This paper introduces Anticipatory Reinforcement Learning (ARL), a novel framework designed to bridge the gap between non-Markovian decision processes and classical reinforcement learning architectures, specifically under the constraint of a single observed trajectory. In environments characterised by jump-diffusions and structural breaks, traditional state-based methods often fail to capture the essential path-dependent geometry required for accurate foresight. We resolve this by lifting the state space into a signature-augmented manifold, where the history of the process is embedded as a dynamical coordinate. By utilising a self-consistent field approach, the agent maintains an anticipated proxy of the future path-law, allowing for a deterministic evaluation of expected returns. This transition from stochastic branching to a single-pass linear evaluation significantly reduces computational complexity and variance. We prove that this framework preserves fundamental contraction properties and ensures stable generalisation even in the presence of heavy-tailed noise. Our results demonstrate that by grounding reinforcement learning in the topological features of path-space, agents can achieve proactive risk management and superior policy stability in highly volatile, continuous-time environments.
Figures & tables
Parameter
Value
Signature Truncation ( k )
4
Nyström Landmarks ( M )
128
Latent CDE Solver
Log-ODE (Marcus-compliant)
Discount Factor ( γ )
0.99
SCF Penalty ( η )
0.1
Optimiser
AdamW ( lr=3×10−4 )
Table 1: Baseline Configuration for Jump-Diffusion Environment
This paper introduces a novel generative framework for synthesising forward-looking, càdlàg stochastic trajectories that are sequentially consistent with time-evolving path-law proxies, thereby incorporating anticipated structural breaks, regime shifts, and non-autonomous dynamics. By framing path synthesis as a sequential matching problem on restricted Skorokhod manifolds, we develop the Anticipatory Neural Jump-Diffusion (ANJD) flow, a generative mechanism that effectively inverts the time-extended Marcus-sense signature. Central to this approach is the Anticipatory Variance-Normalised Signature Geometry (AVNSG), a time-evolving precision operator that performs dynamic spectral whitening on the signature manifold to ensure contractivity during volatile regime shifts and discrete aleatoric shocks. We provide a rigorous theoretical analysis demonstrating that the joint generative flow constitutes an infinitesimal steepest descent direction for the Maximum Mean Discrepancy functional relative to a moving target proxy. Furthermore, we establish statistical generalisation bounds within the restricted path-space and analyse the Rademacher complexity of the whitened signature functionals to characterise the expressive power of the model under heavy-tailed innovations. The framework is implemented via a scalable numerical scheme involving Nyström-compressed score-matching and an anticipatory hybrid Euler-Maruyama-Marcus integration scheme. Our results demonstrate that the proposed method captures the non-commutative moments and high-order stochastic texture of complex, discontinuous path-laws with high computational efficiency.
Daniel Bloch
UNIVERSITY OF PARIS 6 & VINUNIVERSITY · Visting Professor at the College of Engineering and Computer Science, VinUniversity, Hanoi.
Reinforcement learning algorithms are commonly analyzed (and designed) under the Markov assumption. This is unrealistic, as most environments encountered in practice are either partially observable, or require function approximation that restricts the agent to access non-Markovian state features. We consider the problem of learning an optimal reactive policy in a finite environment with deterministic observations (or equivalently, hard state aggregation). We introduce a new algorithm, Committed Q-learning, and prove almost-sure convergence to the optimal reactive policy under an intuitive assumption we call rewire-robustness. This assumption is strictly weaker than the q⋆-realizability condition used in prior work. Our algorithm is a variant of classical Q-learning in which the behavior policy commits to a single action upon entering a feature, and only resamples actions when the observed feature changes. A crucial part of our analysis is the introduction of quasi-Markov environments.
Onno Eberhard, Claire Vernade, Michael Muehlebach
Max Planck Institute for Intelligent Systems, Tübingen, Germany · University of Tübingen · University of Technology Nuremberg.
Signal delay poses a fundamental challenge in continuous control and reinforcement learning (RL) by introducing a temporal gap between interaction and perception. Current solutions have largely evolved along two distinct paradigms: model-free approaches which utilize state augmentation to preserve Markovian properties, and model-based methods which focus on inferring latent beliefs via dynamics modeling. In this paper, we bridge these perspectives by introducing State-Action Inpainting Diffuser (SAID), a framework that integrates the inductive bias of dynamics learning with the direct decision-making capability of policy optimization. By formulating the problem as a joint sequence inpainting task, SAID implicitly captures environmental dynamics while directly generating consistent plans, effectively operating at the intersection of model-based and model-free paradigms. Crucially, this generative formulation allows SAID to be seamlessly applied to both online and offline RL. Extensive experiments on delayed continuous control benchmarks demonstrate that SAID achieves state-of-the-art and robust performance. Our study suggests a new methodology to advance the field of RL with delay.
Dongqi Han, Wei Wang, Enze Zhang +1
Microsoft Research Asia · University of Pennsylvania · Shanghai Jiaotong University