# On Reward-Balancing Methods for Reinforcement Learning

arXiv: https://arxiv.org/abs/2604.20433 · HTML: https://mlsanity.com/paper/2604.20433/

## 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 8 of its 16 references that are in the map.
- First posted on arXiv 22 Apr 2026.

## 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, 8 of 8)

- [MDP Homomorphic Networks: Group Symmetries in Reinforcement Learning](https://mlsanity.com/paper/2006.16908/) (2020)
- [Learning to Utilize Shaping Rewards: A New Approach of Reward Shaping](https://mlsanity.com/paper/2011.02669/) (2020)
- [The Blessing of Heterogeneity in Federated Q-Learning: Linear Speedup and Beyond](https://mlsanity.com/paper/2305.10697/) (2023)
- [Reward Shaping via Meta-Learning](https://mlsanity.com/paper/1901.09330/) (2019)
- [The Scenario Approach for Stochastic Model Predictive Control with Bounds on Closed-Loop Constraint Violations](https://mlsanity.com/paper/1307.5640/) (2013)
- [Data-driven distributionally robust LQR with multiplicative noise](https://mlsanity.com/paper/1912.09990/) (2019)
- [MDP Geometry, Normalization and Reward Balancing Solvers](https://mlsanity.com/paper/2407.06712/) (2024)
- [Robust Control Design for Linear Systems via Multiplicative Noise](https://mlsanity.com/paper/2004.08019/) (2020)

## Abstract (arXiv)

This paper investigates the so-called reward-balancing methods, a novel class of algorithms for solving discounted-return reinforcement learning (RL) problems. These methods consist of iteratively adjusting the reward function to transform the RL problem into an equivalent one in which the optimal policies are greedy. For this procedure, referred to as normalization process, we provide a theoretical analysis of the involved transformations, emphasizing their algebraic structure. Then, we introduce a control-theoretic reformulation, recasting the reward-balancing procedure into an optimal control framework. The approach is further extended to address model uncertainty through stochastic model sampling, yielding normalization guarantees and probabilistic bounds on stochastic fluctuations. Using the proposed optimal control framework within a scenario model predictive control (MPC) setting, we demonstrate, through simulation studies, performance improvements over the current state-of-the-art.