Questions tagged [sutton-barto]

For questions related to the book "Reinforcement Learning: An Introduction" (by Andrew Barto and Richard S. Sutton).

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1answer
63 views

Why do we have two similar action selection strategies for UCB1?

In the literature, there are at least two action selection strategies associated with the UCB1's action selection strategy/policy. For example, in the paper Algorithms for the multi-armed bandit ...
2
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1answer
39 views

Why is the fraction of time spent in state $s$, $\mu(s)$, not in the update rule of the parameters?

I am reading "Reinforcement Learning: An Introduction (2nd edition)" authored by Sutton and Barto. In Section 9, On-policy prediction with approximation, it first gives the mean squared ...
2
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1answer
31 views

How do we derive the expression for average reward setting in continuing tasks?

In the average reward setting we have: $$r(\pi)\doteq \lim_{h\rightarrow\infty}\frac{1}{h}\sum_{t=1}^{h}\mathbb{E}[R_{t}|S_0,A_{0:t-1}\sim\pi]$$ $$r(\pi)\doteq \lim_{t\rightarrow\infty}\mathbb{E}[R_{t}...
3
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2answers
75 views

Why do all states appear identical under the function approximation in the Short Corridor task?

This is the Short Corridor problem taken from the Sutton & Barto book. Here it's written: The problem is difficult because all the states appear identical under the function approximation But ...
3
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1answer
89 views

What is wrong with equation 7.3 in Sutton & Barto's book?

Equation 7.3 of Sutton Barto book: $$\text{Equation: } max_s|\mathbb{E}_\pi[G_{t:t+n}|S_t = s] - v_\pi| \le \gamma^nmax_s|V_{t+n-1}(s) - v_\pi(s)| $$ $$\text{where }G_{t:t+n} = R_{t+1} + \gamma R_{t+2}...
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0answers
36 views

How to prove variance infinite of monte carlo ordinary importance sampling estimator

In example 5.5 of Sutton and Barto's book for proving infinite variance of first visit monte carlo ordinary importance sampling estimator, $\mathbb{E}[(\Pi_t\frac{\pi(A_t|S_t)}{b(A_t|S_t)}G_0)^2]$ is ...
1
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1answer
108 views

Value Iteration failing to converge to optimal value function in Sutton-Barto's Gambler problem

In Example 4.3:Gambler's Problem of Sutton and Barto's book whose code is given here. In this code the value function array is initialized as np.zeros(states) where ...
2
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1answer
52 views

Doubt regarding the proof of convergence of $\epsilon$ soft policies without exploring starts

In page 125 of Sutton and Barto (second last paragraph) the proof for equality of $v_{\pi}$ and $v_*$ for $\epsilon$ soft policies is given. But I could not understand the statement explaining the ...
2
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1answer
81 views

What does the figure “Blackjack Value Function…” from Sutton represent?

I came across this graph in David Silver's youtube lecture and Sutton's book on reinforcement learning. Can anyone help me understand the graph? From the graph, for 10000 episodes what i see is ...
2
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2answers
58 views

On-policy state distribution for episodic tasks on Sutton & Barto, page 199

In Sutton & Barto's "Reinforcement Learning: An Introduction", 2nd edition, page 199, they describe the on-policy distribution for episodic tasks in the following box: I don't understand how this ...
6
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3answers
412 views

Counterexamples to the reward hypothesis

On Sutton and Barto's RL book, the reward hypothesis is stated as that all of what we mean by goals and purposes can be well thought of as the maximization of the expected value of the cumulative ...
3
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1answer
55 views

Sutton & Barto's notation $V_{t+n}$ in Chapter 7: $n$-step Bootstrapping

Until Chapter 6 of Sutton & Barto's book on Reinforcement Learning, the authors use $V$ for the current estimate of a state value. Equation (6.1), for example, shows: $$ V(S_t) \leftarrow V(S_t) +...
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0answers
73 views

Doubt regarding improvement of State Value by n-step returns

Excerpt from Sutton and Barto: The expected value of all $n$-step returns is guaranteed to improve in a certain way over the current value function as an approximation to the true value ...
3
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1answer
103 views

Why is an average of all returns used to update the value in the first-visit MC control?

In Sutton & Barto's Reinforcement Learning: An Introduction, in page 83 (101 of the pdf), there is a description of first-visit MC control. In the phase where they update $Q(s, a)$, they do an ...
2
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2answers
82 views

How do we get the true value in the prediction objective in reinforcement learning?

