Distributed training and increasing the gradient update frequency are practical strategies to accelerate learning and improve performance, but both exacerbate a central challenge: policy lag, which is the mismatch between the behavior policy generating data and the learning policy being updated. Policy lag can hinder the scaling of on-policy learning algorithms to larger problems. In this paper, we identify the sources of policy lag caused by distributed learning and high update frequency. We use the findings to propose total Variation-based Advantage aligned Constrained policy Optimization (\methodacronym) as a practical approach to mitigate policy lag. We empirically validate our method and show that it offers better robustness to policy lag in classic RL tasks and a modern RL for LLM math reasoning task.
Figures & tables
Figure 1: (left) Simulated Asynchronous RL setup. After the end of each training phase we store the weights of the new policy in the policy buffer. Subsequently, we sample random policies from the buffer and assign them to the actors. We then generated the trajectories in a synchronous fashion. The setup aims to simulate an asynchronous RL training setup to control the backward policy lag. (right) The typical asynchronous RL training setup. The actors generate the trajectories and train the policy simultaneously. The actor would receive the new policy whenever it is ready. Therefore, the new dataset would contain trajectories from older policies.
Figure 2: Algorithmic Choices in VACO . (Top) VACO vs. PPO Clipping : To maintain a fixed Total Variation (TV) divergence, VACO(shown as ’TV Filtering’) selectively removes gradients that would increase the TV divergence. In contrast, PPO naively clips gradients if their policy ratio exceeds a predefined threshold. (Bottom) IMPALA vs. Advantage Realignment : While IMPALA estimates advantage values for the most recent policy using an asynchronously generated dataset, VACO’s ’Advantage Realignment’ first aligns the dataset to the initial policy of the optimization process, then iteratively optimizes based on this aligned dataset. This approach significantly reduces the computational load compared to IMPALA’s on-the-fly realignment.
Figure 3: With more backward policy lag (higher degree of asynchronicity) VACO achieves better performance on the aggregate metrics across various MuJoCo tasks. Higher Median, IQM, and Mean values and lower Optimality Gap imply better performance. The scores are computed over 100M steps across 10 independent random seeds and the shades represent 95% confidence intervals of the metrics.
Figure 4: IQM values of the comparison algorithms in the simulated asynchronous setups during the training process. The scores are computed over 100M steps across 10 independent random seeds and the shades represent the 95% confidence interval. (bottom right) IQM values of the Area under the curve of the normalized return plots. Higher values imply better sample efficiency during the training process.
Figure 5: VACO improves over PPO-clipping for training LLMs to reason on GSM8k. (Top) Forward policy lag can improve training efficiency at the cost of eval performance. VACO maintains higher performance as lag increases. (Bottom) PPO-clip is always clipping, proportional to the forward lag. VACO filters more rarely, enabling learning from highly policy-lagged samples, but still maintains stability by filtering a larger part of the batch when activated.
Appendix figures & tables9 assets
Supplementary material from the paper’s appendix.
Appendix
Hyperparameter
Value
Clip Ratio/TV Threshold
0.2
Learning Rate
3e-4
Learning Rate Annealing
True
Num Envs
500
Num Steps
1000
Discount Factor
0.99
Appendix
Table 1: Important Hyperparameters of PPO, SPO, IMPALA, and VACO
Hyperparameter
Value
PPO-Clip Lower Ratio
0.2
PPO-Clip Higher Ratio
0.272
TV Threshold
0.05
Learning Rate
1e-6
Num Prompts Per Minibatch
32
Num Completions Per Prompt
8
Appendix
Table 2: Hyperparameters of GRPO, PPO-Clip and VACO for GSM8k
Figure 6: Return plot of the comparison algorithms in five environments across five degrees of asynchronicity. The plot represent the average return of the policy over 10 random seeds and the shades showcase the standard deviation of the returns.
Figure 7: IQM values of VACO with various values of δ for TV divergence threshold in the simulated asynchronous setups during the training process. The scores are computed over 100M steps across 10 independent random seeds and the shades represent the 95% confidence interval. (bottom right) IQM values of the Area under the curve of the normalized return plots. Higher values imply better sample efficiency during the training process.
Figure 8: Ablation analysis on the performance of VACO with various value of the TV divergence threshold δ . Higher Median, IQM, and Mean values and lower Optimality Gap imply better performance. The scores are computed over 100M steps across 10 independent random seeds and the shades represent 95% confidence intervals of the metrics.
Figure 9: IQM values of VACO with various values of ρ for advantage realignment in the simulated asynchronous setups during the training process. The scores are computed over 100M steps across 10 independent random seeds and the shades represent the 95% confidence interval. (bottom right) IQM values of the Area under the curve of the normalized return plots. Higher values imply better sample efficiency during the training process.
Figure 10: Ablation analysis on the performance of VACO with various value of ρ for advantage realignment. Higher Median, IQM, and Mean values and lower Optimality Gap imply better performance. The scores are computed over 100M steps across 10 independent random seeds and the shades represent 95% confidence intervals of the metrics.
Figure 11: The average Total Variation Divergence between the final policy of the training phase and the behavior policy distribution for VACO and PPO in the simulated asynchronous RL training setup. We can see that VACO with the constraint of 1/2E[∣π/β−1∣]≤δ/2 where δ=0.2 , consistently maintains the same level of TV divergence across all environments and degrees of asynchronicity. The plot represent the average estimate of the TV value over 10 random seeds and the shades showcase the standard deviation.
Figure 12: The performance of VACO with and without the advantage realignment process. We can see that on average, return realignment offers better robustness to off-policy data. The scores are computed over 100M steps across 10 independent random seeds and the shades represent the 95% confidence interval.