Deep Deterministic Policy Gradient

Also known as DDPG

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Oct 7, 2026math.OC

Boundary-aware Reinforcement Learning for Hypercube State Spaces via Deterministic Policy Gradient

We develop a continuous-time deterministic policy gradient framework for reinforcement learning with reflected state dynamics, where the state process is governed by a controlled reflected stochastic differential equation on a hypercube. Under suitable regularity assumptions, we establish the connection between the value function and the Neumann Bellman equation, introduce an advantage-rate function that yields a deterministic policy gradient formula, and prove the martingale characterization theorem. Motivated by these theoretical results, we propose a continuous-time deep deterministic policy gradient algorithm for reflected stochastic systems, in which the Neumann boundary condition is imposed via either soft penalization or hard architectural constraint. We further quantify the discrepancy between the ideal continuous-time dynamics and the discretely sampled exploratory dynamics executed in practice, showing that the error decays as the time grid is refined and exploration noise vanishes. Our experiments on reservoir control problems illustrate the effectiveness of the RL framework, highlighting that boundary-aware methods substantially reduce Neumann boundary residuals and enhance learning stability.

Lijun Bo, Yijie Huang, Chenhao Lu

RL ControlReinforcement LearningContinuous-Time RLDeep Deterministic Policy GradientStochastic Differential Equations
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Jul 21, 2026cs.LG

A Self-Evolving Default Action for Cooperative Tasks with Continuous Action Space

Counterfactual credit assignment has proven effective in multi-agent reinforcement learning (MARL) for discrete action spaces, yet its extension to continuous-action cooperative tasks remains challenging. Existing methods that approximate the counterfactual baseline via Monte Carlo sampling often introduce bias into policy gradients and fail to guarantee convergence to local optima, as the sampled actions may not have been sufficiently trained. To address these limitations, we propose SAFE, a novel MARL framework that employs a counterfactual baseline conditioned on a self-evolving default action sampled from each agent's experience buffer. This design naturally extends to continuous action spaces without relying on additional simulations, reward models, or environment-specific prior knowledge. The baseline accurately quantifies each agent's contribution, and introduces no bias into the deterministic policy gradient, ensuring convergence to local optima. Extensive experiments on cooperative vehicular tasks demonstrate that SAFE consistently outperforms state-of-the-art models.

Shuangyao Huang

Xi’an Jiaotong-Liverpool University School of Internet of Things

Policy GradientCredit AssignmentDeep Deterministic Policy GradientCooperative MARLCounterfactual Credit AssignmentMulti-Agent Reinforcement Learning
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Jul 17, 2026cs.LG

CLaC@FinMMEval 2026 Task 3: Sentiment-Augmented Deep Reinforcement Learning for Active Trading -- An Alpha-Reward Approach

This paper presents our system for Task 3 of the CLEF 2026 FinMMEval Lab, which requires daily long, flat, or short trading decisions for Bitcoin (BTC) and Tesla (TSLA) using news and historical market data. We formulate the problem as a discrete-action Markov Decision Process and compare four deep reinforcement learning algorithms: Policy Gradient (PG), Proximal Policy Optimization (PPO), Deep Q-Learning (DQL), and Deep Deterministic Policy Gradient (DDPG). The agents use technical indicators, cyclical calendar encodings, and daily news sentiment scores produced by LLaMA 3.2 1B. To reduce overfitting and align training with the objective of outperforming buy-and-hold, we introduce an alpha reward based on excess market return and randomize episode start dates. Hyperparameters are optimized with Ray Tune over 180 trials per algorithm-asset pair, with early stopping and model selection based on validation Sharpe ratio. On the CLEF Task 3 test set, DDPG achieves the strongest overall performance. DQL was selected a priori for the live endpoint because it obtained the highest validation Sharpe ratio, with selection performed without access to the test period. For TSLA, DDPG and DQL achieve cumulative returns of 54.96% and 52.62%, respectively, compared with 16.45% for buy-and-hold. For BTC, DDPG achieves a positive return of 1.58% while buy-and-hold declines by -34.27%. The results also reveal a substantial validation-to-test generalization gap, highlighting the difficulty of transferring policies selected in bull-market conditions to a bear-market regime.

