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Minimax Regret for Stochastic Shortest Path
Alon Cohen · Yonathan Efroni · Yishay Mansour · Aviv Rosenberg

Fri Dec 10 08:30 AM -- 10:00 AM (PST) @
We study the Stochastic Shortest Path (SSP) problem in which an agent has to reach a goal state in minimum total expected cost. In the learning formulation of the problem, the agent has no prior knowledge about the costs and dynamics of the model. She repeatedly interacts with the model for $K$ episodes, and has to minimize her regret. In this work we show that the minimax regret for this setting is $\widetilde O(\sqrt{ (B_\star^2 + B_\star) |S| |A| K})$ where $B_\star$ is a bound on the expected cost of the optimal policy from any state, $S$ is the state space, and $A$ is the action space. This matches the $\Omega (\sqrt{ B_\star^2 |S| |A| K})$ lower bound of Rosenberg et al. [2020] for $B_\star \ge 1$, and improves their regret bound by a factor of $\sqrt{|S|}$. For $B_\star < 1$ we prove a matching lower bound of $\Omega (\sqrt{ B_\star |S| |A| K})$. Our algorithm is based on a novel reduction from SSP to finite-horizon MDPs. To that end, we provide an algorithm for the finite-horizon setting whose leading term in the regret depends polynomially on the expected cost of the optimal policy and only logarithmically on the horizon.

Author Information

Alon Cohen (Technion, Google)
Yonathan Efroni (Microsoft Research, New York)
Yishay Mansour (Tel Aviv University & Google)
Aviv Rosenberg (Tel Aviv University)
Aviv Rosenberg

I am an Applied Scientist at Amazon Alexa Shopping, Tel Aviv. Previously, I obtained my PhD from the department of computer science at Tel Aviv University, where I was fortunate to have Prof. Yishay Mansour as my advisor. Prior to that, I received my Bachelor's degree in Mathematics and Computer Science from Tel Aviv University. My primary research interest lies in theoretical and applied machine learning. More specifically, my PhD focused on data-driven sequential decision making such as reinforcement learning, online learning and multi-armed bandit.

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