Stochastic Shortest Path with Adversarially Changing Costs

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 consider adversarial SSPs that also account for adversarial changes in the costs over time, while the dynamics (i.e., transition function) remains unchanged. Formally, an agent interacts with an SSP environment for $K$ episodes, the cost function changes arbitrarily between episodes, and the fixed dynamics are unknown to the agent. We give high probability regret bounds of $\widetilde O (\sqrt{K})$ assuming all costs are strictly positive, and $\widetilde O (K^{3/4})$ for the general case. To the best of our knowledge, we are the first to consider this natural setting of adversarial SSP and obtain sub-linear regret for it.