Optimizing Anytime Reasoning via Budget Relative Policy Optimization

Penghui Qi, Zichen Liu, Tianyu Pang, Chao Du, Wee Sun Lee, Min Lin

Overview

Figure 1: The comparison of anytime reasoning performance between GRPO and our AnytimeReasoner with various prior budget distributions. Notably, the accuracies at the maximum token budget (8000) reflect the performance in the standard reasoning task.

Getting Started 🎯

Installation

./setup.sh

Data

To process the data for training and validation, run:

python anytime_reasoner/scripts/data/deepscaler_dataset.py

Training Scripts

export MODEL_PATH="deepseek-ai/DeepSeek-R1-Distill-Qwen-1.5B"

# GRPO baseline
./anytime_reasoner/scripts/train/run_1.5b_8k.sh --model $MODEL_PATH actor_rollout_ref.rollout.n_summary=1 actor_rollout_ref.rollout.summary_method=grpo actor_rollout_ref.rollout.n_budget_support=1 actor_rollout_ref.rollout.budget_probs=base actor_rollout_ref.rollout.variance_reduction=v2only trainer.experiment_name=GRPO

################################## Main results ##################################
## AnytimeReasoner-linear
./anytime_reasoner/scripts/train/run_1.5b_8k.sh --model $MODEL_PATH actor_rollout_ref.rollout.n_summary=4 actor_rollout_ref.rollout.summary_method=brpo actor_rollout_ref.rollout.n_budget_support=4 actor_rollout_ref.rollout.budget_probs=linear actor_rollout_ref.rollout.variance_reduction=brpo trainer.experiment_name=AR-linear
## AnytimeReasoner-uniform
./anytime_reasoner/scripts/train/run_1.5b_8k.sh --model $MODEL_PATH actor_rollout_ref.rollout.n_summary=4 actor_rollout_ref.rollout.summary_method=brpo actor_rollout_ref.rollout.n_budget_support=4 actor_rollout_ref.rollout.budget_probs=uniform actor_rollout_ref.rollout.variance_reduction=brpo trainer.experiment_name=AR-uniform
## AnytimeReasoner-base
./anytime_reasoner/scripts/train/run_1.5b_8k.sh --model $MODEL_PATH actor_rollout_ref.rollout.n_summary=4 actor_rollout_ref.rollout.summary_method=brpo actor_rollout_ref.rollout.n_budget_support=4 actor_rollout_ref.rollout.budget_probs=base actor_rollout_ref.rollout.variance_reduction=brpo trainer.experiment_name=AR-base

################################## Ablations ##################################
## GRPO+linear
./anytime_reasoner/scripts/train/run_1.5b_8k.sh --model $MODEL_PATH actor_rollout_ref.rollout.n_summary=1 actor_rollout_ref.rollout.summary_method=grpo actor_rollout_ref.rollout.n_budget_support=4 actor_rollout_ref.rollout.budget_probs=linear actor_rollout_ref.rollout.variance_reduction=v2only trainer.experiment_name=GRPO+linear
## GRPO+decouple
./anytime_reasoner/scripts/train/run_1.5b_8k.sh --model $MODEL_PATH actor_rollout_ref.rollout.n_summary=4 actor_rollout_ref.rollout.summary_method=brpo actor_rollout_ref.rollout.n_budget_support=4 actor_rollout_ref.rollout.budget_probs=base actor_rollout_ref.rollout.variance_reduction=v2only trainer.experiment_name=GRPO+decouple
## GRPO+vr
./anytime_reasoner/scripts/train/run_1.5b_8k.sh --model $MODEL_PATH actor_rollout_ref.rollout.n_summary=1 actor_rollout_ref.rollout.summary_method=grpo actor_rollout_ref.rollout.n_budget_support=4 actor_rollout_ref.rollout.budget_probs=base actor_rollout_ref.rollout.variance_reduction=brpo trainer.experiment_name=GRPO+vr
## GRPO+vr+decouple
./anytime_reasoner/scripts/train/run_1.5b_8k.sh --model $MODEL_PATH actor_rollout_ref.rollout.n_summary=4 actor_rollout_ref.rollout.summary_method=brpo actor_rollout_ref.rollout.n_budget_support=4 actor_rollout_ref.rollout.budget_probs=base actor_rollout_ref.rollout.variance_reduction=brpo trainer.experiment_name=GRPO+vr+decouple

Evaluation

Run evaluation:

./anytime_reasoner/scripts/eval/eval_1.5b_8k.sh --model $MODEL_PATH trainer.resume_mode=$RESUME_PATH

Acknowledgements

• Our training experiments are powered by our heavily modified fork of Verl, an open-source RLHF library.
• Our model is trained on top of DeepSeek-R1-Distill-Qwen-1.5B.
• We use the training/validation data provided by DeepScaler.

Citation

If you find our works useful for your research, please consider citing:

@article{qi2025anytimereasoner,
  title={Optimizing Anytime Reasoning via Budget Relative Policy Optimization},
  author={Qi, Penghui and Liu, Zichen and Pang, Tianyu and Du, Chao and Lee, Wee Sun and Lin, Min},
  journal={arXiv preprint arXiv:2505.13438},
  year={2025}
}