Questions tagged [eligibility-traces]

For questions related to the reinforcement learning technique called "eligibility traces", which combines temporal-difference and Monte Carlo methods.

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How to deal with delay in reinforcement learning, an unclear case

According to the question in How to deal with the time delay in reinforcement learning?, we can tell the delay in the reinforcement learning can be observation delay, action delay and reward delay. I ...
1 vote
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What is 'eligibility' in intuitive terms in TD($\lambda$) learning?

I am watching the lecture from Brown University (in udemy) and I am in the portion of Temporal Difference Learning. In the pseudocode/algorithm of TD(1) (seen in the screenshot below), we initialise ...
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2 votes
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Watkins' Q(λ) with function approximation: why is gradient not considered when updating eligibility traces for the exploitation phase?

I'm implementing the Watkins' Q(λ) algorithm with function approximation (in 2nd edition of Sutton & Barto). I am very confused about updating the eligibility traces because, at the beginning of ...
3 votes
0 answers
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How to implement REINFORCE with eligibility traces?

The pseudocode below is taken from Barto and Sutton's "Reinforcement Learning: an introduction". It shows an actor-critic implementation with eligibility traces. My question is: if I set $\...
2 votes
1 answer
113 views

How to prove the formula of eligibility traces operator in reinforcement learning?

I don't understand how the formula in the red circle is derived. The screenshot is taken from this paper
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3 votes
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Why weighting by lambda that sums to 1 ensures convergence in eligibility trace?

In Sutton and Barto's Book in chapter 12, they state that if weights sum to 1, then an equation's updates have "guaranteed convergence properties". Actually why it ensures convergence? There ...
2 votes
1 answer
124 views

How do I derive the gradient with respect to the parameters of the softmax policy?

The gradient of the softmax eligibility trace is given by the following: \begin{align} \nabla_{\theta} \log(\pi_{\theta}(a|s)) &= \phi(s,a) - \mathbb E[\phi (s, \cdot)]\\ &= \phi(s,a) - \sum_{...
1 vote
1 answer
89 views

Applying Eligibility Traces to Q-Learning algorithm does not improve results (And might not function well)

I am trying to apply Eligibility Traces to a currently working Q-Learning algorithm. The reference code for the Q-Learning algorithm was taken from this great blog ...
5 votes
1 answer
573 views

Why not more TD(𝜆) in actor-critic algorithms?

Is there either an empirical or theoretical reason that actor-critic algorithms with eligibility traces have not been more fully explored? I was hoping to find a paper or implementation or both for ...
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1 vote
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38 views

How is the general return-based off-policy equation derived?

I'm wondering how is the general return-based off-policy equation in Safe and efficient off-policy reinforcement learning derived $$\mathcal{R} Q(x, a):=Q(x, a)+\mathbb{E}_{\mu}\left[\sum_{t \geq 0} \...
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2 votes
1 answer
878 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})...
4 votes
1 answer
85 views

How to apply or extend the $Q(\lambda)$ algorithm to semi-MDPs?

I want to model an SMDP such that time is discretized and the transition time between the two states follows an exponential distribution and there would be no reward between the transition. Can I ...
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6 votes
1 answer
2k views

Can TD($\lambda$) be used with deep reinforcement learning?

TD lambda is a way to interpolate between TD(0) - bootstrapping over a single step, and, TD(max), bootstrapping over the entire episode length, or, Monte Carlo. Reading the link above, I see that an ...
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1 vote
0 answers
81 views

Eligibility trace In Model-based Reinforcement Learning

In model-based reinforcement learning algorithms, the model of the environment is constructed to efficiently use samples, models such as Dyna, and Prioritize Sweeping. Moreover, eligibility trace ...
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2 votes
1 answer
279 views

Does eligibility traces and epsilon-greedy do the same task in different ways?

I understand that, in Reinforcement Learning algorithms, such as Q-learning, to prevent selecting the actions with greatest q-values too fast and allow for exploration, we use eligibility traces. Here ...