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Replacing Eligibility Trace

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In a Replacing Eligibility Trace, each time the state is revisited, the trace is reset to $1$ regardless of the presence of a prior trace.. For the memory vector eₜ ∈ℝᵇ ≥0:

𝐞₀ = 0

eₜ = γλeₜ₋₁(s) if s ≠sₜ

eₜ = 1 if s = sₜ

They can be seen as crude approximation to dutch traces, which have largely superseded them as they perform better than replacing traces and have a clearer theoretical basis. Accumulating traces remain of interest for nonlinear function approximations where dutch traces are not available.

Source: Sutton and Barto, Reinforcement Learning, 2nd Edition

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Eligibility Traces

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