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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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
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1answer
84 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
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1answer
33 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 ...
4
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1answer
103 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 ...
1
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0answers
33 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} \...
1
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1answer
273 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
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1answer
64 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 ...
6
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1answer
1k 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 ...
2
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0answers
61 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 ...