Andrei Neagu, Eeham Khan, Leila Kosseim

Department of Computer Science and Software Engineering, Concordia University, Montréal, Canada

Reinforcement LearningDeep Q-LearningPolicy Gradient MethodsDeep Deterministic Policy GradientReward Design for RLFinance+1
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Jul 16, 2026cs.CV

3D Geometric Tooth Alignment Planning via Deep Reinforcement Learning

3D geometric tooth alignment planning, which determines sequential trajectories from initial malocclusion to the final target alignment, is a cornerstone of modern digital orthodontics. This paper presents a novel deep reinforcement learning (DRL) framework to automate the generation of these alignment paths. We formulate the planning process as a Markov Decision Process (MDP) to capture its sequential decision-making nature, focusing on optimizing geometric trajectories while integrating essential spatial constraints, such as inter-dental collision avoidance and path efficiency. The proposed method leverages the Deep Deterministic Policy Gradient (DDPG) algorithm, enhanced by three key innovations: (1) a Transformer-based agent to model complex spatial interactions between teeth and manage high-dimensional state-action spaces; (2) a dynamic masking scheme that restricts movement to a sparse subset of teeth per step, better reflecting the clinical logic of sequential alignment; and (3) a two-stage curriculum learning strategy that gradually increases task difficulty to ensure training stability and efficient path discovery. We evaluate our approach on a dataset of 10K expert-designed treatment plans based on clinical data. Experimental results demonstrate that our method outperforms existing baselines in terms of path safety and geometric efficiency, providing a robust and automated solution for 3D geometric orthodontic alignment planning.

Yong Li, Jianwen Lou, Jiayue Ma +3

School of Software Technology, Zhejiang University, Hangzhou, China · State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou, China · Stomatology Hospital, Zhejiang University School of Medicine, Hangzhou, China

Reinforcement LearningHealthcareDeep Deterministic Policy Gradient
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Jul 13, 2026math.OC

Actor-Critic Learning for Extended Mean Field Control with Deterministic Policies

This paper develops a model-free reinforcement learning framework for continuous--time extended mean field control problems, where both the dynamics and reward may depend on the joint distribution of states and controls. We adopt deterministic feedback policies, under which the state--action distribution is induced directly as a push--forward of the state law. This avoids optimization over stochastic kernels and bypasses key limitations of existing approaches in extended mean field settings. We first establish a model--free sensitivity formula for parameterized McKean--Vlasov dynamics and use it to derive a deterministic policy gradient formula expressed through an advantage--rate function on the Wasserstein space. We then refine this formula by introducing local value and advantage--rate representations that depend on the state, action, and joint state--action distribution, yielding a policy gradient that includes both action derivatives and measure--derivative terms with respect to the control distribution. These characterizations lead to a martingale--based learning principle and motivate a continuous--time deep deterministic policy gradient algorithm combining particle approximations, measure--dependent neural networks, temporal--difference learning, and exploration in either action or parameter space. Numerical experiments on stochastic Cucker--Smale consensus control and optimal liquidation with trade crowding demonstrate the efficiency, stability, and robustness of the proposed method, including problems with explicit dependence on the control distribution.

Ziheng Cheng, Xin Guo, Huyên Pham +1

University of California, Berkeley · Ecole Polytechnique, CMAP · Imperial College London

Policy GradientContinuous-Time RLModel-Free RLDeep Deterministic Policy GradientActor-Critic MethodsPolicy Learning
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Jul 2, 2026cs.AI

DRL-CLBA: A Clean Label Backdoor Attack for Speech Classification via DDPG Reinforcement Learning

Deep learning models for speech classification are vulnerable to backdoor attacks, where malicious triggers cause misclassification at inference time. While sample-specific attacks can bypass many defenses, they often rely on poisoned label attack, making them detectable via manual data defense. In this paper, we propose DRL-CLBA, a novel clean label backdoor attack for speech classification that leverages Deep Deterministic Policy Gradient (DDPG) reinforcement learning. We also utilize deep audio steganography to embed sample-specific triggers into source audio, creating feature-space anchors. The proposed reinforcement learning framework effectively optimizes target samples toward trigger-bearing anchor points in the model's deep latent space, enabling label-migration-free poisoning of target samples. Experimental results across three datasets and four different DNNs demonstrate that DRL-CLBA achieves a high attack success rate, effectively bypassing some backdoor defenses. The attack demonstrates strong resistance against fine-tuning, pruning, and spectral signature defenses, exposing critical vulnerabilities in speech-controlled systems.

