# APF+: Boosting adaptive-potential function reinforcement learning methods with a W-shaped network for high-dimensional games

arXiv: https://arxiv.org/abs/2503.13557 · HTML: https://mlsanity.com/paper/2503.13557/

## 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 13 of its 31 references that are in the map.
- First posted on arXiv 17 Mar 2025.

## 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, 13 of 13)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Dueling Network Architectures for Deep Reinforcement Learning](https://mlsanity.com/paper/1511.06581/) (2015)
- [Solving Rubik's Cube with a Robot Hand](https://mlsanity.com/paper/1910.07113/) (2019)
- [Towards a Definition of Disentangled Representations](https://mlsanity.com/paper/1812.02230/) (2018)
- [Embed to Control: A Locally Linear Latent Dynamics Model for Control from Raw Images](https://mlsanity.com/paper/1506.07365/) (2015)
- [First return, then explore](https://mlsanity.com/paper/2004.12919/) (2020)
- [Unsupervised State Representation Learning in Atari](https://mlsanity.com/paper/1906.08226/) (2019)
- [State Representation Learning for Control: An Overview](https://mlsanity.com/paper/1802.04181/) (2018)
- [Playing hard exploration games by watching YouTube](https://mlsanity.com/paper/1805.11592/) (2018)
- [Read and Reap the Rewards: Learning to Play Atari with the Help of Instruction Manuals](https://mlsanity.com/paper/2302.04449/) (2023)
- [A Survey on Reinforcement Learning in Aviation Applications](https://mlsanity.com/paper/2211.02147/) (2022)
- [A new Potential-Based Reward Shaping for Reinforcement Learning Agent](https://mlsanity.com/paper/1902.06239/) (2019)

## Abstract (arXiv)

Studies in reward shaping for reinforcement learning (RL) have flourished in recent years due to its ability to speed up training. Our previous work proposed an adaptive potential function (APF) and showed that APF can accelerate the Q-learning with a Multi-layer Perceptron algorithm in the low-dimensional domain. This paper proposes to extend APF with an encoder (APF+) for RL state representation, allowing applying APF to the pixel-based Atari games using a state-encoding method that projects high-dimensional game's pixel frames to low-dimensional embeddings. We approach by designing the state-representation encoder as a W-shaped network (W-Net), by using which we are able to encode both the background as well as the moving entities in the game frames. Specifically, the embeddings derived from the pre-trained W-Net consist of two latent vectors: One represents the input state, and the other represents the deviation of the input state's representation from itself. We then incorporate W-Net into APF to train a downstream Dueling Deep Q-Network (DDQN), obtain the APF-WNet-DDQN, and demonstrate its effectiveness in Atari game-playing tasks. To evaluate the APF+W-Net module in such high-dimensional tasks, we compare with two types of baseline methods: (i) the basic DDQN; and (ii) two encoder-replaced APF-DDQN methods where we replace W-Net by (a) an unsupervised state representation method called Spatiotemporal Deep Infomax (ST-DIM) and (b) a ground truth state representation provided by the Atari Annotated RAM Interface (ARI). The experiment results show that out of 20 Atari games, APF-WNet-DDQN outperforms DDQN (14/20 games) and APF-STDIM-DDQN (13/20 games) significantly. In comparison against the APF-ARI-DDQN which employs embeddings directly of the detailed game-internal state information, the APF-WNet-DDQN achieves a comparable performance.