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Cast-R1: Learning Tool-Augmented Sequential Decision Policies for Time Series Forecasting

Xiaoyu Tao, Mingyue Cheng, Chuang Jiang, Tian Gao, Huanjian Zhang, Yaguo Liu

arXiv:2602.13802v1cs.LG

TL;DR

Single-pass forecasting methods are limited in complex, evolving settings because they do not autonomously acquire evidence, reason about changes, or revise predictions. Cast-R1 reformulates forecasting as sequential decision making with memory, tools, and staged policy learning; experiments report consistent improvements over strong baselines.

  • Problem

    Existing forecasting approaches commonly use single-pass, model-centric formulations that do not autonomously acquire evidence, reason about future changes, or revise predictions iteratively.

  • Method

    Cast-R1 combines memory-based state management, a tool-augmented agentic workflow, and supervised fine-tuning with multi-turn reinforcement learning and curriculum learning.

  • Results

    Cast-R1 achieves consistent improvements over strong baselines on real-world time series datasets.

  • Takeaways & Limitations

    The paper supports sequential decision making and tool augmentation as an effective framework for agentic time series forecasting.

Abstract

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Time series forecasting has long been dominated by model-centric approaches that formulate prediction as a single-pass mapping from historical observations to future values. Despite recent progress, such formulations often struggle in complex and evolving settings, largely because most forecasting models lack the ability to autonomously acquire informative evidence, reason about potential future changes, or revise predictions through iterative decision processes. In this work, we propose Cast-R1, a learned time series forecasting framework that reformulates forecasting as a sequential decision-making problem. Cast-R1 introduces a memory-based state management mechanism that maintains decision-relevant information across interaction steps, enabling the accumulation of contextual evidence to support long-horizon reasoning. Building on this formulation, forecasting is carried out through a tool-augmented agentic workflow, in which the agent autonomously interacts with a modular toolkit to extract statistical features, invoke lightweight forecasting models for decision support, perform reasoning-based prediction, and iteratively refine forecasts through self-reflection. To train Cast-R1, we adopt a two-stage learning strategy that combines supervised fine-tuning with multi-turn reinforcement learning, together with a curriculum learning scheme that progressively increases task difficulty to improve policy learning. Extensive experiments on multiple real-world time series datasets demonstrate the effectiveness of Cast-R1. We hope this work provides a practical step towards further exploration of agentic paradigms for time series modeling. Our code is available at https://github.com/Xiaoyu-Tao/Cast-R1-TS.

1 Introduction

Cast-R1 argues that forecasting should move beyond single-pass, model-centric prediction toward sequential decision making that incorporates evolving evidence and iterative revision. It introduces a memory-based, tool-augmented framework trained with supervised fine-tuning, reinforcement learning, and curriculum learning.

  • Real-world time series involve evolving trends, distribution shifts, and external disturbances that require reasoning over historical observations and contextual features.
  • Most existing forecasting methods assume the task is fully defined before prediction and therefore follow a model-centric formulation.
  • Experienced forecasting is characterized as a sequence of interdependent decisions involving feature preparation, model selection, prediction, and forecast revision.
  • Cast-R1 maintains decision-relevant context across forecasting steps and uses tools for feature extraction, diagnostics, model invocation, reasoning, and prediction refinement.
  • Cast-R1 combines supervised fine-tuning, multi-turn reinforcement learning, and curriculum learning to train long-horizon forecasting policies.
  • Experiments on real-world datasets report effectiveness across diverse forecasting scenarios.

2 Related Work

The related work spans conventional time series forecasting methods and agentic decision-making systems. Cast-R1 is positioned at their intersection by treating forecasting as sequential policy learning.

  • The paper organizes related work around advances in forecasting methods and developments in agentic and decision-making systems.
  • Advances in Time Series Forecasting: Prior time series forecasting research includes statistical, machine learning, and deep learning methods.
  • Agentic and Decision-Making Systems: Agentic and decision-making research provides reinforcement-learning frameworks for mapping states to actions in dynamic environments.