In the book "Reinforcement Learning: An Introduction" (2018) Sutton and Barto define the prediction objective ($\overline{VE}$) as follows (page 199): $$\overline{VE}\doteq\sum_{s\epsilon S} \mu(s)[v_{...
2
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0answers
125 views

Hashed Tile Coding vs Regular Tile Coding

In the book "Reinforcement Learning: An Introduction" (2018) Sutton and Barto explain at page 221 a form of tile coding using hashing, to reduce memory consumption. I have two questions about that: ...
2
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1answer
60 views

Possible inconsistency in the Policy Improvement equation

I came across this formula in Sutton And Barto: RL an Intro (2nd Edition) equation number 4.7 (page number 78). If $\pi$ and $\pi'$ are deterministic policies and $q_\pi(s, \pi'(s)) \geq v_\pi(s)$ ...
6
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1answer
402 views

How is the policy gradient calculated in REINFORCE?

Reading Sutton and Barto, I see the following in describing policy gradients: How is the gradient calculated with respect to an action (taken at time t)? I've read implementations of the algorithm, ...
1
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1answer
306 views

How can the $\lambda$-return be defined recursively?

The $\lambda$-return is defined as $$G_t^\lambda = (1-\lambda)\sum_{n=1}^\infty \lambda^{n-1}G_{t:t+n}$$ where $$G_{t:t+n} = R_{t+1}+\gamma R_{t+2}+\dots +\gamma^{n-1}R_{t+n} + \gamma^n\hat{v}(S_{t+n})...
3
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1answer
158 views

Understanding the n-step off-policy SARSA update

In Sutton & Barto's book (2nd ed) page 149, there is the equation 7.11 I am having a hard time understanding this equation. I would have thought that we should be moving $Q$ towards $G$, where $...
7
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2answers
4k views

What is the difference between reinforcement learning and optimal control?

Coming from a process (optimal) control background, I have begun studying the field of deep reinforcement learning. Sutton & Barto (2015) state that particularly important (to the writing of the ...
3
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2answers
378 views

Difference in continuing and episodic cases in Sutton and Barto - Introduction to RL, exercise 3.5

Excercise 3.5 The equastions in Section 3.1 are for the continuing case and need to be modified (very slightly) to apply to episodic tasks. Show that you know the modifications needed by giving ...
4
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1answer
3k views

Expected SARSA vs SARSA in “RL: An Introduction”

Sutton and Barto state in the 2018-version of "Reinforcement Learning: An Introduction" in the context of Expected SARSA (p. 133) the following sentences: Expected SARSA is more complex ...
1
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1answer
137 views

How do I apply the value iteration algorithm when there are two goal states?

I am working through the famous RL textbook by Sutton & Barto. Currently, I am on the value iteration chapter. To gain better understanding, I coded up a small example, inspired by this article. ...
5
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2answers
231 views

How can the importance sampling ratio be different than zero when the target policy is deterministic?

In the book Reinforcement Learning: An Introduction (2nd edition) Sutton and Barto define at page 104 (p. 126 of the pdf), equation (5.3), the importance sampling ratio, $\rho _{t:T-1}$, as follows: $$...
2
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1answer
75 views

What is the meaning of Model(s, a) in the prioritized sweeping algorithm?

I'm reading the book "Reinforcement Learning: An Introduction" (by Andrew Barto and Richard S. Sutton). The authors provide the pseudocode of the prioritized sweeping algorithm, but I do not know ...
11
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2answers
1k views

How do we prove the n-step return error reduction property?

In section 7.1 (about the n-step bootstrapping) of the book Reinforcement Learning: An Introduction (2nd edition), by Andrew Barto and Richard S. Sutton, the authors write about what they call the "n-...
2
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1answer
120 views

Understanding the notation in the definition of the expected reward

I am new to RL and I am trying to work through the book Reinforcement Learning: An Introduction I (Sutton & Barto, 2018). In chapter 3 on Finite Markov Decision Processes, the authors write the ...
3
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1answer
69 views

Is my interpretation of the return correct?

Sutton and Barto 2018 define the discounted return $G_t$ the following way (p 55): Is my interpretation correct? Or should all "1" be in the same column?
14
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3answers
1k views

Why does the discount rate in the REINFORCE algorithm appear twice?

I was reading the book Reinforcement Learning: An Introduction by Richard S. Sutton and Andrew G. Barto (complete draft, November 5, 2017). On page 271, the pseudo-code for the episodic Monte-Carlo ...
3
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1answer
519 views

When does backward propagation occur in n-step SARSA?

I am trying to understand the algorithm for n-step SARSA from Sutton and Barto (2nd Edition). As I understand it, this algorithm should update n state-action values, but I cannot see where it is ...