# Regularized Reward-Punishment Reinforcement Learning

arXiv: https://arxiv.org/abs/2606.28152 · HTML: https://mlsanity.com/paper/2606.28152/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Deep RL algorithms and representations, one of 15 directions in Deep reinforcement learning methods.
- Builds on 17 of its 38 references that are in the map.
- First posted on arXiv 26 Jun 2026.

## Placed in

- Deep reinforcement learning methods / [Deep RL algorithms and representations](https://mlsanity.com/deeprl/deep-rl-algorithms-and-representations/)

## Builds on (most cited first, 17 of 17)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control](https://mlsanity.com/paper/2307.15818/) (2023)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [π0: A Vision-Language-Action Flow Model for General Robot Control](https://mlsanity.com/paper/2410.24164/) (2024)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [RT-1: Robotics Transformer for Real-World Control at Scale](https://mlsanity.com/paper/2212.06817/) (2022)
- [Reinforcement Learning with Deep Energy-Based Policies](https://mlsanity.com/paper/1702.08165/) (2017)
- [Policy Distillation](https://mlsanity.com/paper/1511.06295/) (2015)
- [Distral: Robust Multitask Reinforcement Learning](https://mlsanity.com/paper/1707.04175/) (2017)
- [A Review of Safe Reinforcement Learning: Methods, Theory and Applications](https://mlsanity.com/paper/2205.10330/) (2022)
- [Actor-Mimic: Deep Multitask and Transfer Reinforcement Learning](https://mlsanity.com/paper/1511.06342/) (2015)
- [Taming the Noise in Reinforcement Learning via Soft Updates](https://mlsanity.com/paper/1512.08562/) (2015)
- [Hybrid Reward Architecture for Reinforcement Learning](https://mlsanity.com/paper/1706.04208/) (2017)
- [A Story of Two Streams: Reinforcement Learning Models from Human Behavior and Neuropsychiatry](https://mlsanity.com/paper/1906.11286/) (2019)
- [Reward-Punishment Reinforcement Learning with Maximum Entropy](https://mlsanity.com/paper/2405.11784/) (2024)

## Abstract (arXiv)

We propose KL-Coupled Policy Regularization (KCPR), a policy coordination framework for Reward-Punishment Reinforcement Learning (RPRL). Based on KCPR, we derive KL-Coupled Soft Optimality (KCSO) and develop its deep realization, klDMP. Unlike existing RPRL approaches that optimize reward-seeking and punishment-related policies largely independently, KCPR enables direct interactions between companion policies by treating each as a dynamically learned prior for the other. KCSO yields coupled soft-optimal policies and KL-regularized Bellman operators, allowing reward and punishment information to jointly influence value propagation. To improve learning stability, we introduce a companion-prior softening mechanism and evaluate separate replay-buffer designs for balancing reward- and punishment-related experience. Experiments in grid-world and Gazebo robotic navigation tasks demonstrate that klDMP improves safety and learning stability while maintaining competitive task performance compared with DQN, SQL and softDMP. These results suggest that policy-level coordination provides an effective mechanism for integrating multiple behavioral objectives and may serve as a useful design principle for reinforcement learning systems with interacting motivational processes.