  Stochastic shortest path (SSP) is a well-known problem in planning and
control, in which an agent has to reach a goal state in minimum total expected
cost. In this paper we present the adversarial SSP model that also accounts for
adversarial changes in the costs over time, while the underlying transition
function remains unchanged. Formally, an agent interacts with an SSP
environment for $K$ episodes, the cost function changes arbitrarily between
episodes, and the transitions are unknown to the agent. We develop the first
algorithms for adversarial SSPs and prove high probability regret bounds of
$\widetilde O (\sqrt{K})$ assuming all costs are strictly positive, and
$\widetilde O (K^{3/4})$ in the general case. We are the first to consider this
natural setting of adversarial SSP and obtain sub-linear regret for it.

Machine Learning;Machine Learning