# Recursive Reward Aggregation

arXiv: https://arxiv.org/abs/2507.08537 · HTML: https://mlsanity.com/paper/2507.08537/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- First posted on arXiv 11 Jul 2025.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Built on by (most cited first, 2 of 2)

- [Emergence of Exploration in Policy Gradient Reinforcement Learning via Retrying](https://mlsanity.com/paper/2606.00151/) (2026)
- [Generalised Bellman recurrence and three dualities in sequential decision-making](https://mlsanity.com/paper/2607.18077/) (2026)

## Abstract (arXiv)

In reinforcement learning (RL), aligning agent behavior with specific objectives typically requires careful design of the reward function, which can be challenging when the desired objectives are complex. In this work, we propose an alternative approach for flexible behavior alignment that eliminates the need to modify the reward function by selecting appropriate reward aggregation functions. By introducing an algebraic perspective on Markov decision processes (MDPs), we show that the Bellman equations naturally emerge from the recursive generation and aggregation of rewards, allowing for the generalization of the standard discounted sum to other recursive aggregations, such as discounted max and Sharpe ratio. Our approach applies to both deterministic and stochastic settings and integrates seamlessly with value-based and actor-critic algorithms. Experimental results demonstrate that our approach effectively optimizes diverse objectives, highlighting its versatility and potential for real-world applications.