# Reward-Punishment Reinforcement Learning with Maximum Entropy

arXiv: https://arxiv.org/abs/2405.11784 · HTML: https://mlsanity.com/paper/2405.11784/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 7 of its 26 references that are in the map.
- First posted on arXiv 20 May 2024.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 7 of 7)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Reinforcement Learning with Deep Energy-Based Policies](https://mlsanity.com/paper/1702.08165/) (2017)
- [Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review](https://mlsanity.com/paper/1805.00909/) (2018)
- [Maximum Entropy RL (Provably) Solves Some Robust RL Problems](https://mlsanity.com/paper/2103.06257/) (2021)
- [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)

## Built on by (most cited first, 2 of 2)

- [Performative Policy Gradient: Optimality in Performative Reinforcement Learning](https://mlsanity.com/paper/2512.20576/) (2025)
- [Regularized Reward-Punishment Reinforcement Learning](https://mlsanity.com/paper/2606.28152/) (2026)

## Abstract (arXiv)

We introduce the ``soft Deep MaxPain'' (softDMP) algorithm, which integrates the optimization of long-term policy entropy into reward-punishment reinforcement learning objectives. Our motivation is to facilitate a smoother variation of operators utilized in the updating of action values beyond traditional ``max'' and ``min'' operators, where the goal is enhancing sample efficiency and robustness. We also address two unresolved issues from the previous Deep MaxPain method. Firstly, we investigate how the negated (``flipped'') pain-seeking sub-policy, derived from the punishment action value, collaborates with the ``min'' operator to effectively learn the punishment module and how softDMP's smooth learning operator provides insights into the ``flipping'' trick. Secondly, we tackle the challenge of data collection for learning the punishment module to mitigate inconsistencies arising from the involvement of the ``flipped'' sub-policy (pain-avoidance sub-policy) in the unified behavior policy. We empirically explore the first issue in two discrete Markov Decision Process (MDP) environments, elucidating the crucial advancements of the DMP approach and the necessity for soft treatments on the hard operators. For the second issue, we propose a probabilistic classifier based on the ratio of the pain-seeking sub-policy to the sum of the pain-seeking and goal-reaching sub-policies. This classifier assigns roll-outs to separate replay buffers for updating reward and punishment action-value functions, respectively. Our framework demonstrates superior performance in Turtlebot 3's maze navigation tasks under the ROS Gazebo simulation.