Bilevel reinforcement learning via the development of hyper-gradient without lower-level convexity

• URL: http://arxiv.org/abs/2405.19697v2
• Date: Thu, 27 Feb 2025 06:52:19 GMT
• Title: Bilevel reinforcement learning via the development of hyper-gradient without lower-level convexity
• Authors: Yan Yang, Bin Gao, Ya-xiang Yuan,
• Abstract summary: Bilevel reinforcement learning (RL) features intertwined two-level problems.<n>Non-level convex information is an impediment to developing bilevel optimization methods.<n>Hyper-gradient serves as an integration of exploitation and exploration.
• Score: 4.917399520581689
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bilevel reinforcement learning (RL), which features intertwined two-level problems, has attracted growing interest recently. The inherent non-convexity of the lower-level RL problem is, however, to be an impediment to developing bilevel optimization methods. By employing the fixed point equation associated with the regularized RL, we characterize the hyper-gradient via fully first-order information, thus circumventing the assumption of lower-level convexity. This, remarkably, distinguishes our development of hyper-gradient from the general AID-based bilevel frameworks since we take advantage of the specific structure of RL problems. Moreover, we design both model-based and model-free bilevel reinforcement learning algorithms, facilitated by access to the fully first-order hyper-gradient. Both algorithms enjoy the convergence rate $O(\epsilon^{-1})$. To extend the applicability, a stochastic version of the model-free algorithm is proposed, along with results on its iteration and sample complexity. In addition, numerical experiments demonstrate that the hyper-gradient indeed serves as an integration of exploitation and exploration.

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