# Dense and Diverse Goal Coverage in Multi Goal Reinforcement Learning

arXiv: https://arxiv.org/abs/2510.25311 · HTML: https://mlsanity.com/paper/2510.25311/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 35 of its 47 references that are in the map.
- First posted on arXiv 29 Oct 2025.

## 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, 30 of 35)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [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)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Curiosity-driven Exploration by Self-supervised Prediction](https://mlsanity.com/paper/1705.05363/) (2017)
- [Hindsight Experience Replay](https://mlsanity.com/paper/1707.01495/) (2017)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Exploration by Random Network Distillation](https://mlsanity.com/paper/1810.12894/) (2018)
- [Diversity is All You Need: Learning Skills without a Reward Function](https://mlsanity.com/paper/1802.06070/) (2018)
- [Unifying Count-Based Exploration and Intrinsic Motivation](https://mlsanity.com/paper/1606.01868/) (2016)
- [Brax -- A Differentiable Physics Engine for Large Scale Rigid Body Simulation](https://mlsanity.com/paper/2106.13281/) (2021)
- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [Deep Reinforcement Learning for Robotic Manipulation with Asynchronous Off-Policy Updates](https://mlsanity.com/paper/1610.00633/) (2016)
- [Maximum a Posteriori Policy Optimisation](https://mlsanity.com/paper/1806.06920/) (2018)
- [#Exploration: A Study of Count-Based Exploration for Deep Reinforcement Learning](https://mlsanity.com/paper/1611.04717/) (2016)
- [Contrastive Learning as Goal-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2206.07568/) (2022)
- [Trajectory balance: Improved credit assignment in GFlowNets](https://mlsanity.com/paper/2201.13259/) (2022)
- [Batch Policy Learning under Constraints](https://mlsanity.com/paper/1903.08738/) (2019)
- [Provably Efficient Maximum Entropy Exploration](https://mlsanity.com/paper/1812.02690/) (2018)
- [Efficient Exploration via State Marginal Matching](https://mlsanity.com/paper/1906.05274/) (2019)
- [Understanding the impact of entropy on policy optimization](https://mlsanity.com/paper/1811.11214/) (2018)
- [Goal-Conditioned Reinforcement Learning: Problems and Solutions](https://mlsanity.com/paper/2201.08299/) (2022)
- [Planning with Goal-Conditioned Policies](https://mlsanity.com/paper/1911.08453/) (2019)
- [HIQL: Offline Goal-Conditioned RL with Latent States as Actions](https://mlsanity.com/paper/2307.11949/) (2023)
- [C-Learning: Learning to Achieve Goals via Recursive Classification](https://mlsanity.com/paper/2011.08909/) (2020)
- [Maximum Entropy Gain Exploration for Long Horizon Multi-goal Reinforcement Learning](https://mlsanity.com/paper/2007.02832/) (2020)
- [Surprise-Based Intrinsic Motivation for Deep Reinforcement Learning](https://mlsanity.com/paper/1703.01732/) (2017)
- [Maximum Entropy-Regularized Multi-Goal Reinforcement Learning](https://mlsanity.com/paper/1905.08786/) (2019)
- [A Max-Min Entropy Framework for Reinforcement Learning](https://mlsanity.com/paper/2106.10517/) (2021)

## Abstract (arXiv)

Reinforcement Learning algorithms are primarily focused on learning a policy that maximizes expected return. As a result, the learned policy can exploit one or few reward sources. However, in many natural situations, it is desirable to learn a policy that induces a dispersed marginal state distribution over rewarding states, while maximizing the expected return which is typically tied to reaching a goal state. This aspect remains relatively unexplored. Existing techniques based on entropy regularization and intrinsic rewards use stochasticity for encouraging exploration to find an optimal policy which may not necessarily lead to dispersed marginal state distribution over rewarding states. Other RL algorithms which match a target distribution assume the latter to be available apriori. This may be infeasible in large scale systems where enumeration of all states is not possible and a state is determined to be a goal state only upon reaching it. We formalize the problem of maximizing the expected return while uniformly visiting the goal states as Multi Goal RL in which an oracle classifier over the state space determines the goal states. We propose a novel algorithm that learns a high-return policy mixture with marginal state distribution dispersed over the set of goal states. Our algorithm is based on optimizing a custom RL reward which is computed - based on the current policy mixture - at each iteration for a set of sampled trajectories. The latter are used via an offline RL algorithm to update the policy mixture. We prove performance guarantees for our algorithm, showing efficient convergence bounds for optimizing a natural objective which captures the expected return as well as the dispersion of the marginal state distribution over the goal states. We design and perform experiments on synthetic MDPs and standard RL environments to evaluate the effectiveness of our algorithm.