Purpose of trace-decay parameter in eligibility traces In TD/SARSA-lambda, eligibility traces are decayed after each step by multiplying by the discount rate and the trace-decay parameter.



I understand that:


The discount rate is used to reduce the value of future actions relative to a state.
An eligibility trace should decay over time, as it represents how "responsible" a state-action pair is for an obtained reward.


What I don't understand why the trace-decay parameter is required, given that multiplying by the discount rate after each step will cause it to decay over time anyways. What does the trace-decay parameter add to the algorithm?
The beauty of eligibility trace lies in the fact that it generalizes and unifies TD and Monte-Carlo methods.

When lambda=0, only the present state will get updated, because for the other states eligibility trace will be 0 and they will not be updated. This will be a TD update.

For larger values of 0 &lt; lambda &lt; 1, more of the preceding states are changed, but each state which is more temporally distant is changed less due to decaying property of eligibility traces.

When lambda=1, the preceding states with positive eligibility traces will be updated. This allows us to achieve monte-carlo updation method by backward view. Eligibility trace allows us to look backward and perform updated to the preceding states. Here, the decay parameter is used to achieve the discounted reward setting for the monte-carlo updates. This property of eligibility trace will also allow us to use monte-carlo approaches for continuing tasks.