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Improved No-Regret Algorithms for Stochastic Shortest Path with Linear MDP
Liyu Chen · Rahul Jain · Haipeng Luo

Tue Jul 19 08:00 AM -- 08:20 AM (PDT) @ Hall F
We introduce two new no-regret algorithms for the stochastic shortest path (SSP) problem with a linear MDP that significantly improve over the only existing results of (Vial et al., 2021).Our first algorithm is computationally efficient and achieves a regret bound $O(\sqrt{d^3\B^2\T K})$, where $d$ is the dimension of the feature space, $\B$ and $\T$ are upper bounds of the expected costs and hitting time of the optimal policy respectively, and $K$ is the number of episodes.The same algorithm with a slight modification also achieves logarithmic regret of order $O(\frac{d^3\B^4}{\cmin^2\mingap}\ln^5\frac{d\B K}{\cmin})$, where $\mingap$ is the minimum sub-optimality gap and $\cmin$ is the minimum cost over all state-action pairs.Our result is obtained by developing a simpler and improved analysis for the finite-horizon approximation of (Cohen et al., 2021) with a smaller approximation error, which might be of independent interest.On the other hand, using variance-aware confidence sets in a global optimization problem,our second algorithm is computationally inefficient but achieves the first ``horizon-free'' regret bound $O(d^{3.5}\B\sqrt{K})$ with no polynomial dependency on $\T$ or $1/\cmin$,almost matching the $\Omega(d\B\sqrt{K})$ lower bound from (Min et al., 2021).

Author Information

Liyu Chen (USC)
Rahul Jain (USC)
Haipeng Luo (University of Southern California)

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