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Chapter 10: On-policy Control with
Approximation
Seungjae Ryan Lee
Episodic 1-step semi-gradient Sarsa
● Approximate action values (instead of state values)
● Use Sarsa to define target
● Converges the same ways as TD(0) with same error bound
Control with Episodic 1-step semi-gradient Sarsa
● Select action and improve policy using an ε-greedy action w.r.t.
Mountain Car Example
● Task: Drive an underpowered car up a steep mountain road
○ Gravity is stronger than car’s engine
○ Must swing back and forth to build enough inertia
● State: position , velocity
● Actions: Forward (+1), Reverse (-1), No-op (0)
● Reward: -1 until the goal is reached
Approximation for Mountain Car
● Tile coding used to select binary features (8 tiles)
Results of Mountain Car
● Plot the cost-to-go function:
● Initial action values set to 0
○ Very optimistic
Results of Mountain Car
Episodic n-step Semi-gradient Sarsa
● Use n-step return as the update target
Episodic n-step Semi-gradient Sarsa in Practice
Episodic n-step Semi-gradient Sarsa Results
● Faster learning
● Better asymptotic performance
Episodic n-step Semi-gradient Sarsa Results
● Best performance for intermediate values of n-step
Average Reward Setting
● Quality of policy defined by the average reward following policy
● Continuing tasks without discounting
Differential Return and Value Functions
Differential Return: differences between rewards and average reward
Differential Value Functions: Expected differential returns
Bellman Equations
● Remove all
● Replace rewards with difference of rewards
Differential semi-gradient Sarsa
● Same update rule with differential TD error
● Original TD error:
● Differential TD error:
Differential semi-gradient Sarsa
Access-Control Queuing Example
● Agent can grant access to 10 servers
○ Agent can accept or reject customers
● Customers arrive at a single queue
○ Customers have 4 different priorities, randomly distributed
○ Pay a reward of 1, 2, 4, or 8 when granted access to a server
● A busy server is freed with some probability
Access-Control Queuing Results
● Tabular solution with differential semi-gradient Sarsa
n-step Semi-gradient Sarsa
● Use n-step return
○
Thank you!
Original content from
● Reinforcement Learning: An Introduction by Sutton and Barto
You can find more content in
● github.com/seungjaeryanlee
● www.endtoend.ai

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Reinforcement Learning 10. On-policy Control with Approximation