arXiv:2608.07228cs.LGmath.OC2026-08

在部分可观测环境下,学习失败主因是评判标准偏差,而非策略表达能力不足。

Learning Suffers More Than the Policy Class Under Partial Observability: A Closed-Form Analysis

  • 通过闭式解分析部分可观测线性二次问题
  • 算法收敛到比可用最优策略差35%的解
  • 调整预测前瞻步数可消除偏差,适合研究者与调参人员

当强化学习智能体无法观测完整状态时,通常归因于策略表达能力不足。我们发现,在可解情形下,更大问题是价值函数学习偏差。即使存在接近最优的策略且价值函数足够表达,学习仍会陷入远差于最优的解。我们研究了一个部分可观测的线性二次问题,其中标准演员-评论家算法可求得闭式解。默认设置下,智能体可表示的最佳策略比全观理想控制器代价高10.4%。但学习最终停留在比该策略还差35%的解上,且可精确说明其位置与原因。根源在于评论家对不可观测状态引起的未解释变化产生误判,将其视为自身价值估计的剧烈曲率,导致演员偏离最优。我们推导出该策略、其代价及唯一可消除问题的设计选择——即学习前信任自身价值估计的前瞻距离。深度强化学习实验结果与此预测高度一致:增加历史记忆无效,而调整前瞻步数有效。

原文摘要 · Abstract (English)

When a reinforcement learning agent cannot observe the full state, we usually blame its policies: it cannot see enough to represent a good one. We show that in a solvable case the bigger problem lies elsewhere. Even when a good policy is available and the agent's value function is expressive enough to describe it exactly, learning still ends up somewhere far worse. We study a partially observed linear-quadratic problem in which a standard actor-critic learner can be solved in closed form. At our default setting the best policy the agent can represent is already close to optimal, costing 10.4% more than the ideal controller that observes everything. Learning does not find it. The algorithm instead comes to rest at a policy that is 35% worse than the best one available to it, and we can say exactly where and why. The cause is a bias in what the critic learns rather than a limit on what the actor can express. Because the agent cannot attribute what it sees to the part of the state it cannot observe, the critic misreads that unexplained variation as sharp curvature in its own value estimates, and the actor follows that error away from the optimum. We derive closed-form expressions for the resulting policy, for its cost, and for the one design choice that removes the problem, which is how far the learner looks ahead before trusting its own value estimates. Deep reinforcement learning experiments follow these predictions closely. Notably, giving the agent memory of past observations does not help, while changing how far it looks ahead does.

强化学习部分可观测闭式解价值偏差

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