How to prevent the eligibility trace in SARSA with lambda = 1 from exploding for state-action pairs that are visited a huge number of times?

Question

I was testing SARSA with lambda = 1 with Windy Grid World and if the exploration causes the same state-action pair to be visited many times before reaching the goal, the eligibility trace gets incremented each time without any decay, therefore it explodes and causes everything to overflow. How can this be avoided?

Answer 1

If I've understood correctly your question, the problem is that the trace for a given state gets incremented too much. In this case, a potential solution is to use replacing traces instead of the classic incremental traces.

The idea in replacing traces is to reset the trace to a value (typically 1) each time the state is visited. The following figure illustrates the main difference between both kinds of traces:

You can find more information in the classical Sutton & Barto book Reinforcement Learning: An Introduction, especifically in Section 7.8.