---
title: "Proximal policy optimization (PPO): formula and papers"
description: "Proximal policy optimization (PPO) was mentioned in 17 papers in the last 30 days (2026-09-27 to 2026-10-26), ranking #51 of the 104 equations and models mentioned."
url: https://scholar4ai.com/equations/proximal-policy-optimization-ppo
markdown_url: https://scholar4ai.com/equations/proximal-policy-optimization-ppo.md
license: CC BY-NC 4.0 (https://creativecommons.org/licenses/by-nc/4.0/)
share_text: "Proximal policy optimization (PPO) was mentioned in 17 papers in the last 30 days (2026-09-27 to 2026-10-26), ranking #51 of the 104 equations and models mentioned."
data_url: https://scholar4ai.com/data/rankings.json
updated: 2026-10-26T14:32:25+09:00
window: 2026-09-27 to 2026-10-26
source: OpenAlex (CC0)
---

# Proximal policy optimization (PPO)

$$
L(\theta) = E_t\big[\min\big(r_t(\theta)\hat A_t,\ \mathrm{clip}(r_t(\theta), 1 - \epsilon, 1 + \epsilon)\,\hat A_t\big)\big]
$$

Policy-gradient reinforcement learning with a clipped objective that keeps updates small.

- area: Machine learning
- 1 papers in the last 7 days
- Names searched for: proximal policy optimization, proximal policy optimisation, PPO

Back to the ranking: https://scholar4ai.com/rankings/equations.md

## Key findings

- Proximal policy optimization (PPO) was mentioned in 17 papers in the last 30 days (2026-09-27 to 2026-10-26), ranking #51 of the 104 equations and models mentioned.
- By journal category: AI (9), Operations Research (7) and Economics (1).
- Most of them appeared in Expert Systems with Applications (2), Applied Intelligence (2) and Annals of Operations Research (2).
- Often mentioned together with Q-learning (4), Scaled dot-product attention (Transformer) (4) and Linear and integer programming (3).
- Datasets named in the same papers: OR-Library (2), MNIST / Fashion-MNIST (1) and UCI Machine Learning Repository (1).
- From Oct 2023 to Sep 2026, 135 archived papers mentioned Proximal policy optimization (PPO) in their title, abstract or keywords, most of them in May 2025 (9).

## Mentions over 36 months

*Papers mentioning it by publication month, Oct 2023 to Sep 2026 (titles, abstracts and keywords)*

| Trend | Oct 23–Sep 24 | Oct 24–Sep 25 | Oct 25–Sep 26 | 36 months |
|---|---:|---:|---:|---:|
|  | 35 | 64 | 36 | 135 |

