail & Related papers  (2025-01-08T23:22:08Z)
• Last-Iterate Global Convergence of Policy Gradients for Constrained Reinforcement Learning [62.81324245896717]
  We introduce an exploration-agnostic algorithm, called C-PG, which exhibits global last-ite convergence guarantees under (weak) gradient domination assumptions. We numerically validate our algorithms on constrained control problems, and compare them with state-of-the-art baselines.
  arXiv  Detail & Related papers  (2024-07-15T14:54:57Z)
• On the Global Convergence of Policy Gradient in Average Reward Markov Decision Processes [50.68789924454235]
  We present the first finite time global convergence analysis of policy gradient in the context of average reward Markov decision processes (MDPs) Our analysis shows that the policy gradient iterates converge to the optimal policy at a sublinear rate of $Oleft(frac1Tright),$ which translates to $Oleft(log(T)right)$ regret, where $T$ represents the number of iterations.
  arXiv  Detail & Related papers  (2024-03-11T15:25:03Z)
• 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)
• Policy Optimization over General State and Action Spaces [3.722665817361884]
  Reinforcement learning (RL) problems over general state and action spaces are notoriously challenging. We first present a substantial generalization of the recently developed policy mirror descent method to deal with general state and action spaces. We introduce new approaches to incorporate function approximation into this method, so that we do not need to use explicit policy parameterization at all.
  arXiv  Detail & Related papers  (2022-11-30T03:44:44Z)
• PC-PG: Policy Cover Directed Exploration for Provable Policy Gradient Learning [35.044047991893365]
  This work introduces the the Policy Cover-Policy Gradient (PC-PG) algorithm, which balances the exploration vs. exploitation tradeoff using an ensemble of policies (the policy cover) We show that PC-PG has strong guarantees under model misspecification that go beyond the standard worst case $ell_infty$ assumptions. We also complement the theory with empirical evaluation across a variety of domains in both reward-free and reward-driven settings.
  arXiv  Detail & Related papers  (2020-07-16T16:57:41Z)

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.