3 The Proposed Cast-R1

Cast-R1 formulates forecasting as a sequence of interdependent decisions supported by memory, modular tools, and multi-turn agent interaction. The framework incrementally acquires evidence, invokes models, and refines forecasts.

  • Sequential Forecasting Formulation: Cast-R1 represents forecasting as finite sequential decisions over states, actions, and a fixed future prediction horizon.
  • Memory-Based State Management: Memory-based state management preserves decision-relevant information and accumulated evidence across forecasting steps for long-horizon reasoning.
  • Modular Toolkit: The modular toolkit exposes analytical and forecasting operations as callable actions, allowing adaptive information acquisition and prediction.
  • Modular Toolkit: Toolkit capabilities include data-quality assessment, global statistics, structural analysis, event summarization, residual diagnostics, and forecasting-model invocation.
  • Agentic Workflow: The workflow incrementally constructs context, generates predictions, and refines results through multiple interaction turns.
  • Agentic Workflow: Cast-R1 first plans information acquisition and calls relevant tools to produce structured summaries of the observed series.
  • Agentic Workflow: The system adaptively selects a forecasting model, incorporates its output as predictive evidence, and uses the updated state for reasoning-based forecasting.
  • Learning Strategy: The training strategy progressively equips the system with forecasting competence and sequential decision-making capability.

4 Experiments

Experiments evaluate Cast-R1 on diverse real-world forecasting benchmarks and through component ablations. Results show consistent gains from the tool-augmented workflow, dynamic memory, two-stage training, curriculum learning, and larger backbones.

  • Experimental Settings: Experiments cover real-world datasets spanning multiple domains, temporal resolutions, and forecasting horizons, with comparisons against statistical, deep learning, foundation, and LLM-based baselines.The evaluation includes short-term and long-term forecasting settings.
  • Main Results: Cast-R1 achieves the lowest MSE on all evaluated datasets and ranks first or second on most MAE metrics across short- and long-horizon benchmarks.The method outperforms diverse statistical, deep learning, foundation-model, and LLM-based baselines.
  • Forecasting Toolkit Ablation: Removing feature extraction reduces accuracy across all benchmarks, while removing model prediction causes a more severe error increase on complex datasets such as Wind and PJM.The results support combining diagnostic insight with adaptive invocation of specialized forecasting models.
  • State Management Ablation: Removing dynamic memory consistently increases forecasting error across volatile and long-term datasets, indicating that memory preserves context across sequential reasoning steps.The memory mechanism provides a compact state abstraction for retaining historical information and supporting credit assignment.
  • Learning Strategy Ablation: Removing reinforcement learning produces the largest training-strategy performance drop, while supervised fine-tuning provides a higher-reward warm start and accelerates convergence.The combined strategy is reported as necessary because neither stage alone fully internalizes task-specific decision policies.
  • Curriculum and Scalability Analysis: Curriculum learning lowers forecasting errors across datasets, with the largest gap on complex benchmarks such as PJM, while larger Qwen3 backbones reduce errors and improve reward accumulation.The backbone analysis compares Qwen3-1.7B, 4B, and 8B variants; the 8B model performs best.
  • Qualitative Analysis: A qualitative case shows the agent using statistical diagnosis, adaptive routing to Chronos-2, and self-reflection to smooth an unrealistic spike and improve physical consistency.The agent validates its prediction against historical constraints before refining the output.

5 Conclusion

The conclusion presents Cast-R1 as a sequential decision-making alternative to single-pass forecasting. It reports consistent improvements on real-world datasets and motivates further study of trainable, agentic forecasting systems.

