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Traditional approaches to the design of multi-agent navigation algorithmsconsider the environment as a fixed constraint, despite the influence ofspatial constraints on agents' performance. Yet hand-designing conduciveenvironment layouts is inefficient and potentially expensive. The goal of thispaper is to consider the environment as a decision variable in a system-leveloptimization problem, where both agent performance and environment cost areincorporated. Towards this end, we propose novel problems of unprioritized andprioritized environment optimization, where the former considers agentsunbiasedly and the latter accounts for agent priorities. We show, throughformal proofs, under which conditions the environment can change whileguaranteeing completeness (i.e., all agents reach goals), and analyze the roleof agent priorities in the environment optimization. We proceed to imposereal-world constraints on the environment optimization and formulate itmathematically as a constrained stochastic optimization problem. Since therelation between agents, environment and performance is challenging to model,we leverage reinforcement learning to develop a model-free solution and aprimal-dual mechanism to handle constraints. Distinct information processingarchitectures are integrated for various implementation scenarios, includingonline/offline optimization and discrete/continuous environment. Numericalresults corroborate the theory and demonstrate the validity and adaptability ofour approach.

Constrained Environment Optimization for Prioritized Multi-Agent Navigation