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Implicit Finite-Horizon Approximation for Stochastic Shortest Path
Liyu Chen · Mehdi Jafarnia · Rahul Jain · Haipeng Luo

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in Workshop on Reinforcement Learning Theory »

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.

Author Information

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

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