  • Conclusion: Cast-R1 reformulates forecasting as interconnected decisions involving information preparation, reasoning-based prediction, and forecast refinement.The framework combines memory-based state management, tool augmentation, supervised fine-tuning, and multi-turn reinforcement learning.
  • Conclusion: Extensive experiments on real-world time series datasets demonstrate consistent improvements over strong baselines.The conclusion presents these results as evidence for sequential decision making and tool-augmented forecasting in practical scenarios.
  • Conclusion: The work frames time series forecasting as an adaptive, decision-centric process and motivates further exploration of learning-based sequential decision-making frameworks.

A Detailed Dataset Descriptions

The experiments cover diverse real-world forecasting datasets spanning electricity prices, transformer temperatures, and wind generation, alongside statistical, deep learning, and foundation-model baselines.

  • Datasets: The evaluation spans short-term electricity price forecasting and long-term forecasting benchmarks across energy economics, industrial monitoring, and renewable generation.The datasets include EPF benchmarks and LTSF benchmarks.
  • Short-term forecasting: The EPF datasets contain hourly regional day-ahead electricity prices forecast 24 steps ahead using historical observations and exogenous variables.The benchmark includes NP, PJM, BE, FR, and DE markets.
  • Long-term forecasting: The LTSF benchmarks include ETT transformer-temperature series and Wind renewable-generation data with complex temporal dependencies, high volatility, or high stochasticity.ETT uses hourly and 15-minute resolutions, while Wind is sampled every 15 minutes with meteorological covariates.
  • Baselines: Cast-R1 is compared with classical statistical methods, neural forecasting models, and foundation or language-model-based forecasters.Representative baselines include ARIMA, Prophet, DLinear, PatchTST, iTransformer, Chronos-2, TimesFM, OFA, and Time-LLM.
  • Dataset organization: The dataset summary organizes each benchmark by domain, sampling frequency, variable dimensions, forecasting setting, and specific content.These dimensions are documented in the experiment dataset table.
  • Implementation: Experiments use Qwen3-1.7B as the Cast-R1 backbone and run training and inference on a single NVIDIA RTX 4090D GPU.Gradient checkpointing and BF16 precision are used during reinforcement learning for memory efficiency.

C.2 Training Protocol

Cast-R1 is trained in two stages: supervised fine-tuning establishes the tool-augmented interaction format, and multi-turn reinforcement learning optimizes the long-horizon forecasting policy.

  • Training stages: The training pipeline combines Supervised Fine-Tuning with multi-turn Reinforcement Learning using Group Relative Policy Optimization.The two phases are applied sequentially.
  • Supervised Fine-Tuning: SFT uses 200 curated instruction-tuning samples that demonstrate tool invocation formats, reasoning traces, and optimal workflow execution paths.The backbone is fine-tuned for one epoch with AdamW.
  • Reinforcement Learning: GRPO optimizes the long-horizon forecasting policy by estimating baselines from group scores instead of using a separate critic network.Eight trajectories are sampled per input query to compute relative advantages, with temperature set to 1.0.
  • Configuration: The hyperparameter configuration for Cast-R1 training is summarized in Table 6.The table accompanies the described SFT and RL protocol.
  • Baseline training: Deep learning baselines use official implementations, recommended learning rates, early stopping, and Z-score input normalization for fair comparison.Outputs are denormalized after inference.

C.4 Forecasting Task Configuration

The forecasting setup standardizes input-output lengths across short- and long-term tasks, evaluates raw-scale errors, and uses persistent memory with progress-aware prompts to structure sequential decisions.

