Questions tagged [return]

For questions related to the concept of return in reinforcement learning, which is defined as the future cumulative (discounted) reward or, in simple words, the reward in the long run.

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79 views

Is the expected value we sample in TD-learning action-value Q or state-value V?

Both MC and TD are model-free and they both follow a sample trajectory (in the case of TD, the trajectory is cut-short) to estimate the return (we basically are sampling Q values). Other than that, ...
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1answer
53 views

When learning off-policy with multi-step returns, why do we use the current behaviour policy in importance sampling?

When learning off-policy with multi-step returns, we want to update the value of $Q(s_1, a_1)$ using rewards from the trajectory $\tau = (s_1, a_1, r_1, s_2, a_2, r_2, ..., s_n, a_n, r_n, s_n+1)$. We ...
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2answers
132 views

What is the difference between return and expected return?

At a time step $t$, for a state $S_{t}$, the return is defined as the discounted cumulative reward from that time step $t$. If an agent is following a policy (which in itself is a probability ...
3
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1answer
88 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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2answers
603 views

Why are lambda returns so rarely used in policy gradients?

I've seen monte-carlo reward $G_{t}$ used in REINFORCE and TD($0$) reward $r_t + \gamma Q(s', a')$ used in vanilla actor-critic. I've never seen someone use lambda reward $G^{\lambda}_{t}$ in these ...
2
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1answer
126 views

Why is the expected return in Reinforcement Learning (RL) computed as a sum of cumulative rewards?

Why is the expected return in Reinforcement Learning (RL) computed as a sum of cumulative rewards? Would it not make more sense to compute $\mathbb{E}(R \mid s, a)$ (the expected return for taking ...
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2answers
58 views

How do I calculate the return given the discount factor and a sequence of rewards?

I know that $G_t = R_{t+1} + G_{t+1}$. Suppose $\gamma = 0.9$ and the reward sequence is $R_1 = 2$ followed by an infinite sequence of $7$s. What is the value of $G_0$? As it's infinite, how can we ...
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0answers
48 views

Why does the n-step return being zero result in high variance in off policy n-step TD?

In the paragraph given between eq 7.12 and 7.13 in Sutton & Barto's book: $G_{t:h} = R_{t+1} + G_{t+1:h} , t < h < T$ where $G_{h:h} = V_{h-1}(S_h)$. (Recall that this return is used at ...
4
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2answers
87 views

Is there any difference between reward and return in reinforcement learning?

I am reading Sutton and Barto's book on reinforcement learning. I thought that reward and return were the same things. However, in Section 5.6 of the book, 3rd line, first paragraph, it is written: ...
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2answers
107 views

Why is $G_{t+1}$ is replaced with $v_*(S_{t+1})$ in the Bellman optimality equation?

In equation 3.17 of Sutton and Barto's book: $$q_*(s, a)=\mathbb{E}[R_{t+1} + \gamma v_*(S_{t+1}) \mid S_t = s, A_t = a]$$ $G_{t+1}$ here have been replaced with $v_*(S_{t+1})$, but no reason has ...
3
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1answer
39 views

Shouldn't expected return be calculated for some faraway time in the future $t+n$ instead of current time $t$?

I am learning RL for the first time. It may be naive, but it is a bit odd to grasp this idea that, if the goal of RL is to maximize the expected return, then shouldn't the expected return be ...
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2answers
86 views

Is my understanding of the value function, Q function, policy, reward and return correct?

I'm a beginner in the RL field, and I would like to check that my understanding of certain RL concepts. Value function: How good it is to be in a state S following policy π. ...
1
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1answer
305 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
75 views

Given specific rewards, how can I calculate the returns for each time step?

Let's use Excercise 3.8 from Sutton, Barto - Introduction to RL: Suppose $\gamma = 0.5$ and following sequence of rewards is received $R_1=-1$ , $R_2=2$ , $R_3=6$ , $R_4=3$ , $R_5=2$ , with $T=5$ ...
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?