Continuous RTS-PnO: Constraint-Aware Training for Robust Rolling-Horizon Budget Allocation

Fund allocation in financial markets requires decision-making frameworks that effectively balance forecasting accuracy with execution robustness. Recent advancements have successfully integrated uncertainty quantification into end-to-end learning. However, these frameworks fundamentally rely on open-loop control, where the entire execution plan is fixed at the initial time step conditioned solely on the initial information. This static dependency ignores intermediate market feedback, making the model vulnerable to evolving dynamics. In this work, we propose Continuous RTS-PnO, a unified framework that transitions to a closed-loop rolling-horizon paradigm, where the decision is adjusted conditioning on the latest information at each step. Apart from dynamic adjustments, closed-loop paradigm also needs to prevent overconfidence in planning. Our approach introduces two key innovations targeting these challenges: (1) Constraint-Aware Training, which embeds execution safety caps directly into the SPO+ loss function to prevent overconfident planning, and (2) Continuous Rolling Execution, which enables dynamic replanning over each time step. Empirical results across 11 currency pairs demonstrate that our method outperforms static baselines in 7 out of 11 cases. The gains are particularly pronounced in low-volatility regimes, achieving up to 48% reduction in regret by effectively mitigating model overconfidence.