UC-Search: Risk-Aware Test-Time Search for Delayed Constrained Time-Series Control

UC-Search is a model-agnostic test-time algorithm that combines time-series forecasting with constrained decision-making under uncertainty. The approach uses beam search and Monte Carlo tree search variants to optimize delayed control decisions while respecting feasibility constraints, demonstrating measurable improvements over existing methods like CEM and MPPI across inventory control and financial forecasting benchmarks.

UC-Search addresses a critical gap between how time-series models are typically evaluated and how they function in real-world systems. Academic models optimize forecast accuracy, but operational systems must make delayed decisions subject to hard constraints—inventory levels cannot go negative, trading positions have exposure limits, and system states evolve unpredictably. This research bridges that divide by treating forecasts as inputs to a constrained search process rather than end products.

The technical innovation lies in decomposing uncertainty into epistemic (model uncertainty), aleatoric (inherent randomness), and propagated (compounding forecast errors) components, then encoding these as risk penalties within a search framework. The myopic-collapse theorem provides theoretical grounding, identifying conditions where non-sequential optimization fails versus where delayed feasibility coupling creates meaningful value. This is not trivial: it explains when one-step greedy decisions suffice and when forward-looking search matters.

Empirical validation across three distinct domains—synthetic control suites, ETT/LTSF inventory problems, and M4 periodic-review lost-sales scenarios—demonstrates consistent improvements. Against CEM and MPPI, UC-Search shows positive margins ranging from +2.34 to +3.17 normalized units. In M4 audits, advantages over base-stock control exceed 13,500 units, suggesting substantial operational gains. The researchers deliberately report boundary cases and mechanism tests rather than claiming universal dominance, which strengthens credibility.

The work's impact extends beyond academia into production systems. Practitioners deploying time-series models in supply chains, energy systems, or financial operations face identical constraints. UC-Search provides a generalizable wrapper applicable to any pre-trained forecaster, reducing implementation barriers. As enterprises increasingly rely on neural forecasters, frameworks handling uncertainty under constraints become infrastructure-critical.

• →UC-Search wraps existing forecasting models to optimize constrained decisions under uncertainty, improving over standard methods like CEM and MPPI across multiple benchmarks.
• →The approach decomposes uncertainty into epistemic, aleatoric, and propagated components, using these as risk signals within bounded search to find feasible trajectories.
• →A theoretical myopic-collapse theorem characterizes when one-step greedy optimization fails and when forward-looking search creates non-trivial value.
• →Empirical validation spans synthetic control suites, inventory systems, and financial forecasting, with improvements ranging from +2.3 to +3.2 normalized units and up to +13,556 units in lost-sales audits.
• →The model-agnostic wrapper architecture enables deployment across existing time-series forecasters without retraining, lowering adoption barriers for production systems.