Soft Deterministic Policy Gradient with Gaussian Smoothing

• URL: http://arxiv.org/abs/2605.06228v1
• Date: Thu, 07 May 2026 13:21:01 GMT
• Title: Soft Deterministic Policy Gradient with Gaussian Smoothing
• Abstract summary: We use a smoothed Bellman equation to derive the soft deterministic policy gradient (Soft-DPG)<n>We instantiate this framework into a deep reinforcement learning algorithm, which we call soft deep deterministic policy gradient (Soft DDPG)
• Score: 6.622208195193136
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Deterministic policy gradient (DPG) is widely utilized for continuous control; however, it inherently relies on the differentiability of the critic with respect to the action during policy updates. This assumption is violated in practical control problems involving sparse or discrete rewards, leading to ill-defined policy gradients and unstable learning. To address these challenges, we propose a principled alternative based on a smoothed Bellman equation formulated via Gaussian smoothing. Specifically, we define a novel action-value function based on a smoothed Bellman equation and derive the soft deterministic policy gradient (Soft-DPG). Our formulation eliminates explicit dependence on critic action-gradients and ensures that the gradient remains well-defined even for non-smooth Q-functions. We instantiate this framework into a deep reinforcement learning algorithm, which we call soft deep deterministic policy gradient (Soft DDPG). Empirical evaluations on standard continuous control benchmarks and their discretized-reward variants show that Soft DDPG remains competitive in dense-reward settings and provides clear gains in most discretized-reward environments, where standard DDPG is more sensitive to irregular critic landscapes.

Related papers

• Wasserstein Proximal Policy Gradient [10.574676421687718]
  We study policy gradient methods for continuous-action, entropy-regularized learning through the lens of Wasserstein geometry.<n>We derive Wasserstein Proximal Policy Gradient (WWPG) via an operator-splitting scheme that alternates an optimal transport update with a heat step implemented by WPPG.<n>We establish a global linear convergence rate for WPPG, covering both exact policy evaluation and actor-critic implementations with controlled approximation error.
  arXiv  Detail & Related papers  (2026-03-03T03:48:09Z)
• Not All Preferences Are Created Equal: Stability-Aware and Gradient-Efficient Alignment for Reasoning Models [52.48582333951919]
  We propose a dynamic framework designed to enhance alignment reliability by maximizing the Signal-to-Noise Ratio of policy updates.<n>SAGE (Stability-Aware Gradient Efficiency) integrates a coarse-grained curriculum mechanism that refreshes candidate pools based on model competence.<n> Experiments on multiple mathematical reasoning benchmarks demonstrate that SAGE significantly accelerates convergence and outperforms static baselines.
  arXiv  Detail & Related papers  (2026-02-01T12:56:10Z)
• Stabilizing the Q-Gradient Field for Policy Smoothness in Actor-Critic [7.536387580547838]
  We argue that policy non-smoothness is governed by the differential geometry of the critic.<n>We introduce PAVE, a critic-centric regularization framework.<n>PAVE rectifies the learning signal by minimizing the Q-gradient volatility while preserving local curvature.
  arXiv  Detail & Related papers  (2026-01-30T13:32:52Z)
• Learning Deterministic Policies with Policy Gradients in Constrained Markov Decision Processes [59.27926064817273]
  We introduce an exploration-agnostic algorithm, called C-PG, which enjoys global last-iterate convergence guarantees under domination assumptions.<n>We empirically validate both the action-based (C-PGAE) and parameter-based (C-PGPE) variants of C-PG on constrained control tasks.
  arXiv  Detail & Related papers  (2025-06-06T10:29:05Z)
• Learning Optimal Deterministic Policies with Stochastic Policy Gradients [62.81324245896716]
  Policy gradient (PG) methods are successful approaches to deal with continuous reinforcement learning (RL) problems. In common practice, convergence (hyper)policies are learned only to deploy their deterministic version. We show how to tune the exploration level used for learning to optimize the trade-off between the sample complexity and the performance of the deployed deterministic policy.
  arXiv  Detail & Related papers  (2024-05-03T16:45:15Z)
• Policy Gradient for Rectangular Robust Markov Decision Processes [62.397882389472564]
  We introduce robust policy gradient (RPG), a policy-based method that efficiently solves rectangular robust Markov decision processes (MDPs) Our resulting RPG can be estimated from data with the same time complexity as its non-robust equivalent.
  arXiv  Detail & Related papers  (2023-01-31T12:40:50Z)
• Optimal Estimation of Off-Policy Policy Gradient via Double Fitted Iteration [39.250754806600135]
  Policy (PG) estimation becomes a challenge when we are not allowed to sample with the target policy. Conventional methods for off-policy PG estimation often suffer from significant bias or exponentially large variance. In this paper, we propose the double Fitted PG estimation (FPG) algorithm.
  arXiv  Detail & Related papers  (2022-01-31T20:23:52Z)
• Improper Learning with Gradient-based Policy Optimization [62.50997487685586]
  We consider an improper reinforcement learning setting where the learner is given M base controllers for an unknown Markov Decision Process. We propose a gradient-based approach that operates over a class of improper mixtures of the controllers.
  arXiv  Detail & Related papers  (2021-02-16T14:53:55Z)
• Zeroth-order Deterministic Policy Gradient [116.87117204825105]
  We introduce Zeroth-order Deterministic Policy Gradient (ZDPG) ZDPG approximates policy-reward gradients via two-point evaluations of the $Q$function. New finite sample complexity bounds for ZDPG improve upon existing results by up to two orders of magnitude.
  arXiv  Detail & Related papers  (2020-06-12T16:52:29Z)

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.