通过时间抽象实现前向-后向表示中的谱对齐

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Abstract:Forward-backward (FB) representations provide a powerful framework for learning the successor representation (SR) in continuous spaces by enforcing a low-rank factorization. However, a fundamental spectral mismatch often exists between the high-rank transition dynamics of continuous environments and the low-rank bottleneck of the FB architecture, making accurate low-rank representation learning difficult. In this work, we analyze temporal abstraction as a mechanism to mitigate this mismatch. By characterizing the spectral properties of the transition operator, we show that temporal abstraction acts analogously to a low-pass filter that suppresses high-frequency spectral components. This suppression reduces the effective rank of the induced SR while preserving a formal bound on the resulting value function error. Empirically, we show that this alignment is a key factor for stable FB learning, particularly at high discount factors where bootstrapping becomes error-prone. Our results identify temporal abstraction as a principled mechanism for shaping the spectral structure of the underlying MDP and enabling effective long-horizon representations in continuous control.

Subjects:	Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Robotics (cs.RO)
Cite as:	arXiv:2603.20103 [cs.LG]
	(or arXiv:2603.20103v4 [cs.LG] for this version)
	https://doi.org/10.48550/arXiv.2603.20103 arXiv-issued DOI via DataCite

Submission history

From: Seyed Mahdi Basiri Azad [view email]
[v1] Fri, 20 Mar 2026 16:28:33 UTC (495 KB)
[v2] Mon, 23 Mar 2026 14:27:29 UTC (482 KB)
[v3] Thu, 7 May 2026 12:03:06 UTC (6,748 KB)
[v4] Fri, 2 Oct 2026 13:00:39 UTC (7,226 KB)