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Improving Generalization in Reinforcement Learning with Mixture Regularization

Kaixin Wang, Bingyi Kang, Jie Shao, Jiashi Feng

arXiv:2010.10814v1cs.LGcs.AIstat.ML

TL;DR

Deep RL agents can generalize poorly to unseen environments, and existing augmentation methods make only local observation changes. Mixreg interpolates observations and their supervision from different training environments; on Procgen, it outperforms well-established baselines by large margins.

  • Problem

    Limited training-environment diversity is identified as a main cause of poor generalization, while existing augmentation locally perturbs observations and offers limited diversity gains.

    Source: §1 · p. 1

  • Method

    Mixreg trains agents on convex mixtures of observations sampled from a batch, with interpolated supervision, and regularizes policy and value functions toward piece-wise linearity.

    Source: §1 · pp. 1–2, §3.2 · p. 4

  • Results

    On the large-scale Procgen benchmark, mixreg outperforms well-established baselines by a large margin and further improves performance when combined with ℓ2 regularization.

    Source: §1 · p. 2

  • Takeaways & Limitations

    The authors attribute mixreg’s effectiveness to increased data diversity, smoother policies, and better observation representations.

    Source: §6 · p. 9

    The broader-impact discussion projects benefits across environments, but the reported evaluation is on Procgen; performance in other domains remains to be explored.

    Source: §1 · p. 2, Broader Impact · p. 9, §6 · p. 9

Abstract

from arXiv · show

Deep reinforcement learning (RL) agents trained in a limited set of environments tend to suffer overfitting and fail to generalize to unseen testing environments. To improve their generalizability, data augmentation approaches (e.g. cutout and random convolution) are previously explored to increase the data diversity. However, we find these approaches only locally perturb the observations regardless of the training environments, showing limited effectiveness on enhancing the data diversity and the generalization performance. In this work, we introduce a simple approach, named mixreg, which trains agents on a mixture of observations from different training environments and imposes linearity constraints on the observation interpolations and the supervision (e.g. associated reward) interpolations. Mixreg increases the data diversity more effectively and helps learn smoother policies. We verify its effectiveness on improving generalization by conducting extensive experiments on the large-scale Procgen benchmark. Results show mixreg outperforms the well-established baselines on unseen testing environments by a large margin. Mixreg is simple, effective and general. It can be applied to both policy-based and value-based RL algorithms. Code is available at https://github.com/kaixin96/mixreg .

1 Introduction

Deep RL agents often generalize poorly to unseen environments, and existing observation-level augmentations provide limited diversity gains. Mixreg combines observations from different training environments with interpolated supervision, and outperforms well-established baselines on Procgen.

1 Introduction

  • Limited training-environment diversity is identified as a main cause of poor generalization, while local image augmentations provide only incremental diversity and limited performance gains.The paper contrasts these methods with mixing observations from different training environments.Source: §1 · pp. 1–2
  • Mixreg convexly combines observations sampled from a collected batch and trains on interpolated supervision, such as rewards or state values.It encourages piece-wise linearity in policy and value functions, helping agents learn smoother policies; the scheme applies to policy-based and value-based algorithms.Source: §1 · pp. 1–2
  • The authors present mixreg as a simple approach for improving RL generalization by learning smooth policies over mixed observations.The introduction also identifies mixing observations from different environments as a distinct direction from conventional data augmentation.Source: §1 · p. 2
  • On Procgen, mixreg outperforms well-established baselines by large margins and boosts generalization more significantly than the compared augmentation and regularization methods.It also brings further improvement when combined with methods such as ℓ2 regularization.Source: §1 · p. 2

2 Background

The background defines an RL task as an MDP paired with an initial-state distribution and frames the objective as maximizing expected cumulative reward. It briefly introduces policy-gradient and deep Q-learning approaches.

2 Background

  • An RL task is represented by an MDP and an initial-state distribution, and its goal is to find a policy maximizing expected cumulative reward.The policy objective is evaluated over trajectories, with a discount factor and trajectory distribution specified.Source: §2 · pp. 2–3
  • Policy-gradient methods directly optimize a policy using an estimated policy gradient, and this work uses PPO for its performance and comparability with prior work.A learned state-value function is often used to reduce the variance of advantage estimation.Source: §2 · p. 3
  • Deep Q-learning estimates a value function and constructs a policy from it; the paper uses Rainbow, a DQN variant combining six extensions.The value target is computed using target-network parameters.Source: §2 · p. 3

3 Method

The method addresses generalization from fixed training environments, focusing on visual changes while noting applicability to other kinds of environment changes. Mixreg interpolates observations and their supervision, and can be used with policy-gradient and deep Q-learning algorithms.

