  We introduce a generic template for developing regret minimization algorithms
in the Stochastic Shortest Path (SSP) model, which achieves minimax optimal
regret as long as certain properties are ensured. The key of our analysis is a
new technique called implicit finite-horizon approximation, which approximates
the SSP model by a finite-horizon counterpart only in the analysis without
explicit implementation. Using this template, we develop two new algorithms:
the first one is model-free (the first in the literature to our knowledge) and
minimax optimal under strictly positive costs; the second one is model-based
and minimax optimal even with zero-cost state-action pairs, matching the best
existing result from [Tarbouriech et al., 2021b]. Importantly, both algorithms
admit highly sparse updates, making them computationally more efficient than
all existing algorithms. Moreover, both can be made completely parameter-free.
