# Generalizing Across Multi-Objective Reward Functions in Deep Reinforcement Learning

arXiv: https://arxiv.org/abs/1809.06364 · HTML: https://mlsanity.com/paper/1809.06364/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2018.

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

- [Evaluating MLLMs with Multimodal Multi-image Reasoning Benchmark](https://mlsanity.com/paper/2506.04280/) (2025)
- [C-MORL: Multi-Objective Reinforcement Learning through Efficient Discovery of Pareto Front](https://mlsanity.com/paper/2410.02236/) (2024)
- [Multi-Objective reward generalization: Improving performance of Deep Reinforcement Learning for applications in single-asset trading](https://mlsanity.com/paper/2203.04579/) (2022)
- [gTLO: A Generalized and Non-linear Multi-Objective Deep Reinforcement Learning Approach](https://mlsanity.com/paper/2204.04988/) (2022)
- [Interpretability by Design for Efficient Multi-Objective Reinforcement Learning](https://mlsanity.com/paper/2506.04022/) (2025)

## Abstract (arXiv)

Many reinforcement-learning researchers treat the reward function as a part of the environment, meaning that the agent can only know the reward of a state if it encounters that state in a trial run. However, we argue that this is an unnecessary limitation and instead, the reward function should be provided to the learning algorithm. The advantage is that the algorithm can then use the reward function to check the reward for states that the agent hasn't even encountered yet. In addition, the algorithm can simultaneously learn policies for multiple reward functions. For each state, the algorithm would calculate the reward using each of the reward functions and add the rewards to its experience replay dataset. The Hindsight Experience Replay algorithm developed by Andrychowicz et al. (2017) does just this, and learns to generalize across a distribution of sparse, goal-based rewards. We extend this algorithm to linearly-weighted, multi-objective rewards and learn a single policy that can generalize across all linear combinations of the multi-objective reward. Whereas other multi-objective algorithms teach the Q-function to generalize across the reward weights, our algorithm enables the policy to generalize, and can thus be used with continuous actions.