  We study the problem of learning in the stochastic shortest path (SSP)
setting, where an agent seeks to minimize the expected cost accumulated before
reaching a goal state. We design a novel model-based algorithm EB-SSP that
carefully skews the empirical transitions and perturbs the empirical costs with
an exploration bonus to induce an optimistic SSP problem whose associated value
iteration scheme is guaranteed to converge. We prove that EB-SSP achieves the
minimax regret rate $\tilde{O}(B_{\star} \sqrt{S A K})$, where $K$ is the
number of episodes, $S$ is the number of states, $A$ is the number of actions,
and $B_{\star}$ bounds the expected cumulative cost of the optimal policy from
any state, thus closing the gap with the lower bound. Interestingly, EB-SSP
obtains this result while being parameter-free, i.e., it does not require any
prior knowledge of $B_{\star}$, nor of $T_{\star}$, which bounds the expected
time-to-goal of the optimal policy from any state. Furthermore, we illustrate
various cases (e.g., positive costs, or general costs when an order-accurate
estimate of $T_{\star}$ is available) where the regret only contains a
logarithmic dependence on $T_{\star}$, thus yielding the first (nearly)
horizon-free regret bound beyond the finite-horizon MDP setting.