Yueming Huang, Wenhan Yao, Fen Xiao +2

Xiangtan University, Yuhu District Xiangda Road, Xiangtan, 411100, Hunan, China · Peking University, No.5, Summer Palace Road, Haidian District, Beijing, China, Beijing, 100871, Beijing, China

Backdoor AttacksDeep Deterministic Policy GradientAudio Classification
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Jun 21, 2026cs.RO

FlowDPG: Deterministic Policy Gradient on Flow Matching Policies for Real-World Manipulation

Real-world reinforcement learning for robotic manipulation remains challenging, and this difficulty is amplified for flow matching policies: policy gradients must be backpropagated through time (BPTT) along the multi-step ODE that maps noise to actions, which is computationally prohibitive and numerically fragile. We propose FlowDPG, a DDPG-style method for flow matching policies that bypasses BPTT entirely. FlowDPG evaluates the critic gradient at a one-step estimate of the clean action and distills the resulting correction into the velocity field at training time, leaving multi-step inference unchanged. Intuitively, it combines two complementary vectors: the demonstration-driven velocity that keeps the action feasible, and the critic-driven correction that steers it toward higher value. Our contributions are threefold: (1) a BPTT-free distillation framework for stable DDPG-style improvement of flow matching policies, (2) a formal connection between the FlowDPG update and the vanilla deterministic policy gradient via three explicit approximations, and (3) real-world validation on two long-horizon tasks on different robots. FlowDPG reaches 92% end-to-end success on dual-arm AirPods assembly with Franka arms and an 86% rubric score on scrambled-egg cooking with YAM arms, substantially outperforming recent RL methods. Videos and more results: https://flowdpg.github.io.

Kexin Shi, Junyao Shi, Poorvi Hebbar +5

Skild AI · Carnegie Mellon University · University of Pennsylvania

Flow MatchingPolicy GradientLong-Horizon Robotic ManipulationRobotic RLRobotic ManipulationDeep Deterministic Policy Gradient
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Jun 10, 2026q-fin.CP

Deterministic Policy Gradient for Learning Equilibrium in Time-Inconsistent Control Problems

In this paper, we develop a continuous-time model-free reinforcement learning algorithm to learn deterministic equilibrium policies in general time-inconsistent control problems. Utilizing the extended Hamilton-Jacobi-Bellman system, we recast the original time-inconsistent problem into an equivalent two-stage problem. In the first stage, for given auxiliary functions, we employ the deterministic policy gradient approach to learn an optimal policy in an auxiliary time-consistent control problem. In the second stage, given the updated policy, we exploit the inner fixed point iterations and some martingale characterizations to learn the auxiliary functions. As a theoretical contribution, we provide some mild model assumptions and establish the convergence of inner fixed point iterations. By repeating this actor-critic style of iterations across two stages, our algorithm aims to learn the equilibrium under different sources of time-inconsistency in a unified manner. The superior effectiveness of the proposed algorithm are illustrated in two classical financial applications with time-inconsistency: mean-variance portfolio management and optimal tracking portfolio under non-exponential discounting.

Xin Guo, Yijie Huang, Xiang Yu

Department of Industrial Engineering and Operations Research, University of California, Berkeley, USA. · Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong.

Policy GradientStochastic Optimal ControlContinuous-Time RLModel-Free RLDeep Deterministic Policy GradientPolicy Learning+1
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Jun 5, 2026cs.RO

Path Planning Using Deep Deterministic Policy Gradient: A Reinforcement Learning Approach

Path-planning for autonomous vehicles in threat-laden environments is a fundamental challenge because the problem is nonlinear and nonconvex even in simplest scenarios. While traditional optimal control methods can be used to find ideal paths, the computational time is often too slow for real-time decision-making. To solve this challenge, we propose a method based on Deep Deterministic Policy Gradient (DDPG) and model the threat as possibly multiple circular 'no-go' zones. A mission is regarded as a failure if the vehicle enters this restricted zone at any time or does not reach a neighborhood of the destination. The DDPG agent is trained through trial and error in a simulated environment, learning a direct mapping from its current state (position and heading) to a series of feasible actions that guide the agent to safely reach its destination. The reword function has three parts: (a) an attractive field centered at the final destination, (b) some repulsive fields centered at the origins of circular obstacles, and (c) a penalty of control energy consumption (the magnitude of heading change) that indirectly in favor for straight path. The DDPG trains the agent using these incentives to find the largest possible set of starting points wherein a safe path to the destination is guaranteed. This provides critical information for mission planning, showing beforehand whether a task is achievable from a given starting point, assisting pre-mission planning activities. The approach is validated in simulation. A comparison between the DDPG method and a traditional optimal control (pseudo-spectral) method is carried out. The results show that the learning-based agent produces effective paths while being significantly faster, making it a better fit for real-time applications.

