提出高效超梯度方法,解决逆强化学习中计算瓶颈问题。
Efficient Hypergradient Descent for Inverse Reinforcement Learning

- 利用策略的费雪信息矩阵替代海森矩阵,构造结构化超梯度。
- 在离散与连续控制任务中,政策性能媲美基线,奖励排序质量高。
- 采用流式谱草图近似求解,显著降低存储与计算开销,适合大规模应用。
逆强化学习(IRL)旨在恢复一个使生成策略匹配专家示范行为的奖励函数。自然方法是将IRL建模为双层优化问题:内层优化基于学习到的奖励进行策略优化,外层衡量诱导策略与专家数据之间的差异。然而,该方法在实践中计算困难,因外层更新需计算涉及内目标海森矩阵-向量逆乘积的超梯度。本文通过证明在内层最优时,内目标的海森矩阵与策略的费雪信息矩阵成比例,从而导出一种基于费雪信息的结构化超梯度,与自然超梯度下降密切相关。为克服大尺寸费雪矩阵带来的可扩展性瓶颈,我们使用流式谱草图近似所需的逆费雪-向量乘积,避免显式构建费雪矩阵。在离散和连续控制环境中,与一阶随机双层基线对比,结果表明本方法具有竞争力的策略性能和出色的奖励排序质量;同时,费雪草图显著降低了曲率存储复杂度,并提升了计算效率。
原文摘要 · Abstract (English)
Inverse reinforcement learning (IRL) aims to recover a reward function under which the resulting policy reproduces the behavior observed in expert demonstrations. A natural approach is to formulate IRL as a bilevel optimization problem, in which the inner level corresponds to policy optimization under the learned reward and the outer level measures the discrepancy between the induced policy and expert data. However, this formulation is computationally challenging in practice because the outer update requires a hypergradient involving an inverse-Hessian-vector product for the inner objective. We address this challenge by showing that, at the inner optimum, the Hessian of the inner objective is proportional to the Fisher information matrix of the policy, yielding a structured Fisher-based hypergradient closely related to Natural Hypergradient Descent. To address the resulting scalability bottleneck associated with large Fisher matrices, we approximate the required inverse-Fisher-vector product using a streaming spectral sketch, avoiding explicit construction of the Fisher matrix. We evaluate our approach against a first-order stochastic bilevel baseline across discrete- and continuous-control environments. The results demonstrate competitive policy performance and strong reward-ranking quality, while Fisher sketching reduces curvature-storage complexity and can improve computational efficiency relative to an explicit Fisher solver.
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