Lagrangian Relaxation for Large-Scale Multi-agent Planning

Abstract

Abstract-Multi-agent planning is a well-studied problem with various applications including disaster rescue, urban transportation and logistics, both for autonomous agents and for decision support to humans. Due to computational constraints, existing research typically focuses on one of two scenarios: unstructured domains with many agents where we are content with heuristic solutions, or domains with small numbers of agents or special structure where we can provide provably near-optimal solutions. By contrast, in this paper, we focus on providing provably near-optimal solutions for domains with large numbers of agents, by exploiting a common domain-general property: if individual agents each have limited influence on the overall solution quality, then we can take advantage of randomization and the resulting statistical concentration to show that each agent can safely plan based only on the average behavior of the other agents. To that end, we make two key contributions: (a) an algorithm, based on Lagrangian relaxation and randomized rounding, for solving multi-agent planning problems represented as large mixedinteger programs; (b) a proof of convergence of our algorithm to a near-optimal solution. We demonstrate the scalability of our approach with a large-scale illustrative theme park crowd management problem.

Dynamic Redeployment to Counter Congestion or Starvation in Vehicle Sharing Systems

“…In order to exploit Observation 1, we use the well known Lagrangian Dual Decomposition (Fisher 1985;Gordon et al 2012) technique. While this is a general purpose approach, its scalability, usability and utility depend significantly on whether the right constraints are dualized 5 and if primal solution can be extracted from an infeasible dual solution 6 .…”

Preallocation and Planning Under Stochastic Resource Constraints

“…Planning for future uncertainties is an effective tool to increase the utility of a system of multiple agents. Particularly when the actions of agents are restricted by scarce resources, planning for resource usage is an important challenge that many authors have addressed (Adelman and Mersereau 2008;Agrawal, Varakantham, and Yeoh 2016;De Nijs, Spaan, and De Weerdt 2015;Gordon et al 2012;Meuleau et al 1998;Wu and Durfee 2010;Yoo, Fitch, and Sukkarieh 2012). These approaches have in common that they consider uncertainty in state transitions, while assuming full knowledge about future resource constraints.…”

“…Therefore, decoupling is a common paradigm to solve resource-constrained factored MMDPs. It enables agent models to be planned individually while taking into account the effects of others on the resource constraints through proxy values such as a (Lagrangian Dual) cost of consumption (Gordon et al 2012), the probability of successful consumption (De Nijs, Spaan, and De Weerdt 2015), or action frequency counts (Varakantham, Adulyasak, and Jaillet 2014). However, when resource constraints are uncertain, and therefore part of the transition model of the MMDP, these approaches result in a poor approximation of the true problem and many constraint violations.…”