Optimize Wider, Not Deeper: Consensus Aggregation for Policy Optimization
Organizations: Lain · Department of Computer Science, University of Texas at Austin · Department of Electrical and Computer Engineering, University of Texas at Austin
Abstract
Proximal policy optimization (PPO) approximates the trust region update using multiple epochs of clipped SGD. Each epoch may drift further from the natural gradient direction, creating path-dependent noise. To understand this drift, we can use Fisher information geometry to decompose policy updates into signal (the natural gradient projection) and waste (the Fisher-orthogonal residual that consumes trust region budget without first-order surrogate improvement). Empirically, signal saturates but waste grows with additional epochs, creating an optimization-depth dilemma. We propose Consensus Aggregation for Policy Optimization (CAPO), which redirects compute from depth to width: PPO replicates are optimized on the same batch, differing only in minibatch shuffling order, and then aggregated into a consensus. We study aggregation in two spaces: Euclidean parameter space, and the natural parameter space of the policy distribution via the logarithmic opinion pool. In natural parameter space, the consensus provably achieves higher KL-penalized surrogate and tighter trust region compliance than the mean expert; parameter averaging inherits these guarantees approximately. On continuous control tasks, CAPO outperforms PPO and compute-matched deeper baselines under fixed sample budgets by up to 8.6x. CAPO demonstrates that policy optimization can be improved by optimizing wider, rather than deeper, without additional environment interactions.
Figures & tables
| Epochs | Return | Signal | Waste | Total KL | ||
|---|---|---|---|---|---|---|
| 2 | 1.5 | 6.0 | 7.5 | 0.20 | 0.43 | |
| 4 | 2.6 | 9.3 | 11.9 | 0.22 | 0.46 | |
| 6 | 3.4 | 11.5 | 15.0 | 0.23 | 0.47 | |
| 10 | 5.3 | 16.3 | 21.5 | 0.24 | 0.49 | |
| 15 | 7.2 | 22.1 | 29.4 | 0.25 | 0.49 | |
| 20 | 8.2 | 31.5 | 39.7 | 0.21 | 0.45 |
| Method | Env. Frames | Grad. Steps | Inference | Update Quality |
|---|---|---|---|---|
| PPO | Baseline | |||
| PPO- (more epochs) | Degrades | |||
| PPO-SWA | Moderate | |||
| Best-of- | Selection only | |||
| Ensemble Methods | Moderate | |||
| CAPO (Ours) | Best |
| Environment | Type | ||
|---|---|---|---|
| Hopper | Hopping locomotion | 11 | 3 |
| HalfCheetah | Locomotion | 17 | 6 |
| Walker2d | Locomotion | 17 | 6 |
| Ant | Multi-legged locomotion | 27 | 8 |
| Humanoid | High-dim locomotion | 376 | 17 |
| HumanoidStandup | High-dim balance | 376 | 17 |
| Method | Hopper | HalfCheetah | Walker2d | Ant | Humanoid | HumanoidStandup |
|---|---|---|---|---|---|---|
| PPO | ||||||
| PPO- | ||||||
| Best-of- | ||||||
| PPO-SWA | ||||||
| TRPO | ||||||
| CAPO-Avg † |
Appendix figures & tables8 assets
Supplementary material from the paper’s appendix.
Appendix
| Environment | (signal) | (waste) | ||
|---|---|---|---|---|
| HalfCheetah | 0.999 | 0.974 | 0.976 | 0.999 |
| Walker2d | 0.999 | 0.961 | 0.966 | 0.999 |
| Hopper | 0.993 | 0.934 | 0.939 | 0.995 |
| Ant | 1.000 | 0.969 | 0.973 | 1.000 |
| Humanoid | 1.000 | 0.774 | 0.837 | 1.000 |
| Environment | Method | Ratio | ||||
|---|---|---|---|---|---|---|
| Hopper | CAPO-Avg | 11 | 3 | |||
| Hopper | CAPO | 11 | 3 | |||
| HalfCheetah | CAPO-Avg | 17 | 6 | |||
| HalfCheetah | CAPO | 17 | 6 | |||
| Walker2d | CAPO-Avg | 17 | 6 | |||
| Walker2d | CAPO | 17 | 6 |
| HalfCheetah | Walker2d | Ant | Hopper | Humanoid † | HumanoidStandup | |
|---|---|---|---|---|---|---|
| PPO | ||||||
| PPO- | 1.37 | 1.36 | 1.38 | 1.41 | 1.21 | 1.65 |
| TRPO | 0.98 | 0.99 | 1.03 | 1.01 | 1.02 | 0.95 |
| PPO-SWA | 0.97 | 0.99 | 1.04 | 1.00 | 0.92 | 1.06 |
| Best-of- | 1.36 | 1.31 | 1.18 | 1.67 | 1.06 | 1.01 |
| CAPO-Avg | 1.12 | 1.16 | 0.96 | 1.40 | 0.99 | 1.00 |
| Method | Env | Incumbent | Reset | Best Expert | Average |
|---|---|---|---|---|---|
| CAPO-Avg | Hopper | ||||
| Walker2d | |||||
| Ant | |||||
| CAPO | Hopper | ||||
| Walker2d | |||||
| Ant |
| HalfCheetah | ||||
|---|---|---|---|---|
| CAPO | ||||
| CAPO-Avg | ||||
| Walker2d | ||||
| CAPO | ||||
| CAPO-Avg | ||||
| HalfCheetah | ||||
|---|---|---|---|---|
| PPO | ||||
| CAPO-Avg | ||||
| CAPO | ||||
| Walker2d | ||||
| PPO | ||||
| HalfCheetah | ||||
|---|---|---|---|---|
| PPO | ||||
| CAPO-Avg | ||||
| CAPO | ||||
| Walker2d | ||||
| PPO | ||||
| 0% | 5% | 10% | 20% | |
| HalfCheetah | ||||
| CAPO-Avg | ||||
| CAPO | ||||
| Walker2d | ||||
| CAPO-Avg | ||||
| CAPO | ||||
Policy Optimization
Policy optimization develops algorithms for improving decision rules in reinforcement learning, language models, and sequential decision systems.
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