Observational Overfitting in Reinforcement Learning

international conference on learning representations, (2020)

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摘要

A major component of overfitting in model-free reinforcement learning (RL) involves the case where the agent may mistakenly correlate reward with certain spurious features from the observations generated by the Markov Decision Process (MDP). We provide a general framework for analyzing this scenario, which we use to design multiple synthe...更多

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简介
  • Generalization for RL has recently grown to be an important topic for agents to perform well in unseen environments.
  • One particular framework, which the authors denote by zero-shot supervised framework (Zhang et al, 2018a;c; Nichol et al, 2018; Justesen et al, 2018) and is used to study RL generalization, is to treat it analogous to a classical supervised learning (SL) problem – i.e. assume there exists a distribution of MDP’s, train jointly on a finite “training set” sampled from this distribution, and check expected performance on the entire distribution, with the fixed trained policy
  • In this framework, there is a spectrum of analysis, ranging from almost purely theoretical analysis (Wang et al, 2019; Asadi et al, 2018) to full empirical results on diverse environments (Zhang et al, 2018c; Packer et al, 2018).
  • Various hyperparameters such as the batch-size in SGD (Smith et al, 2018), choice of optimizer (Kingma & Ba, 2014), discount factor γ (Jiang et al, 2015) and regularizations such as entropy (Ahmed et al, 2018) and weight norms (Cobbe et al, 2018) can affect generalization
重点内容
  • Generalization for reinforcement learning has recently grown to be an important topic for agents to perform well in unseen environments
  • In order to isolate these factors, we study one broad factor affecting generalization that is most correlated with themes in supervised learning, observational overfitting, where an agent overfits due to properties of the observation which are irrelevant to the latent dynamics of the Markov Decision Process family
  • We have identified and isolated a key component of overfitting in reinforcement learning as the particular case of “observational overfitting”, which is attractive for studying architectural implicit regularizations
  • The analytical case of linear quadratic regulators and linear policies under exact gradient descent, which lays the foundation for understanding theoretical properties of networks in reinforcement learning generalization
  • The empirical but principled Projected-Gym case for both multi-layer perceptrons and convolutional networks which demonstrates the effects of neural network policies under nonlinear environments
  • We noted that current network policy bounds using ideas from supervised learning are unable to explain overparametrization effects in reinforcement learning, which is an important further direction. This area of reinforcement learning generalization is an extension of static supervised learning classification from adding extra reinforcement learning components
方法
  • The authors first analyze the case of the LQR as a surrogate for what may occur in deep RL, which has been done before for various topics such as sample complexity (Dean et al, 2019) and model-based RL (Tu & Recht, 2019)
  • This is analogous to analyzing linear/logistic regression (Kakade et al, 2008; McAllester, 2003) as a surrogate to understanding extensions to deep SL techniques (Neyshabur et al, 2018a; Bartlett et al, 2017).
  • There have been multiple recent works on this linear-layer stacking in SL and other theoretical problems such as matrix factorization and matrix completion (Arora et al, 2018b;a; Gunasekar et al, 2017), but to the knowledge, the authors are the first to analyze this case in the context of RL generalization
结论
  • The authors have identified and isolated a key component of overfitting in RL as the particular case of “observational overfitting”, which is attractive for studying architectural implicit regularizations.
  • In terms of architectural design, recent works (Jacot et al, 2018; Garriga-Alonso et al, 2019; Lee et al, 2019) have shed light on the properties of asymptotically overparametrized neural networks in the infinite width and depth cases and their performance in SL
  • Such architectures may be used in the RL setting which can possibly provide benefits, one of which is generalization as shown in this paper.
  • The authors believe that this work provides an important initial step towards solving these future problems
总结
  • Introduction:

    Generalization for RL has recently grown to be an important topic for agents to perform well in unseen environments.
  • One particular framework, which the authors denote by zero-shot supervised framework (Zhang et al, 2018a;c; Nichol et al, 2018; Justesen et al, 2018) and is used to study RL generalization, is to treat it analogous to a classical supervised learning (SL) problem – i.e. assume there exists a distribution of MDP’s, train jointly on a finite “training set” sampled from this distribution, and check expected performance on the entire distribution, with the fixed trained policy
  • In this framework, there is a spectrum of analysis, ranging from almost purely theoretical analysis (Wang et al, 2019; Asadi et al, 2018) to full empirical results on diverse environments (Zhang et al, 2018c; Packer et al, 2018).
  • Various hyperparameters such as the batch-size in SGD (Smith et al, 2018), choice of optimizer (Kingma & Ba, 2014), discount factor γ (Jiang et al, 2015) and regularizations such as entropy (Ahmed et al, 2018) and weight norms (Cobbe et al, 2018) can affect generalization
  • Methods:

    The authors first analyze the case of the LQR as a surrogate for what may occur in deep RL, which has been done before for various topics such as sample complexity (Dean et al, 2019) and model-based RL (Tu & Recht, 2019)
  • This is analogous to analyzing linear/logistic regression (Kakade et al, 2008; McAllester, 2003) as a surrogate to understanding extensions to deep SL techniques (Neyshabur et al, 2018a; Bartlett et al, 2017).
  • There have been multiple recent works on this linear-layer stacking in SL and other theoretical problems such as matrix factorization and matrix completion (Arora et al, 2018b;a; Gunasekar et al, 2017), but to the knowledge, the authors are the first to analyze this case in the context of RL generalization
  • Conclusion:

    The authors have identified and isolated a key component of overfitting in RL as the particular case of “observational overfitting”, which is attractive for studying architectural implicit regularizations.
  • In terms of architectural design, recent works (Jacot et al, 2018; Garriga-Alonso et al, 2019; Lee et al, 2019) have shed light on the properties of asymptotically overparametrized neural networks in the infinite width and depth cases and their performance in SL
  • Such architectures may be used in the RL setting which can possibly provide benefits, one of which is generalization as shown in this paper.
  • The authors believe that this work provides an important initial step towards solving these future problems
表格
  • Table1: Raw Network Performance (rounded to nearest 0.5) on CoinRun, 100 levels. Images scaled to default image sizes (32 × 32 or 224 × 224) depending on network input requirement. See Appendix A.2.1 for training curves
  • Table2: IMPALA vs NatureCNN test rewards, with and without Blackout
  • Table3: Hyperparameters for LQR
Download tables as Excel
基金
  • Studies one broad factor affecting generalization that is most correlated with themes in SL, observational overfitting, where an agent overfits due to properties of the observation which are irrelevant to the latent dynamics of the MDP family
  • Studies observational overfitting with linear quadratic regulators in a synthetic environment and neural networks such as multi-layer perceptrons and convolutions in classic Gym environments
  • A primary novel result demonstrates for all cases is that implicit regularization occurs in this setting in RL
  • Provides an extensive analysis of the convex one-step LQR case under the observational overfitting regime, showing that under Gaussian initialization of the policy and using gradient descent on the training cost, a generalization gap must necessarily exist
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