# Emergence of Exploration in Policy Gradient Reinforcement Learning via Retrying

arXiv: https://arxiv.org/abs/2606.00151 · HTML: https://mlsanity.com/paper/2606.00151/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Deep RL algorithms and representations, one of 15 directions in Deep reinforcement learning methods.
- Builds on 66 of its 99 references that are in the map.
- First posted on arXiv 29 May 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, 30 of 66)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [Dream to Control: Learning Behaviors by Latent Imagination](https://mlsanity.com/paper/1912.01603/) (2019)
- [Curiosity-driven Exploration by Self-supervised Prediction](https://mlsanity.com/paper/1705.05363/) (2017)
- [Exploration by Random Network Distillation](https://mlsanity.com/paper/1810.12894/) (2018)
- [IMPALA: Scalable Distributed Deep-RL with Importance Weighted Actor-Learner Architectures](https://mlsanity.com/paper/1802.01561/) (2018)
- [Deep Reinforcement Learning at the Edge of the Statistical Precipice](https://mlsanity.com/paper/2108.13264/) (2021)
- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [Unifying Count-Based Exploration and Intrinsic Motivation](https://mlsanity.com/paper/1606.01868/) (2016)
- [Deep Exploration via Bootstrapped DQN](https://mlsanity.com/paper/1602.04621/) (2016)
- [Minimax Regret Bounds for Reinforcement Learning](https://mlsanity.com/paper/1703.05449/) (2017)
- [Is Q-learning Provably Efficient?](https://mlsanity.com/paper/1807.03765/) (2018)
- [Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review](https://mlsanity.com/paper/1805.00909/) (2018)
- [Distributional Reinforcement Learning with Quantile Regression](https://mlsanity.com/paper/1710.10044/) (2017)
- [#Exploration: A Study of Count-Based Exploration for Deep Reinforcement Learning](https://mlsanity.com/paper/1611.04717/) (2016)
- [Uncertainty-Based Offline Reinforcement Learning with Diversified Q-Ensemble](https://mlsanity.com/paper/2110.01548/) (2021)
- [First return, then explore](https://mlsanity.com/paper/2004.12919/) (2020)
- [Count-Based Exploration with Neural Density Models](https://mlsanity.com/paper/1703.01310/) (2017)
- [Randomized Prior Functions for Deep Reinforcement Learning](https://mlsanity.com/paper/1806.03335/) (2018)
- [Never Give Up: Learning Directed Exploration Strategies](https://mlsanity.com/paper/2002.06038/) (2020)
- [Benchmarking the Spectrum of Agent Capabilities](https://mlsanity.com/paper/2109.06780/) (2021)
- [The NetHack Learning Environment](https://mlsanity.com/paper/2006.13760/) (2020)
- [Maximum Entropy RL (Provably) Solves Some Robust RL Problems](https://mlsanity.com/paper/2103.06257/) (2021)
- [Deep Exploration via Randomized Value Functions](https://mlsanity.com/paper/1703.07608/) (2017)
- [Incentivizing Exploration In Reinforcement Learning With Deep Predictive Models](https://mlsanity.com/paper/1507.00814/) (2015)
- [Pass@k Training for Adaptively Balancing Exploration and Exploitation of Large Reasoning Models](https://mlsanity.com/paper/2508.10751/) (2025)
- [Meta-Reinforcement Learning of Structured Exploration Strategies](https://mlsanity.com/paper/1802.07245/) (2018)

## Built on by (most cited first, 5 of 5)

- [Using Reward Uncertainty to Induce Diverse Behaviour in Reinforcement Learning](https://mlsanity.com/paper/2606.03962/) (2026)
- [On Advantage Estimates for Max@K Policy Gradients](https://mlsanity.com/paper/2606.06080/) (2026)
- [OrderGrad: Optimizing Beyond the Mean with Order-Statistic Policy Gradient Estimation](https://mlsanity.com/paper/2606.06096/) (2026)
- [Multi-Axis Max@K Reinforcement Learning for Representative Diversity in Text-to-Image Generation](https://mlsanity.com/paper/2607.14962/) (2026)
- [Retry Policy Gradients in Continuous Action Spaces](https://mlsanity.com/paper/2606.05888/) (2026)

## Abstract (arXiv)

In reinforcement learning (RL), agents benefit from exploration only because they repeatedly encounter similar states: trying different actions can improve performance or reduce uncertainty; without such retries, a greedy policy is optimal. We formalize this intuition with ReMax, an objective that evaluates a policy by the expected maximum return over M samples, where M is a positive integer, while accounting for return uncertainty. Optimizing this objective induces stochastic exploration as an emergent property, without explicit bonus terms. For efficient policy optimization, we derive a new policy-gradient formulation for ReMax and introduce ReMax PPO (RePPO), a PPO variant that optimizes ReMax while generalizing the discrete retry count M to a continuous parameter m > 0, enabling fine-grained control of exploration. Empirically, RePPO promotes exploration, without any explicit exploration bonuses, on the MinAtar and Craftax benchmarks. The code is available at https://github.com/nissymori/remax-rl .