From Path Signatures to Sequential Modeling: Incremental Signature Contributions for Offline RL

TL;DR

This paper introduces the Incremental Signature Contribution (ISC) method, which decomposes path signatures into a sequence of incremental elements, enabling sequential modeling for offline reinforcement learning and improving decision-making in temporally sensitive control tasks.

Contribution

The paper proposes ISC, a novel method that preserves temporal structure in path signatures, and integrates it into a Transformer architecture for improved offline RL performance.

Findings

ISC enhances sensitivity to instantaneous trajectory updates.

ISC-Transformer outperforms standard models on control benchmarks.

The method is effective in settings with delayed rewards and degraded data quality.

Abstract

Path signatures embed trajectories into tensor algebra and constitute a universal, non-parametric representation of paths; however, in the standard form, they collapse temporal structure into a single global object, which limits their suitability for decision-making problems that require step-wise reactivity. We propose the Incremental Signature Contribution (ISC) method, which decomposes truncated path signatures into a temporally ordered sequence of elements in the tensor-algebra space, corresponding to incremental contributions induced by last path increments. This reconstruction preserves the algebraic structure and expressivity of signatures, while making their internal temporal evolution explicit, enabling processing signature-based representations via sequential modeling approaches. In contrast to full signatures, ISC is inherently sensitive to instantaneous trajectory updates, which is critical for sensitive and stability-requiring control dynamics. Building on this representation, we introduce ISC-Transformer (ISCT), an offline reinforcement learning model that integrates ISC into a standard Transformer architecture without further architectural modification. We evaluate ISCT on HalfCheetah, Walker2d, Hopper, and Maze2d, including settings with delayed rewards and downgraded datasets. The results demonstrate that ISC method provides a theoretically grounded and practically effective alternative to path processing for temporally sensitive control tasks.