← 研踪 PaperTrailarXiv:2508.18741 · v3
Statistical Complexity of Soft Bellman Residual Minimization
首次提交 2025-08-26 15:15
版本更新 2026-11-09 11:06
雷达观测 2026-11-10 13:18
摘要
Offline reinforcement learning and offline inverse reinforcement learning aim to recover near-optimal value functions or reward models from a fixed batch of logged trajectories, yet current practice still struggles to enforce Bellman consistency scalably. Bellman residual minimization (BRM) has emerged as an attractive remedy. While globally convergent gradient-based soft (i.e., entropy-regularized) BRM methods for neural networks have recently been established, their statistical complexity under stochastic gradient descent remains largely unknown. In this paper, we address this theoretical gap for soft BRM. Through a Lyapunov-based analysis under a uniform PL condition in the auxiliary variable, we establish an $\mathcal{O}(1 / n)$ primal argument stability bound up to optimization error and an $\mathcal{O}(1 / n)$ statistical complexity for the soft BRM objective under the stated sampling conditions.
观测到的版本
相邻记录可能跳过中间版本；首次发现 v2 及以上也会标为版本更新。
v3 · 2026-11-09 11:06 · 最新观测版本
Statistical Complexity of Soft Bellman Residual Minimization
Offline reinforcement learning and offline inverse reinforcement learning aim to recover near-optimal value functions or reward models from a fixed batch of logged trajectories, yet current practice still struggles to enforce Bellman consistency scalably. Bellman residual minimization (BRM) has emerged as an attractive remedy. While globally convergent gradient-based soft (i.e., entropy-regularized) BRM methods for neural networks have recently been established, their statistical complexity under stochastic gradient descent remains largely unknown. In this paper, we address this theoretical gap for soft BRM. Through a Lyapunov-based analysis under a uniform PL condition in the auxiliary variable, we establish an $\mathcal{O}(1 / n)$ primal argument stability bound up to optimization error and an $\mathcal{O}(1 / n)$ statistical complexity for the soft BRM objective under the stated sampling conditions.
查看此版本解读 →查看此版本原文 ↗