Near-optimal regret bounds for stochastic shortest path

Alon Cohen*, Haim Kaplan, Yishay Mansour, Aviv Rosenberg*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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 the learning formulation of the problem, the agent is unaware of the environment dynamics (i.e., the transition function) and has to repeatedly play for a given number of episodes, while learning the problem's optimal solution. Unlike other well-studied models in reinforcement learning (RL), the length of an episode is not predetermined (or bounded) and is influenced by the agent's actions. Recently, Tarbouriech et al. (2020) studied this problem in the context of regret minimization, and provided an algorithm whose regret bound is inversely proportional to the square root of the minimum instantaneous cost. In this work we remove this dependence on the minimum cost-we give an algorithm that guarantees a regret bound of Õ(B∗|S| √|A|K), where B∗ is an upper bound on the expected cost of the optimal policy, S is the set of states, A is the set of actions and K is the number of episodes. We additionally show that any learning algorithm must have at least Ω(B∗ √ |S||A|K) regret in the worst case.

Original languageEnglish
Title of host publication37th International Conference on Machine Learning, ICML 2020
EditorsHal Daume, Aarti Singh
PublisherInternational Machine Learning Society (IMLS)
Number of pages10
ISBN (Electronic)9781713821120
StatePublished - 2020
Event37th International Conference on Machine Learning, ICML 2020 - Virtual, Online
Duration: 13 Jul 202018 Jul 2020

Publication series

Name37th International Conference on Machine Learning, ICML 2020


Conference37th International Conference on Machine Learning, ICML 2020
CityVirtual, Online


FundersFunder number
Israel Science Foundation1595/19


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