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• W3209907215 abstract "We study the stochastic shortest path (SSP) problem in reinforcement learning with linear function approximation, where the transition kernel is represented as a linear mixture of unknown models. We call this class of SSP problems as linear mixture SSPs. We propose a novel algorithm with Hoeffding-type confidence sets for learning the linear mixture SSP, which can attain an $tilde{mathcal{O}}(d B_{star}^{1.5}sqrt{K/c_{min}})$ regret. Here $K$ is the number of episodes, $d$ is the dimension of the feature mapping in the mixture model, $B_{star}$ bounds the expected cumulative cost of the optimal policy, and $c_{min}>0$ is the lower bound of the cost function. Our algorithm also applies to the case when $c_{min} = 0$, and an $tilde{mathcal{O}}(K^{2/3})$ regret is guaranteed. To the best of our knowledge, this is the first algorithm with a sublinear regret guarantee for learning linear mixture SSP. Moreover, we design a refined Bernstein-type confidence set and propose an improved algorithm, which provably achieves an $tilde{mathcal{O}}(d B_{star}sqrt{K/c_{min}})$ regret. In complement to the regret upper bounds, we also prove a lower bound of $Omega(dB_{star} sqrt{K})$. Hence, our improved algorithm matches the lower bound up to a $1/sqrt{c_{min}}$ factor and poly-logarithmic factors, achieving a near-optimal regret guarantee." @default.
• W3209907215 created "2021-11-08" @default.
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• W3209907215 date "2021-10-25" @default.
• W3209907215 modified "2023-09-23" @default.
• W3209907215 title "Learning Stochastic Shortest Path with Linear Function Approximation" @default.
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• W3209907215 doi "https://doi.org/10.48550/arxiv.2110.12727" @default.
• W3209907215 hasPublicationYear "2021" @default.
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