Token-Level Policy Optimization: Linking Group-Level Rewards to Token-Level Aggregation via Sequence-Level Likelihood
Authors: Xingyu Lin, Yilin Wen, Du Su, Jinchang Hou, En Wang, Wenbin Liu, Chenfu Bao, Zhonghou Lv
Organizations: College of Computer Science and Technology, Jilin University · Key Laboratory of Symbolic Computation and Knowledge Engineering of MOE, Jilin University · Baidu Inc. · State Key Laboratory of AI Safety, Institute of Computing Technology, Chinese Academy of Sciences · Tsinghua University.
Group Relative Policy Optimization (GRPO) has significantly advanced the reasoning ability of large language models (LLMs), particularly in their mathemat ical reasoning performance. However, GRPO and related entropy regularization methods still struggle with token-level sparse-rewards, which is an inherent chal lenge in chain-of-thought (CoT) reasoning. These approaches often rely on undifferen tiated token-level entropy regularization, which easily leads to entropy collapse or model degradation under sparse token rewards. In this work, we propose TEPO, a novel token-level framework that (1) leverages sequence-level likelihood to link group-level rewards with individual tokens via token-level aggregation, and (2) introduces a token-level KL-Divergence mask constraint that targets tokens with positive advantages and decreasing entropy to mitigate abrupt policy updates. Experiments demonstrate that TEPO not only achieves state-of-the-art performance on mathematical reasoning benchmarks but also markedly enhances training stability, reducing convergence time by 50% compared with GRPO/DAPO.
Figures & tables
Figure 1: Overview of the TEPO Framework TEPO (1) replaces baselines’ noisy, sparse token-level credit assignment with sequence-level likelihood, using soft aggregation to broadcast group rewards to tokens and stabilize training. (2) A selective KL mask curbs abrupt updates exclusively for tokens with positive advantage and decreasing entropy, balancing entropy reduction and stability.
Figure 2: Lower Gradient Bias and Faster Reasoning Efficiency with Markov Likelihood: The left panel shows that our method with a lower clip ratio effectively mitigates gradient bias, while the right panel indicates that it reduces the generation of redundant reasoning steps. Specifically, the average reasoning time of TEPO is 338 seconds per step , which is lower than that of DAPO/GRPO (357).
Figure 3: Markov Likelihood enhanced performance (We transform the raw data into percentage-based values.): The left panel shows that our method achieves steadier and higher rewards across training steps, demonstrating more efficient learning dynamics. The right panel indicates that our method exhibits consistently higher gradient norms, reflecting more active and effective parameter reasoning.
Method
AIME24
AIME25
AMC
MATH-500
OMNI-MATH
OlympiadBench
Minerva
Avg.
Qwen2.5-7B
0.94
0.94
14.34
43.20
13.73
16.74
21.69
13.30
w. GRPO/DAPO
11.25
5.00
42.80
76.60
25.00
37.92
33.08
30.85
w. ClLIP-Cov
10.83
7.40
42.84
75.60
26.11
39.40
37.86
31.64
w. KL-Cov
12.29
8.23
42.77
75.60
25.64
39.11
34.92
31.60
w. Entropy-based Term
11.35
6.15
43.18
74.80
26.14
40.14
36.02
31.62
w. GPG
13.54
6.04
43.29
75.00
26.28
40.44
34.55
31.91
Table 1: Performance Comparison of 7B and 14B Models on Mathematical Reasoning Benchmarks. Notations: 1-(w/o. GRPO/DAPO) indicates models not applying GRPO/DAPO, while (w. GRPO/DAPO) indicates models applying GRPO/DAPO; 2-higher values indicate better performance; 3-best results are marked in bold ; 4- Δ denotes the performance difference between models without and with our method; .
AIME24
AIME25
AMC
MATH-500
OMNI-MATH
OlympiadBench
Minerva
Avg.
DeepSeek-R1-Distill-Llama-8B
12.70
13.33
46.49
70.40
25.50
36.88
23.52
32.46
w. GRPO/DAPO
27.50
18.43
61.89
78.40
32.97
41.62
26.10
42.23
TEPO
25.72
18.85
60.84
79.60
33.11
43.55
29.77
42.76
Mistral-7B-Instruct-v0.2
-
-
2.1830
9.800
3.9840
1.1850
5.8820
2.7700
w.GRPO/DAPO
-
-
3.1250
10.8000
4.2680
2.3700
8.0880
3.3690
TEPO
-
-
3.5760
12.8000
4.5890
1.9250
8.0880
3.6520
Table 2: Performance Comparison of Various Models on Mathematical Reasoning Benchmarks
Method
AIME24
AIME25
AMC
MATH-500
OMNI-MATH
OlympiadBench
Minerva
Avg.
TEPO -w/o. KL
12.7000
6.3540
43.5600
75.4000
27.0000
39.5500
37.5000
32.21
Panel A: TEPO w. Undifferentiated KL-Divergence
w. β=1 (model collapse in 24 steps)
0
0
0
0
0
0
0
0
w. β=0.1 (leads to Avg drop of 4.6%.)
5.5200
3.9580
42.8400
75.6000
22.4100
32.7400
30.8800
26.2500
w. β=0.01
11.45
7.395
42.2400
76.2000
26.3200
40.5900
33.8200
31.6400
w. β=0.001
12.29
8.958
42.2400
77.2000
25.8900
40.1100
36.3900
31.8100
Table 3: Ablation Studies of Key Components. All panels are compared with TEPO -w/o. KL: Panel A demonstrates the fragility of undifferentiated KL-Divergence and its performance degradation effect; Panel B shows that undifferentiated entropy regularization yields marginal improvements to TEPO -w/o-KL; Panel C validates TEPO ’s effectiveness across different importance sampling strategies and corroborates that GRPO exhibits sparse token-level rewards; Panel D confirms the superiority of token-mean aggregation over alternative strategies; Panel E verifies that TEPO achieves optimal control of token-level KL-Divergence.
