Dueling Network Architectures for Deep Reinforcement Learning (ICML 2016)

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1 Dueling Network Architectures for Deep Reinforcement Learning (ICML 2016) Yoonho Lee Department of Computer Science and Engineering Pohang University of Science and Technology October 11, 2016

2 Outline Reinforcement Learning Definition of RL Mathematical formulations Algorithms Neural Fitted Q Iteration Deep Q Network Double Deep Q Network Prioritized Experience Replay Dueling Network

3 Outline Reinforcement Learning Definition of RL Mathematical formulations Algorithms Neural Fitted Q Iteration Deep Q Network Double Deep Q Network Prioritized Experience Replay Dueling Network

4 Definition of RL general setting of RL

5 Definition of RL atari setting

6 Outline Reinforcement Learning Definition of RL Mathematical formulations Algorithms Neural Fitted Q Iteration Deep Q Network Double Deep Q Network Prioritized Experience Replay Dueling Network

7 Mathematical formulations objective of RL Definition Return G t is the cumulative discounted reward from time t G t = r t+1 + γr t+2 + γ 2 r t

8 Mathematical formulations objective of RL Definition Return G t is the cumulative discounted reward from time t G t = r t+1 + γr t+2 + γ 2 r t Definition A policy π is a function that selects actions given states π(s) = a The goal of RL is to find π that maximizes G 0

9 Mathematical formulations Q-Value G t = γ k r t+i+1 i=0 Definition The action-value (Q-value) function Q π (s, a) is the expectation of G t under taking action a, and then following policy π afterwards Q π (s, a) = E π [G t S t = s, A t = a, A t+i = π(s t+i ) i N] How good is action a in state s?

10 Mathematical formulations Optimal Q-value Definition The optimal Q-value function Q (s, a) is the maximum Q-value over all policies Q (s, a) = max π Q π(s, a)

11 Mathematical formulations Optimal Q-value Definition The optimal Q-value function Q (s, a) is the maximum Q-value over all policies Q (s, a) = max π Q π(s, a) Theorem There exists a policy π such that Q π (s, a) = Q (s, a) for all s, a Thus, it suffices to find Q

12 Mathematical formulations Q-Learning Bellman Optimality Equation Q (s, a) satisfies the following equation: Q (s, a) = R(s, a) + γ s P(s s, a)max a Q (s, a )

13 Mathematical formulations Q-Learning Bellman Optimality Equation Q (s, a) satisfies the following equation: Q (s, a) = R(s, a) + γ s P(s s, a)max a Q (s, a ) Q-Learning Let a be ɛ-greedy w.r.t. Q, and a be optimal w.r.t. Q. Q converges to Q if we iteratively apply the following update: Q(s, a) α(r(s, a) + γq(s, a )) + (1 α)q(s, a)

14 Mathematical formulations Other approcahes to RL Value-Based RL Estimate Q (s, a) Deep Q Network Policy-Based RL Search directly for optimal policy π DDPG, TRPO... Model-Based RL Use the (learned or given) transition model of environment Tree Search, DYNA...

15 Outline Reinforcement Learning Definition of RL Mathematical formulations Algorithms Neural Fitted Q Iteration Deep Q Network Double Deep Q Network Prioritized Experience Replay Dueling Network

16 Neural Fitted Q Iteration Supervised learning on (s,a,r,s )

17 Neural Fitted Q Iteration input

18 Neural Fitted Q Iteration target equation

19 Neural Fitted Q Iteration Shortcomings Exploration is independent of experience Exploitation does not occur at all Policy evaluation does not occur at all Even in exact(table lookup) case, not guaranteed to converge to Q

20 Outline Reinforcement Learning Definition of RL Mathematical formulations Algorithms Neural Fitted Q Iteration Deep Q Network Double Deep Q Network Prioritized Experience Replay Dueling Network

21 Deep Q Network action policy Choose an ɛ-greedy policy w.r.t. Q

22 Deep Q Network network freezing Get a copy of the network every C steps for stability

23 Deep Q Network

24 Deep Q Network

25 Deep Q Network performance

26 Deep Q Network overoptimism What happens when we overestimate Q?

27 Deep Q Network Problems Overestimation of the Q function at any s spills over to actions that lead to s Double DQN Sampling transitions uniformly from D is inefficient Prioritized Experience Replay

28 Outline Reinforcement Learning Definition of RL Mathematical formulations Algorithms Neural Fitted Q Iteration Deep Q Network Double Deep Q Network Prioritized Experience Replay Dueling Network

29 Double Deep Q Network target We can write the DQN target as: Y DQN t = R t+1 + γq(s t+1, argmaxq(s t+1, a; θt ); θt ) a Double DQN s target is: Y DDQN t = R t+1 + γq(s t+1, argmaxq(s t+1, a; θ t ); θt ) a This has the effect of decoupling action selection and action evaluation

30 Double Deep Q Network performance Much stabler with very little change in code

31 Outline Reinforcement Learning Definition of RL Mathematical formulations Algorithms Neural Fitted Q Iteration Deep Q Network Double Deep Q Network Prioritized Experience Replay Dueling Network

32 Prioritized Experience Replay Update more surprising experiences more frequently

33 Outline Reinforcement Learning Definition of RL Mathematical formulations Algorithms Neural Fitted Q Iteration Deep Q Network Double Deep Q Network Prioritized Experience Replay Dueling Network

34 Dueling Network The scalar approximates V, and the vector approximates A

35 Dueling Network forward pass equation The exact forward pass equation is: Q(s, a; θ, α, β) = V (s; θ, β) + (A(s, a; θ, α) maxa(s, a ; θ, α)) a The following module was found to be more stable without losing much performance: Q(s, a; θ, α, β) = V (s; θ, β) + (A(s, a; θ, α) 1 A A(s, a ; θ, α)) a

36 Dueling Network attention Advantage network only pays attention when current action crucial

37 Dueling Network performance Achieves state of the art in the Atari domain among DQN algorithms

38 Dueling Network Summary Since this is an improvement only in network architecture, methods that improve DQN(e.g. Double DQN) are all applicable here as well Solves problem of V and A typically being of different scale Updates Q values more frequently than a single-stream DQN, where only a single Q value is updated for each observation Implicitly splits the credit assignment problem into a recursive binary problem of now or later

39 Dueling Network Shortcomings Only works for A < Still not able to solve tasks involving long-term planning Better than DQN, but sample complexity is still high ɛ-greedy exploration is essentially random guessing

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