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Deep Multi-Agent Reinforcement Learning
  • Deep Multi-Agent Reinforcement Learning
  • Abstract & Contents
    • Abstract
  • 1. Introduction
    • 1. INTRODUCTION
      • 1.1 The Industrial Revolution, Cognition, and Computers
      • 1.2 Deep Multi-Agent Reinforcement-Learning
      • 1.3 Overall Structure
  • 2. Background
    • 2. BACKGROUND
      • 2.1 Reinforcement Learning
      • 2.2 Multi-Agent Settings
      • 2.3 Centralized vs Decentralized Control
      • 2.4 Cooperative, Zero-sum, and General-Sum
      • 2.5 Partial Observability
      • 2.6 Centralized Training, Decentralized Execution
      • 2.7 Value Functions
      • 2.8 Nash Equilibria
      • 2.9 Deep Learning for MARL
      • 2.10 Q-Learning and DQN
      • 2.11 Reinforce and Actor-Critic
  • I Learning to Collaborate
    • 3. Counterfactual Multi-Agent Policy Gradients
      • 3.1 Introduction
      • 3.2 Related Work
      • 3.3 Multi-Agent StarCraft Micromanagement
      • 3.4 Methods
        • 3.4.1 Independent Actor-Critic
        • 3.4.2 Counterfactual Multi-Agent Policy Gradients
        • 3.4.2.1 baseline lemma
        • 3.4.2.2 COMA Algorithm
      • 3.5 Results
      • 3.6 Conclusions & Future Work
    • 4 Multi-Agent Common Knowledge Reinforcement Learning
      • 4.1 Introduction
      • 4.2 Related Work
      • 4.3 Dec-POMDP and Features
      • 4.4 Common Knowledge
      • 4.5 Multi-Agent Common Knowledge Reinforcement Learning
      • 4.6 Pairwise MACKRL
      • 4.7 Experiments and Results
      • 4.8 Conclusion & Future Work
    • 5 Stabilizing Experience Replay
      • 5.1 Introduction
      • 5.2 Related Work
      • 5.3 Methods
        • 5.3.1 Multi-Agent Importance Sampling
        • 5.3.2 Multi-Agent Fingerprints
      • 5.4 Experiments
        • 5.4.1 Architecture
      • 5.5 Results
        • 5.5.1 Importance Sampling
        • 5.5.2 Fingerprints
        • 5.5.3 Informative Trajectories
      • 5.6 Conclusion & Future Work
  • II Learning to Communicate
    • 6. Learning to Communicate with Deep Multi-Agent ReinforcementLearning
      • 6.1 Introduction
      • 6.2 Related Work
      • 6.3 Setting
      • 6.4 Methods
        • 6.4.1 Reinforced Inter-Agent Learning
        • 6.4.2 Differentiable Inter-Agent Learning
      • 6.5 DIAL Details
      • 6.6 Experiments
        • 6.6.1 Model Architecture
        • 6.6.2 Switch Riddle
        • 6.6.3 MNIST Games
        • 6.6.4 Effect of Channel Noise
      • 6.7 Conclusion & Future Work
    • 7. Bayesian Action Decoder
      • 7.1 Introduction
      • 7.2 Setting
      • 7.3 Method
        • 7.3.1 Public belief
        • 7.3.2 Public Belief MDP
        • 7.3.3 Sampling Deterministic Partial Policies
        • 7.3.4 Factorized Belief Updates
        • 7.3.5 Self-Consistent Beliefs
      • 7.4 Experiments and Results
        • 7.4.1 Matrix Game
        • 7.4.2 Hanabi
        • 7.4.3 Observations and Actions
        • 7.4.4 Beliefs in Hanabi
        • 7.4.5 Architecture Details for Baselines and Method
        • 7.4.6 Hyperparamters
        • 7.4.7 Results on Hanabi
      • 7.5 Related Work
        • 7.5.1 Learning to Communicate
        • 7.5.2 Research on Hanabi
        • 7.5.3 Belief State Methods
      • 7.6 Conclusion & Future Work
  • III Learning to Reciprocate
    • 8. Learning with Opponent-Learning Awareness
      • 8.1 Introduction
      • 8.2 Related Work
      • 8.3 Methods
        • 8.3.1 Naive Learner
        • 8.3.2 Learning with Opponent Learning Awareness
        • 8.3.3. Learning via Policy gradient
        • 8.3.4 LOLA with Opponent modeling
        • 8.3.5 Higher-Order LOLA
      • 8.4 Experimental Setup
        • 8.4.1 Iterated Games
        • 8.4.2 Coin Game
        • 8.4.3 Training Details
      • 8.5 Results
        • 8.5.1 Iterated Games
        • 8.5.2 Coin Game
        • 8.5.3 Exploitability of LOLA
      • 8.6 Conclusion & Future Work
    • 9. DiCE: The Infinitely Differentiable Monte Carlo Estimator
      • 9.1 Introduction
      • 9.2 Background
        • 9.2.1 Stochastic Computation Graphs
        • 9.2.2 Surrogate Losses
      • 9.3 Higher Order Gradients
        • 9.3.1 Higher Order Gradient Estimators
        • 9.3.2 Higher Order Surrogate Losses
        • 9.3.3. Simple Failing Example
      • 9.4 Correct Gradient Estimators with DiCE
        • 9.4.1 Implement of DiCE
        • 9.4.2 Casuality
        • 9.4.3 First Order Variance Reduction
        • 9.4.4 Hessian-Vector Product
      • 9.5 Case Studies
        • 9.5.1 Empirical Verification
        • 9.5.2 DiCE For multi-agent RL
      • 9.6 Related Work
      • 9.7 Conclusion & Future Work
  • Reference
    • Reference
  • After
    • 보충
    • 역자 후기
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  1. III Learning to Reciprocate
  2. 9. DiCE: The Infinitely Differentiable Monte Carlo Estimator
  3. 9.3 Higher Order Gradients