Method
AIME24
AIME25
AMC
MATH-500
OMNI-MATH
OlympiadBench
Minerva
Avg.
GRPO/DAPO (72 steps, seed1)
11.56
6.25
40.47
72.40
26.00
37.77
36.76
30.30
GRPO/DAPO (72 steps, seed2)
11.25
5.00
42.80
76.60
25.00
37.92
33.08
30.85
GRPO/DAPO (132 steps, seed1)
12.08
7.08
42.65
76.20
26.07
39.85
37.86
31.73
GRPO/DAPO (132 steps, seed2)
12.08
6.98
41.67
74.20
27.42
39.85
36.76
31.69
TEPO (72 steps, seed1)
12.50
7.60
45.18
77.80
26.78
41.03
38.97
32.62
TEPO (72 steps, seed2)
12.60
8.75
43.48
77.40
27.17
40.44
34.92
32.59
Table 4: Ablation Studies of Random Seeds. We report performance on seven mathematical reasoning benchmarks using two different random seeds for each method. “Mean” denotes the average performance over two seeds. TEPO consistently outperforms baseline methods across all settings.
Appendix figures & tables1 asset
Supplementary material from the paper’s appendix.
Appendix
Notation
Definition
{(xi,yi/oi)}i=1G
Batch of prompt-response pairs, x denotes the prompt, and y/oi denotes the response generated by LLMs
yi,j≤t
Prefix of the i -th sentence up to the t -th token
G
Number of responses generated by LLMs per prompt
∥oi∥
Length of yi/oi
θ(a∣s)
Score assigned by large language models (LLMs)
τ
A complete solution trajectory for a single math problem.
Reinforcement learning from verifiable rewards has significantly advanced the reasoning capabilities of large language models. However, Group Relative Policy Optimization (GRPO) typically assigns a uniform, sequence-level advantage to all tokens, thereby overlooking the intrinsic information heterogeneity along reasoning chains. We show that this coarse-grained credit assignment leads to premature entropy collapse and encourages the model to generate redundant, low-quality reasoning paths. Through systematic empirical analysis, we identify Critical Decision Pivots (CDPs): transient high-entropy states where the policy's trajectory is most sensitive to perturbations. These pivots represent the "forks in the road" where effective multi-path exploration is most crucial yet often suppressed by uniform advantage signals. Building on these insights, we propose Entropy-Regulated Policy Optimization (ERPO), which transitions the optimization focus from coarse sequences to fine-grained token dynamics. ERPO introduces three synergistic components: (i) Entropy-aware Gating, which adaptively amplifies exploration at CDPs to facilitate diverse path discovery; (ii) Bucket-based Implicit Normalization, which mitigates difficulty bias by aligning token progress windows; and (iii) Result-anchored Advantage Synthesis, which re-weights token-level signals via outcome-driven anchors. Extensive experiments on competitive mathematical benchmarks demonstrate that ERPO significantly outperforms GRPO. Notably, ERPO not only boosts reasoning accuracy but also yields significantly more concise and robust derivation paths, while achieving performance comparable to large models with orders of magnitude more parameters.
Song Yu, Li Li, Wenwen Zhao +1
School of Computer and Information Science, Southwest University, Chongqing, 400715, China
Existing policy-gradient methods for auto-regressive language models typically select subsequent tokens one at a time as actions in the policy. While effective for many generation tasks, such an approach may not fully capture the structure of complex reasoning tasks, where a single semantic decision is often realized across multiple tokens--for example, when defining variables or composing equations. This introduces a potential mismatch between token-level optimization and the inherently block-level nature of reasoning in these settings. To bridge this gap, we propose Multi-token Policy Gradient Optimization (MPO), a framework that treats sequences of K consecutive tokens as unified semantic actions. This block-level perspective enables our method to capture the compositional structure of reasoning trajectories and supports optimization over coherent, higher-level objectives. Experiments on mathematical reasoning and coding benchmarks show that MPO outperforms standard token-level policy gradient baselines, highlight the limitations of token-level policy gradients for complex reasoning, motivating future research to look beyond token-level granularity for reasoning-intensive language tasks.
Mufan Xu, Kehai Chen, Xuefeng Bai +4
School of Computer Science and Technology, Harbin Institute of Technology, China · Baidu Inc., Beijing, China
Reinforcement learning with verifiable rewards (RLVR), particularly Group Relative Policy Optimization (GRPO), has advanced LLM reasoning. However, GRPO suffers from three credit assignment failures: uniform token-level granularity that ignores heterogeneous informational value, uniform polarity that penalizes correct steps and rewards incorrect ones, and zero-variance collapse that erases outcome-driven gradients. We systematically quantify these failures, revealing highly non-uniform token informativeness, widespread step-level polarity misalignment, and substantial training waste. To address these limitations, we propose Entropy-Progress Aligned GRPO (EP-GRPO), a framework that mines the model's intrinsic information flow for dense, self-supervised guidance. EP-GRPO integrates entropy-gated modulation to prioritize high entropy decision pivots, implicit process signals from policy divergence anchored to outcome advantages for directional token-level feedback without external reward models, and cumulative entropy mapping that enables progress-aligned advantage normalization, naturally maintaining gradient flow under zero reward variance. Extensive experiments on mathematical reasoning benchmarks demonstrate that EP-GRPO achieves superior accuracy and efficiency compared to GRPO and its variants. The code will be available.
Song Yu, Li Li, Wenwen Zhao +1
School of Computer and Information Science, Southwest University, Chongqing 400715, China