Implicit Finite-Horizon Approximation and Efficient Optimal Algorithms for Stochastic Shortest Path

• URL: http://arxiv.org/abs/2106.08377v1
• Date: Tue, 15 Jun 2021 19:15:17 GMT
• Title: Implicit Finite-Horizon Approximation and Efficient Optimal Algorithms for Stochastic Shortest Path
• Authors: Liyu Chen, Mehdi Jafarnia-Jahromi, Rahul Jain, Haipeng Luo
• Abstract summary: We introduce a generic template for developing regret algorithms in the Shortest Path (SSP) model. We develop two new algorithms: the first is model-free and minimax optimal under strictly positive costs. Both algorithms admit highly sparse updates, making them computationally more efficient than all existing algorithms.
• Score: 29.289190242826688
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a generic template for developing regret minimization algorithms in the Stochastic Shortest Path (SSP) model, which achieves minimax optimal regret as long as certain properties are ensured. The key of our analysis is a new technique called implicit finite-horizon approximation, which approximates the SSP model by a finite-horizon counterpart only in the analysis without explicit implementation. Using this template, we develop two new algorithms: the first one is model-free (the first in the literature to our knowledge) and minimax optimal under strictly positive costs; the second one is model-based and minimax optimal even with zero-cost state-action pairs, matching the best existing result from [Tarbouriech et al., 2021b]. Importantly, both algorithms admit highly sparse updates, making them computationally more efficient than all existing algorithms. Moreover, both can be made completely parameter-free.

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