arXiv:2607.12590eess.SYcs.LG2026-07

提出环境参数梯度定理,实现策略与环境协同优化。

Environment Parameter Gradient Theorem for Policy-Environment Co-Design in Reinforcement Learning

  • 引入双参数Q函数,解耦当前与未来环境影响
  • 推导出环境参数的闭式梯度表达式
  • 在无人机网络中联合优化部署位置与通信路径

强化学习传统上关注为固定环境学习控制策略。但在许多工程系统中,环境本身可调节:物理或操作参数可调以改变智能体经历的转移动态和成本。这促使同时优化策略与环境设计参数。为此,我们建立环境参数梯度定理——价值函数关于环境参数的梯度形式化表达。关键理论工具是广义动作价值函数 $Q_{π,ξ}(s,a,ζ)$,包含两组环境参数:ζ 控制当前状态-动作对的成本与转移动态,ξ 控制未来轨迹。这种解耦使梯度表达可计算,并构成定理推导的核心。基于此结果,我们开发了一种无需模型的算法,可同时学习最优策略与环境参数。我们在无人机网络设计问题上验证了该框架的有效性,联合学习最优无人机部署(环境参数)与通信路由(由策略决定),以最小化网络总通信成本。

原文摘要 · Abstract (English)

Reinforcement learning (RL) is traditionally concerned with learning a control policy for a fixed environment. In many engineering systems, however, the environment itself is alterable: physical or operational parameters can be tuned to shape the transition dynamics and costs experienced by the agent. This motivates jointly optimizing both the policy and the environment design parameters. To this end, we establish an Environment Parameter Gradient Theorem -- a formal expression for the gradient of the value function with respect to environment parameters. The key theoretical device is a generalized action-value function $Q_{π,ξ}(s,a,ζ)$, which comprises two copies of the environment parameters: $ζ$ governs the cost and transition dynamics at the current state--action pair, while $ξ$ governs the future rollouts. This decoupling yields a tractable closed-form gradient expression and is essential to the theorem's derivation. Building on this result, we develop a model-free algorithm that simultaneously learns the optimal policy and the environment parameters. We demonstrate the efficacy of our framework on a UAV network design problem, where the optimal UAV placement (environment parameters) and communication routes (governed by the policy) are learned jointly to minimize the total communication cost in the network.

强化学习协同设计梯度优化

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