Qiang Le, Yaguang Yang, Isaac E. Weintraub

Hampton University, Hampton, VA 23669, USA · Air Force Research Laboratory, Wright-Patterson AFB, OH 45433, USA

Constrained Motion PlanningSafe Motion PlanningAutonomous Driving PlanningRL for Autonomous DrivingDeep Deterministic Policy Gradient
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May 27, 2026cs.AI

Modeling Vehicle-Type-Specific Pedestrian Crash Avoidance Behavior in Safety-Critical Interactions Using Smooth-Mamba Deep Reinforcement Learning

As automated vehicles (AVs) increasingly share roadways with human-driven vehicles (HDVs), understanding how pedestrians respond to different vehicle types in safety-critical interactions is essential for the safe deployment of automated driving technologies. This study extracts safety-critical pedestrian-vehicle interactions from the Argoverse 2 dataset to capture real-world crash avoidance behaviors in encounters involving AVs and HDVs. To model vehicle-type-specific pedestrian crash avoidance behavior, we develop a Smooth-Mamba Deep Deterministic Policy Gradient framework, termed SMamba-DDPG, which integrates smooth action constraints with efficient temporal representation learning. To quantify pedestrian behavioral differences, the framework trains separate crash avoidance policies for pedestrian interactions with AVs and HDVs. Results show that SMamba-DDPG outperforms baseline reinforcement learning and supervised learning models in reproducing pedestrian crash avoidance behaviors. Reconstructed trajectories demonstrate strong behavioral realism, accurately reproducing crash avoidance kinematics in both AV and HDV scenarios. Reaction time analysis shows that the model captures human-like response delays and reveals that pedestrians respond more quickly to AVs than to HDVs. Counterfactual analysis further indicates that pedestrians adopt lower crossing speeds when interacting with AVs. Large-scale safety analysis of model-generated data revealed that pedestrian-AV interactions consistently yielded lower conflict rates and higher pedestrian yielding rates compared to pedestrian-HDV interactions. The findings highlight the importance of incorporating vehicle-type-specific pedestrian behavioral models for safer automated driving system design and more realistic traffic simulations in mixed-traffic environments.

Qingwen Pu, Kun Xie, Hong Yang +2

Transportation Informatics Lab, Department of Civil and Environmental Engineering, Old Dominion University, Norfolk, VA 23529, United States · Department of Electrical and Computer Engineering, Old Dominion University, Norfolk, VA, United States · Department of Transportation and Urban Infrastructure Studies, SMARTER Center, Morgan State University, 1700 E Cold Spring Ln, Baltimore, MD 21251, USA

Collision AvoidancePedestrian Behavior ModelingHuman Behavior SimulationPolicy Gradient MethodsDeep Deterministic Policy GradientAutonomous Driving Simulation
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May 14, 2026cs.AI

Identifying Culprits Through Deep Deterministic Policy Gradient Deep Learning Investigation

In the world of AI and advanced technologies investigation aspects identification of a crime or criminal plays a major problem. In this research we focus on a Conventional ways of implicating criminal investigations usually rely on limited data analysis. Finding an optimal and efficient method that will effectively identify criminals from complex datasets and minimise false positives and false negatives is the considered as a challenge. The main novelty approach of this work is based on the deep learning algorithm Deep Deterministic Policy Gradient (DDPG) is presented in this paper. We train the DDPG model with a dataset of crime scene material, witness statements and suspect profiles. The algorithm uses features to maximise the likelihood of identifying the offender while minimising the noise impact and irrelevant data. We show the efficacy of the proposed method, where DDPG identified criminals with an amazing accuracy of 95% than other several existing methods.

Lata B T, Savitha N J

Dept. of CSE, UVCE, Bengaluru, India.

Deep Deterministic Policy Gradient
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May 7, 2026cs.LG

Soft Deterministic Policy Gradient with Gaussian Smoothing

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.

Hyunjun Na, Donghwan Lee

School of Electrical Engineering, KAIST 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Korea

RL ControlPolicy GradientPolicy Gradient MethodsSparse-Reward RLDeep Deterministic Policy Gradient
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