# PairVDN - Pair-wise Decomposed Value Functions

arXiv: https://arxiv.org/abs/2503.09521 · HTML: https://mlsanity.com/paper/2503.09521/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Deep RL algorithms and representations, one of 15 directions in Deep reinforcement learning methods.
- Builds on 1 of its 4 references that are in the map.
- First posted on arXiv 12 Mar 2025.

## Placed in

- Deep reinforcement learning methods / [Deep RL algorithms and representations](https://mlsanity.com/deeprl/deep-rl-algorithms-and-representations/)

## Builds on (most cited first, 1 of 1)

- [Monotonic Value Function Factorisation for Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2003.08839/) (2020)

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

- [Enhancing Multi-Agent Collaboration with Attention-Based Actor-Critic Policies](https://mlsanity.com/paper/2507.22782/) (2025)

## Abstract (arXiv)

Extending deep Q-learning to cooperative multi-agent settings is challenging due to the exponential growth of the joint action space, the non-stationary environment, and the credit assignment problem. Value decomposition allows deep Q-learning to be applied at the joint agent level, at the cost of reduced expressivity. Building on past work in this direction, our paper proposes PairVDN, a novel method for decomposing the value function into a collection of pair-wise, rather than per-agent, functions, improving expressivity at the cost of requiring a more complex (but still efficient) dynamic programming maximisation algorithm. Our method enables the representation of value functions which cannot be expressed as a monotonic combination of per-agent functions, unlike past approaches such as VDN and QMIX. We implement a novel many-agent cooperative environment, Box Jump, and demonstrate improved performance over these baselines in this setting. We open-source our code and environment at https://github.com/zzbuzzard/PairVDN.