# Constrained Multiagent Rollout and Multidimensional Assignment with the Auction Algorithm

arXiv: https://arxiv.org/abs/2002.07407 · HTML: https://mlsanity.com/paper/2002.07407/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Feb 2020.

## Built on by (most cited first, 4 of 4)

- [Lessons from AlphaZero for Optimal, Model Predictive, and Adaptive Control](https://mlsanity.com/paper/2108.10315/) (2021)
- [Multiagent Reinforcement Learning for Autonomous Routing and Pickup Problem with Adaptation to Variable Demand](https://mlsanity.com/paper/2211.14983/) (2022)
- [Approximate Multiagent Reinforcement Learning for On-Demand Urban Mobility Problem on a Large Map (extended version)](https://mlsanity.com/paper/2311.01534/) (2023)
- [New Auction Algorithms for Path Planning, Network Transport, and Reinforcement Learning](https://mlsanity.com/paper/2207.09588/) (2022)

## Abstract (arXiv)

We consider an extension of the rollout algorithm that applies to constrained deterministic dynamic programming, including challenging combinatorial optimization problems. The algorithm relies on a suboptimal policy, called base heuristic. Under suitable assumptions, we show that if the base heuristic produces a feasible solution, the rollout algorithm has a cost improvement property: it produces a feasible solution, whose cost is no worse than the base heuristic's cost. We then focus on multiagent problems, where the control at each stage consists of multiple components (one per agent), which are coupled either through the cost function or the constraints or both. We show that the cost improvement property is maintained with an alternative implementation that has greatly reduced computational requirements, and makes possible the use of rollout in problems with many agents. We demonstrate this alternative algorithm by applying it to layered graph problems that involve both a spatial and a temporal structure. We consider in some detail a prominent example of such problems: multidimensional assignment, where we use the auction algorithm for 2-dimensional assignment as a base heuristic. This auction algorithm is particularly well-suited for our context, because through the use of prices, it can advantageously use the solution of an assignment problem as a starting point for solving other related assignment problems, and this can greatly speed up the execution of the rollout algorithm.