# Deep W-Networks: Solving Multi-Objective Optimisation Problems With Deep Reinforcement Learning

arXiv: https://arxiv.org/abs/2211.04813 · HTML: https://mlsanity.com/paper/2211.04813/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 22 references that are in the map.
- First posted on arXiv 9 Nov 2022.

## Builds on (most cited first, 7 of 7)

- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Prioritized Experience Replay](https://mlsanity.com/paper/1511.05952/) (2015)
- [Dueling Network Architectures for Deep Reinforcement Learning](https://mlsanity.com/paper/1511.06581/) (2015)
- [Dynamic Weights in Multi-Objective Deep Reinforcement Learning](https://mlsanity.com/paper/1809.07803/) (2018)
- [Multi-Objective Deep Reinforcement Learning](https://mlsanity.com/paper/1610.02707/) (2016)
- [A Multi-Objective Deep Reinforcement Learning Framework](https://mlsanity.com/paper/1803.02965/) (2018)
- [Energy Aware Deep Reinforcement Learning Scheduling for Sensors Correlated in Time and Space](https://mlsanity.com/paper/2011.09747/) (2020)

## Built on by (most cited first, 1 of 1)

- [Multi-Objective Deep Reinforcement Learning for Optimisation in Autonomous Systems](https://mlsanity.com/paper/2408.01188/) (2024)

## Abstract (arXiv)

In this paper, we build on advances introduced by the Deep Q-Networks (DQN) approach to extend the multi-objective tabular Reinforcement Learning (RL) algorithm W-learning to large state spaces. W-learning algorithm can naturally solve the competition between multiple single policies in multi-objective environments. However, the tabular version does not scale well to environments with large state spaces. To address this issue, we replace underlying Q-tables with DQN, and propose an addition of W-Networks, as a replacement for tabular weights (W) representations. We evaluate the resulting Deep W-Networks (DWN) approach in two widely-accepted multi-objective RL benchmarks: deep sea treasure and multi-objective mountain car. We show that DWN solves the competition between multiple policies while outperforming the baseline in the form of a DQN solution. Additionally, we demonstrate that the proposed algorithm can find the Pareto front in both tested environments.