3.1 Generalization in RL

  • Generalization is assessed by zero-shot performance on test environments after training on a fixed set, with this work focusing on visual changes while noting other types.The paper identifies dynamical and structural changes as other possible sources of train-test differences.Source: §3.1 · p. 3

3.2 Mixture regularization

  • Mixreg convexly combines observations and interpolates their reward or value supervision, imposing linearity regularization that helps learn smoother policy and value functions.The paper notes that mixing observations alone may not always improve generalization; Figure 2 shows smoother values when supervision is mixed too.Source: §3.2 · p. 4, Figure 2 · p. 4

3.3 Application to policy gradient and deep Q-learning

  • Mixreg applies to policy-gradient and deep Q-learning methods by optimizing augmented transitions with interpolated supervision and algorithm-specific action or value targets.The passage describes policy-gradient and DQN formulations and sampling a mixing coefficient for each transition before optimization.Source: §3.3 · pp. 4–5

4 Experiments

The experiments test mixreg on Procgen for unseen-level generalization, varying the number of training levels and model sizes, applying it to Rainbow, and probing supervision mixing and learned representations.

4.1 Can mixreg improve generalization performance of RL agents?

  • Mixreg outperforms PPO by a large margin; cutout-color, random crop, and random convolution perform worse, sometimes even than PPO, while mixreg can further improve methods on Starpilot.The authors suggest local perturbations may fail to increase training diversity and create a discrepancy between training and testing.Source: §4.1 · p. 6
  • Across different numbers of training levels, mixreg improves zero-shot testing performance, reaches PPO’s testing performance with fewer levels, and is less prone to overfitting.Figure 5 plots training and testing performance by training-level count, with circles marking individual runs.Source: §4.1 · p. 6, Figure 5 · p. 6

4.2 Is mixreg widely applicable?

  • Across model sizes, mixreg improves generalization over PPO and remains more sample-efficient even on Fruitbot, where final testing improvement is small.The networks vary the number of convolutional channels at each layer by a factor of 2 or 4.Source: §4.2 · p. 6, Figure 6 · p. 7
  • With Rainbow, a value-based algorithm, mixreg yields significant improvement in generalization.The comparison also includes a variant using ℓ2 regularization.Source: §4.2 · p. 7, Figure 7 · p. 7

4.3 How does mixreg benefit generalization performance?

  • In some games, mixing observations alone brings no improvement over the baseline; the authors report that interpolating supervision is necessary for effective training-diversity increases and policy generalizability.Figure 8 presents the ablation of whether supervision signals are interpolated.Source: §4.3 · p. 7, Figure 8 · p. 7
  • On testing levels, mixreg-trained policies achieve much higher performance after policy- and value-head fine-tuning with fixed features for 60M timesteps; fine-tuning the entire model significantly improves sample efficiency versus training from scratch in new environments.Source: §4.3 · pp. 7–8

5 Related works

Prior RL work links generalization gaps to limited training-environment diversity and explores data augmentation and regularization. Mixreg draws on mixup but differs from an earlier RL use of mixup in its goal.

5 Related works

  • Prior work attributes RL generalization gaps to limited training-environment diversity and explores cutout, random convolution, other data augmentations, and regularization.The passage names ℓ2 regularization, dropout, and batch normalization among regularization techniques used to improve generalizability.Source: §5 · p. 8
  • Mixreg follows the training-diversity direction but proposes mixing observations from different environments as a more effective approach than prior data augmentations.The paper also says mixreg can combine with methods such as ℓ2 regularization for further improvement.Source: §5 · p. 8
  • Inspired by mixup [32], the work studies linear interpolation of observations and supervision for RL generalization; an earlier RL use [22] instead targets reward-function learning.The paper frames its questions as whether this interpolation helps generalization and how it affects the learned policy.Source: §5 · p. 8

6 Conclusion

The conclusion presents mixreg as a training-diversity approach for RL generalization and reports strong Procgen results. It identifies smoother policies and better observation representations as additional contributing factors, while leaving broader domains and more flexible mixing schemes for future work.

