# Policy Gradient for Reinforcement Learning with General Utilities

arXiv: https://arxiv.org/abs/2210.00991 · HTML: https://mlsanity.com/paper/2210.00991/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 15 references that are in the map.
- First posted on arXiv 3 Oct 2022.

## Builds on (most cited first, 6 of 6)

- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Provably Efficient Maximum Entropy Exploration](https://mlsanity.com/paper/1812.02690/) (2018)
- [Variational Policy Gradient Method for Reinforcement Learning with General Utilities](https://mlsanity.com/paper/2007.02151/) (2020)
- [Reward is enough for convex MDPs](https://mlsanity.com/paper/2106.00661/) (2021)
- [Concave Utility Reinforcement Learning: the Mean-Field Game Viewpoint](https://mlsanity.com/paper/2106.03787/) (2021)
- [Challenging Common Assumptions in Convex Reinforcement Learning](https://mlsanity.com/paper/2202.01511/) (2022)

## Built on by (most cited first, 6 of 6)

- [Reinforcement Learning with General Utilities: Simpler Variance Reduction and Large State-Action Space](https://mlsanity.com/paper/2306.01854/) (2023)
- [On the Global Optimality of Policy Gradient Methods in General Utility Reinforcement Learning](https://mlsanity.com/paper/2410.04108/) (2024)
- [Soft Forward-Backward Representations for Zero-shot Reinforcement Learning with General Utilities](https://mlsanity.com/paper/2602.06769/) (2026)
- [On the Stochastic (Variance-Reduced) Proximal Gradient Method for Regularized Expected Reward Optimization](https://mlsanity.com/paper/2401.12508/) (2024)
- [Robust General Utility for Reinforcement Learning](https://mlsanity.com/paper/2608.03562/) (2026)
- [Theoretical Foundations of max@k Reinforcement Learning](https://mlsanity.com/paper/2607.17823/) (2026)

## Abstract (arXiv)

In Reinforcement Learning (RL), the goal of agents is to discover an optimal policy that maximizes the expected cumulative rewards. This objective may also be viewed as finding a policy that optimizes a linear function of its state-action occupancy measure, hereafter referred as Linear RL. However, many supervised and unsupervised RL problems are not covered in the Linear RL framework, such as apprenticeship learning, pure exploration and variational intrinsic control, where the objectives are non-linear functions of the occupancy measures. RL with non-linear utilities looks unwieldy, as methods like Bellman equation, value iteration, policy gradient, dynamic programming that had tremendous success in Linear RL, fail to trivially generalize. In this paper, we derive the policy gradient theorem for RL with general utilities. The policy gradient theorem proves to be a cornerstone in Linear RL due to its elegance and ease of implementability. Our policy gradient theorem for RL with general utilities shares the same elegance and ease of implementability. Based on the policy gradient theorem derived, we also present a simple sample-based algorithm. We believe our results will be of interest to the community and offer inspiration to future works in this generalized setting.