9.3.1 Higher Order Gradient Estimators

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Last updated 4 years ago

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score function estimator의 미분을 다시 한번 ∇θL\nabla_\theta \mathcal{L}∇θ​L로 표현해 나타내 보겠습니다.

∇θL=∇θEx[f(x;θ)] \nabla_\theta \mathcal{L} = \nabla_{\theta}\mathbb{E}_x[f(x;\theta)]∇θ​L=∇θ​Ex​[f(x;θ)]

=∇θ∑xp(x;θ)f(x;θ)= \nabla_{\theta}\sum_xp(x;\theta)f(x;\theta)=∇θ​∑x​p(x;θ)f(x;θ)

=∑x∇θ(p(x;θ)f(x;θ))= \sum_x\nabla_{\theta}(p(x;\theta)f(x;\theta))=∑x​∇θ​(p(x;θ)f(x;θ))

=∑x(∇θp(x;θ)f(x;θ)+p(x;θ)∇θf(x;θ))= \sum_x(\nabla_{\theta}p(x;\theta)f(x;\theta)+p(x;\theta)\nabla_{\theta}f(x;\theta))=∑x​(∇θ​p(x;θ)f(x;θ)+p(x;θ)∇θ​f(x;θ))

=∑x(p(x;θ)f(x;θ)∇θlog⁡p(x;θ)+p(x;θ)∇θf(x;θ))= \sum_x(p(x;\theta)f(x;\theta)\nabla_{\theta}\log{p(x;\theta)}+p(x;\theta)\nabla_{\theta}f(x;\theta))=∑x​(p(x;θ)f(x;θ)∇θ​logp(x;θ)+p(x;θ)∇θ​f(x;θ))

=E[f(x;θ)∇θlog⁡p(x;θ)+∇θf(x;θ))]= \mathbb{E}[f(x;\theta)\nabla_{\theta}\log{p(x;\theta)}+\nabla_{\theta}f(x;\theta))]=E[f(x;θ)∇θ​logp(x;θ)+∇θ​f(x;θ))]

=E[g(x;θ)]= \mathbb{E}[g(x;\theta)]=E[g(x;θ)]

g(x;θ)g(x;\theta)g(x;θ)는 Ex[f(x;θ)]\mathbb{E}_x[f(x;\theta)]Ex​[f(x;θ)]의 gradient로 두가지 term으로 나타낼 수있습니다.

  • f(x;θ)∇θlog⁡(p(x;θ))f(x;\theta)\nabla_\theta\log(p(x;\theta))f(x;θ)∇θ​log(p(x;θ))는 SF trick에 의해 만들어집니다.

  • ∇θf(x;θ) \nabla_\theta f(x;\theta)∇θ​f(x;θ)는 가끔 fff가 θ\thetaθ가 아닌xxx로 이루어졌기 때문에 종종 제외되는 경향을 보였습니다. 하지만, ggg 는 xxx와 θ\thetaθ 모두로 이루어졌기 때문에, 제외되지 않습니다.

여기서는 높은 차수의 L\mathcal{L}L을 추정하기 위해 SL의 접근 방식으로 ∇θEx[g(x;θ)]\nabla_\theta\mathbb{E}_x [g(x;\theta)]∇θ​Ex​[g(x;θ)]에 적용하는데, 다음 장에서 이 같은 접근이 실패함을 보입니다.