6 Conclusion

  • Mixreg increases training-data diversity by training on mixed observations and their correspondingly mixed supervision signals.The conclusion contrasts this approach with existing augmentations that perform only local perturbations.Source: §6 · p. 8
  • On the large-scale Procgen benchmark, mixreg is reported as more effective than well-established baselines.Source: §6 · pp. 8–9
  • The authors identify increased diversity, smoother policies, and better observation representations as contributing factors, and propose exploring more expressive mixing schemes and other domains.Source: §6 · p. 9

Broader Impact

The paper extends mixreg to PPO and Rainbow by mixing observations with interpolated supervision, and reports smoother learned policies under an empirical Lipschitz comparison. Its broader-impact discussion limits demonstrated effectiveness to games and warns that improper deployment may worsen decisions.

Broader Impact

  • The impact discussion says effectiveness has been verified only in games, leaving performance in domains such as finance unclear, and warns improper deployment may worsen decisions.Source: Broader Impact · p. 9

A.1 PPO

  • For PPO, mixreg interpolates two sampled transitions’ observations and supervision, selects one discrete action by whether λ is at least 0.5, and optimizes on the mixed batch.Source: §A.1 · p. 12

A.2 Rainbow

  • For Rainbow, mixreg interpolates sampled observations and target distributions, while choosing the discrete action from one of the sampled transitions.Source: §A.2 · p. 13

Appendix B On the smoothness of the learned policy and value function

  • Mixreg yields a smaller empirical Lipschitz constant than PPO, which the authors interpret as evidence of a smoother learned policy.The estimate uses the maximum ratio from 106 sampled observation pairs; Figure 10 shows the ratio distribution.Source: Appendix B · p. 13, Figure 10 · p. 13

Appendix C Implementation details and hyperparameters

The implementation details specify the Procgen environments, baseline-method implementations, and PPO and Rainbow training settings used in the experiments.

Appendix C Implementation details and hyperparameters

  • The six-environment comparison uses Caveflyer, Climber, Dodgeball, Fruitbot, Jumper, and Starpilot, selected from 11 games after excluding five environments for stated generalization-gap or training-performance reasons.Source: Appendix C · p. 15
  • Experiments use the IMPALA convolutional architecture; random crop resizes observations to 75 × 75 before cropping a 64 × 64 window.The random-crop implementation is described as a correction to a problematic official implementation.Source: Appendix C · p. 15
  • PPO and Rainbow generally use Procgen hyperparameters, with PPO workers adjusted for hardware and Rainbow settings drawn from anyrl-py and retro-baselines.Both methods are trained for 200M timesteps, and both use beta-distribution parameter α = 0.2.Source: Appendix C · p. 15

Appendix D Ablation results of varying the beta distribution parameter α

The ablation examines mixreg with different beta-distribution parameters and reports degradation in certain environments when α is too large.

Appendix D Ablation results of varying the beta distribution parameter α

  • α = 0.2 is chosen from the suggested interval [0.1, 0.4]; using α = 1.0 leads to performance degradation in certain environments.Figure 12 plots training and testing performance across α settings.Source: Appendix D · p. 16, Figure 12 · p. 16

E.1 Comparing different methods on 500 level generalization in 6 environments

The supplied figures cover training and testing performance and mean normalized scores for method comparisons under 500-level generalization, first across six environments and then across all 16.

E.1 Comparing different methods on 500 level generalization in 6 environments

  • The six-environment comparison plots training and testing performance of different methods under 500-level generalization.Source: Figure 13 · p. 17
  • A separate figure reports mean normalized scores for different methods on 500-level generalization.Source: Figure 14 · p. 17

E.2 Comparing mixreg with PPO baseline on 500 level generalization in all 16 environments

  • For all 16 environments, a figure plots training and testing performance on 500-level generalization.Source: Figure 15 · p. 18
  • Another figure reports mean normalized scores averaged over the 16 environments on 500-level generalization.Source: Figure 16 · p. 18

E.3 Combining mixreg with other methods on 500 level generalization

The supplied figures outline evaluations of combining mixreg with other methods, scaling model size, and varying the number of training levels on 500-level generalization.

E.3 Combining mixreg with other methods on 500 level generalization

  • Figure 17 covers training and testing performance when combining mixreg with other methods on 500-level generalization.Source: Figure 17 · p. 19

E.4 Scaling model size

  • Figure 18 reports mean normalized score across different model sizes on 500-level generalization.Source: Figure 18 · p. 19

E.5 Varying the number of training levels

  • Figures 19 and 20 cover varying training-level counts, showing training and testing performance and mean normalized score, respectively.Source: Figure 19 · p. 20, Figure 20 · p. 20
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