Improving Policy Gradient by Exploring Under-appreciated Rewards
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Abstract (arXiv)
This paper presents a novel form of policy gradient for model-free reinforcement learning (RL) with improved exploration properties. Current policy-based methods use entropy regularization to encourage undirected exploration of the reward landscape, which is ineffective in high dimensional spaces with sparse rewards. We propose a more directed exploration strategy that promotes exploration of under-appreciated reward regions. An action sequence is considered under-appreciated if its log-probability under the current policy under-estimates its resulting reward. The proposed exploration strategy is easy to implement, requiring small modifications to an implementation of the REINFORCE algorithm. We evaluate the approach on a set of algorithmic tasks that have long challenged RL methods. Our approach reduces hyper-parameter sensitivity and demonstrates significant improvements over baseline methods. Our algorithm successfully solves a benchmark multi-digit addition task and generalizes to long sequences. This is, to our knowledge, the first time that a pure RL method has solved addition using only reward feedback.
Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). First posted on arXiv 28 Nov 2016.
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Citing papers per year: 2021: 6; 2022: 1; 2023: 2; 2024: 2; 2025: 2; 2026: 1.
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- 2023Motif: Intrinsic Motivation from Artificial Intelligence Feedbackcited by 99
- 2021Plan Better Amid Conservatism: Offline Multi-Agent Reinforcement Learning with Actor Rectificationcited by 59
- 2024Cal-DPO: Calibrated Direct Preference Optimization for Language Model Alignmentcited by 50
- 2021Greedification Operators for Policy Optimization: Investigating Forward and Reverse KL Divergencescited by 40
- 2021Co-Adaptation of Algorithmic and Implementational Innovations in Inference-based Deep Reinforcement Learningcited by 15
- 2021OPIRL: Sample Efficient Off-Policy Inverse Reinforcement Learning via Distribution Matchingcited by 15
- 2024How to Leverage Demonstration Data in Alignment for Large Language Model? A Self-Imitation Learning Perspectivecited by 14
- 2025On a Connection Between Imitation Learning and RLHFcited by 13
- 2026How to Train Your Deep Research Agent? Prompt, Reward, and Policy Optimization in Search-R1cited by 6
- 2021End-to-End Neuro-Symbolic Architecture for Image-to-Image Reasoning Taskscited by 4
- 2023Policy Gradient Algorithms Implicitly Optimize by Continuationcited by 4
- 2021Bayesian Distributional Policy Gradientscited by 3
- 2026How to Train Your Deep Research Agent? Prompt, Reward, and Policy Optimization in Search-R123 Feb 2026
- 2025Bidirectional Soft Actor-Critic: Leveraging Forward and Reverse KL Divergence for Efficient Reinforcement Learning2 Jun 2025
- 2025On a Connection Between Imitation Learning and RLHF7 Mar 2025
- 2024Cal-DPO: Calibrated Direct Preference Optimization for Language Model Alignment19 Dec 2024
- 2024How to Leverage Demonstration Data in Alignment for Large Language Model? A Self-Imitation Learning Perspective14 Oct 2024
- 2023Motif: Intrinsic Motivation from Artificial Intelligence Feedback29 Sep 2023
- 2023Policy Gradient Algorithms Implicitly Optimize by Continuation11 May 2023
- 2022Network Calculus with Flow Prolongation -- A Feedforward FIFO Analysis enabled by ML7 Feb 2022
- 2021Plan Better Amid Conservatism: Offline Multi-Agent Reinforcement Learning with Actor Rectification22 Nov 2021
- 2021OPIRL: Sample Efficient Off-Policy Inverse Reinforcement Learning via Distribution Matching9 Sep 2021
- 2021Greedification Operators for Policy Optimization: Investigating Forward and Reverse KL Divergences17 Jul 2021
- 2021End-to-End Neuro-Symbolic Architecture for Image-to-Image Reasoning Tasks6 Jun 2021
- 2023Motif: Intrinsic Motivation from Artificial Intelligence Feedbackcited by 99
- 2021Greedification Operators for Policy Optimization: Investigating Forward and Reverse KL Divergencescited by 40
- 2021Co-Adaptation of Algorithmic and Implementational Innovations in Inference-based Deep Reinforcement Learningcited by 15
- 2021End-to-End Neuro-Symbolic Architecture for Image-to-Image Reasoning Taskscited by 4
- 2023Policy Gradient Algorithms Implicitly Optimize by Continuationcited by 4
- 2021Bayesian Distributional Policy Gradientscited by 3
- 2025Bidirectional Soft Actor-Critic: Leveraging Forward and Reverse KL Divergence for Efficient Reinforcement Learningcited by 1
- 2022Network Calculus with Flow Prolongation -- A Feedforward FIFO Analysis enabled by MLcited by 0
- 2025Bidirectional Soft Actor-Critic: Leveraging Forward and Reverse KL Divergence for Efficient Reinforcement Learning2 Jun 2025
- 2023Motif: Intrinsic Motivation from Artificial Intelligence Feedback29 Sep 2023
- 2023Policy Gradient Algorithms Implicitly Optimize by Continuation11 May 2023
- 2022Network Calculus with Flow Prolongation -- A Feedforward FIFO Analysis enabled by ML7 Feb 2022
- 2021Greedification Operators for Policy Optimization: Investigating Forward and Reverse KL Divergences17 Jul 2021
- 2021End-to-End Neuro-Symbolic Architecture for Image-to-Image Reasoning Tasks6 Jun 2021
- 2021Co-Adaptation of Algorithmic and Implementational Innovations in Inference-based Deep Reinforcement Learning31 Mar 2021
- 2021Bayesian Distributional Policy Gradients20 Mar 2021