*Papers mentioning Proximal policy optimization (PPO), newest first.*

| Date | Title | Journal | Authors | Affiliations |
|---|---|---|---|---|
| 2026-10-24 | [Subsidy-Effectiveness Inversion in Green FDI: Dynamic Portfolio Optimization under Supply Chain Complementarity](https://doi.org/10.1007/s10614-026-11454-0) | [Computational Economics](https://scholar4ai.com/journals/computational-economics.md) | Rongliang Xu, Tianming Xu | Central South University |
| 2026-10-17 | [A two-stage ensemble learning framework for imbalanced classification via feature and ensemble selection](https://doi.org/10.1016/j.eswa.2026.134738) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Pengcheng Liu | Southwest Jiaotong University |
| 2026-10-17 | [MO-UDRL-H: hybrid Pareto-safe distributional reinforcement learning for multi-objective cloud task allocation](https://doi.org/10.1007/s10489-026-07534-1) | [Applied Intelligence](https://scholar4ai.com/journals/applied-intelligence.md) | Chunhui Xu, Chundi Hu | Zhejiang Ocean University |
| 2026-10-17 | [D-MAPPO-ABC: distributed multi-agent proximal policy optimization enhanced with artificial bee colony for edge computing task scheduling](https://doi.org/10.1007/s10479-026-07462-w) | [Annals of Operations Research](https://scholar4ai.com/journals/annals-of-operations-research.md) | Muhammed Şara, Koray Ozdemir, Süleyman Eken et al. | Kocaeli Üniversitesi; Yalova University |
| 2026-10-09 | [A reinforcement learning-based EWMA control chart with an application to urban mobility monitoring](https://doi.org/10.1016/j.cie.2026.112440) | [Computers & Industrial Engineering](https://scholar4ai.com/journals/computers-industrial-engineering.md) | Usman Ibrahim, Mohammad M. AlDurgam, Nasir Abbas et al. | King Fahd University of Petroleum and Minerals |
| 2026-10-08 | [JTCSE: Joint tensor-modulus constraints and cross-attention for unsupervised contrastive learning of sentence embeddings](https://doi.org/10.1016/j.neunet.2026.109724) | [Neural Networks](https://scholar4ai.com/journals/neural-networks.md) | Tianyu Zong, Bingkang Shi, Hongzhu Yi et al. | University of Chinese Academy of Sciences |
| 2026-10-05 | [Spatio-temporal graph reinforcement learning for multi-period supply chain synchronization: Joint procurement, warehousing, and multimodal routing with multiple 3PL providers](https://doi.org/10.1016/j.cor.2026.107697) | [Computers & Operations Research](https://scholar4ai.com/journals/computers-operations-research.md) | Jinjin Cai, Rui Song, 何世伟 et al. | Beijing Jiaotong University |
| 2026-10-02 | [RL-Axial: Learning When to Compute Global Context for Multimodal Segmentation](https://doi.org/10.1007/s12559-026-10661-z) | [Cognitive Computation](https://scholar4ai.com/journals/cognitive-computation.md) | Dong Xing, Hang Yang, Jinhe Zhang et al. | Chinese Academy of Sciences; Changchun Institute of Optics, Fine Mechanics and Physics; University of Chinese Academy of Sciences |
| 2026-10-01 | [Knowledge-Driven Optimization and Recurrent Deep Reinforcement Learning for Lean Batch Scheduling in Cutting Tool Manufacturing](https://doi.org/10.1016/j.eswa.2026.134833) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Siwei Fu, Mats Gustafsson, Sunith Bandaru et al. | University of Skövde; Uppsala University |
| 2026-10-01 | [RLAX: A Reinforcement Learning-Based Framework for Explaining Anomalous Data](https://doi.org/10.1007/s10994-026-07182-z) | [Machine Learning](https://scholar4ai.com/journals/machine-learning.md) | Simone Amirato, Fabrizio Angiulli, Fabio Fassetti | University of Calabria |
| 2026-10-01 | [GDPB: a gradient-decoupled privileged baseline for UAV navigation under compound disturbances](https://doi.org/10.1007/s10489-026-07533-2) | [Applied Intelligence](https://scholar4ai.com/journals/applied-intelligence.md) | Xin Wang, 赵健康 | Shanghai Jiao Tong University |
| 2026-10-01 | [Benchmarking adaptive pricing policies for Mississippi River container-on-barge service](https://doi.org/10.1007/s10479-026-07444-y) | [Annals of Operations Research](https://scholar4ai.com/journals/annals-of-operations-research.md) | Alex Carroll | Massachusetts Institute of Technology |
| 2026-09-30 | [Solution methods for the dynamic and probabilistic profitable tour problem](https://doi.org/10.1007/s00291-026-00875-w) | [OR Spectrum](https://scholar4ai.com/journals/or-spectrum.md) | Marvin Caspar, Daniel Schermer, Oliver Wendt | University of Kaiserslautern; Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau |
| 2026-09-29 | [A Deep Reinforcement learning model for centralized route recommendation in multi-modal transit networks](https://doi.org/10.1016/j.tre.2026.105277) | [Transportation Research Part E Logistics and Transportation Review](https://scholar4ai.com/journals/transportation-research-part-e-logistics-and-transportation-review.md) | Zijian Shen, Taijie Chen, Bin Zhou et al. | University of Hong Kong |
| 2026-09-28 | [FreSia: Frequency-semantic instantiation and alignment for multivariate time series analysis](https://doi.org/10.1016/j.patcog.2026.114944) | [Pattern Recognition](https://scholar4ai.com/journals/pattern-recognition.md) | Yubo Wang, Hui He, Hezhe Qiao et al. | Beijing Institute of Technology; Singapore Management University |
| 2026-09-28 | [Distributed order allocation in social additive manufacturing factory clusters using multi-agent reinforcement learning](https://doi.org/10.1016/j.cie.2026.112422) | [Computers & Industrial Engineering](https://scholar4ai.com/journals/computers-industrial-engineering.md) | Inno Lorren Désir Makanda, Maolin Yang, Pingyu Jiang | Xi'an Jiaotong University |
| 2026-09-28 | [Minute-scale training for microrobot navigation](https://doi.org/10.1038/s42256-026-01305-w) | [Nature Machine Intelligence](https://scholar4ai.com/journals/nature-machine-intelligence.md) | Yinghan Sun, Aoji Zhu, Xiang Ji et al. | Hong Kong Polytechnic University; Chinese University of Hong Kong; Harbin Institute of Technology |

## Cite this page

Scholar4AI. (2026). Proximal policy optimization (PPO). Journal Research Rankings. Retrieved October 26, 2026, from https://scholar4ai.com/equations/proximal-policy-optimization-ppo

```bibtex
@misc{scholar4ai-equations-proximal-policy-optimization-ppo,
  author = {{Scholar4AI}},
  title = {Proximal policy optimization (PPO)},
  year = {2026},
  howpublished = {\url{https://scholar4ai.com/equations/proximal-policy-optimization-ppo}},
  urldate = {2026-10-26},
  note = {Journal Research Rankings; data from OpenAlex (CC0); licensed CC BY-NC 4.0}
}
```

License: CC BY-NC 4.0 (https://creativecommons.org/licenses/by-nc/4.0/).