  • Task configuration: Short-term EPF forecasting uses a 168-hour look-back window and a 24-hour prediction horizon, while LTSF uses 96 input and 96 prediction steps.The short-term datasets are NP, PJM, BE, FR, and DE; the long-term datasets are ETTh1, ETTm1, and Wind.
  • Qualitative evaluation: A qualitative comparison on a volatile snapshot contrasts Cast-R1 with statistical and deep learning baselines.The figure focuses on behavior under abrupt structural shifts and complex seasonality.
  • Evaluation metrics: Performance is evaluated with raw-scale Mean Squared Error and Mean Absolute Error, where each metric compares predictions with ground truth across the forecast horizon.The displayed equations define the squared and absolute error averages.
  • Memory management: Cast-R1 maintains persistent memory that separates stored decision context from prompt construction and dynamically assembles prompts as task progress changes.Memory stores analysis history and intermediate prediction results for reuse across turns.
  • Sequential workflow: The workflow restricts admissible actions by stage: feature extraction first, forecasting-model invocation second, and later reflection and output.Prompt contents are selected according to whether analysis and prediction results already exist.
  • Context control: Raw observations are progressively truncated in later turns while accumulated high-level summaries remain in memory to control context length and preserve continuity.Early turns receive full historical data for feature analysis and diagnostics.
  • Ablations: The ablation tables examine reward components, training stages, curriculum learning, and backbone scaling.These tables compare full and component-removed variants across representative settings.

D.3 Visualization Analysis

The visualization examines forecasting under high volatility and abrupt structural change, where conventional baselines miss or smooth the sharp trough while Cast-R1 follows the observed dynamics more closely.

  • Evaluation setting: The visual analysis evaluates Cast-R1 and representative baselines on a volatile segment with irregular structural shifts.The segment is intended to assess adaptability to real-world non-stationarity.
  • Baseline behavior: Statistical models miss the sharp trough, deep learning models show phase lag and smoothing, and foundation or LLM-based models produce noisy, unstable curves.These differences appear around an abrupt downward spike followed by volatile recovery.
  • Cast-R1 behavior: Cast-R1 captures the timing and magnitude of the sudden drop while preserving fine-grained volatility during recovery.The comparison reports closer alignment with the ground-truth series.

E.1 Reward Function Analysis

The reward ablation shows that each reward component contributes to Cast-R1’s forecasting quality. Removing any component degrades both accuracy and structural validity.

  • Removing the length penalty, prediction error term, or structural alignment component degrades performance.The ablation evaluates these components on representative datasets.

E.2 Training Strategy and Curriculum Learning

The full SFT+RL strategy with curriculum learning performs best across datasets, while removing reinforcement learning causes the largest degradation. Larger backbone models also consistently improve forecasting accuracy.

  • The full Cast-R1 configuration, SFT+RL with Curriculum, achieves the lowest errors across all datasets.The comparison covers training strategies and curriculum learning mechanisms.
  • Removing the RL phase causes the largest performance drop, followed by removing SFT initialization.The MAE results corroborate this ordering.
  • As backbone size increases from 1.7B to 8B, both MSE and MAE decrease across all datasets.The scaling comparison reports monotonic improvement across the evaluated sizes.

E.4 Detailed Toolkit and Component Analysis

The ablations identify statistical diagnostics, Chronos2, planning, and refinement as important components of the forecasting workflow. The proposed multi-turn prompt framework separates diagnosis, model selection, and forecast refinement to support grounded, adaptive reasoning.

  • Feature Extraction Tools: Removing Basic Statistics tools causes the largest diagnostic error increase, with MSE +63% on NP.These tools support detection of non-stationarity through statistical context.
  • Model Prediction Tools: Removing Chronos2 increases MSE on volatile NP from 22.5 to 55.4, indicating its role in zero-shot regime adaptation.PatchTST and iTransformer are also described as important, but Chronos2 is pivotal for high volatility.
  • Agent Components: Without Planning, the agent becomes a random trial-and-error process and achieves the worst performance.Table 13 defines “w/o Planning” as removing the chain-of-thought reasoning component.
  • Agent Components: The Refine mechanism reduces MSE by approximately 3.1 on ETTh1 while smoothing artifacts and enforcing physical consistency.The refinement step is described as self-correction in the component ablation.
  • Prompt Engineering Framework: The multi-turn prompt framework uses Stop-and-Look diagnosis, adaptive model routing, and reflection-based refinement within a structured forecasting workflow.The protocol restricts the diagnostic phase to feature-extraction tools, routes forecasts using diagnostic insights, and reviews outputs against historical constraints.
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