Implicit Finite-Horizon Approximation and Efficient Optimal Algorithms for Stochastic Shortest Path
This work addresses the challenge of efficient and optimal algorithms for stochastic shortest path problems, which is incremental as it builds on prior methods but introduces novel techniques and improvements.
The paper tackles the problem of regret minimization in the Stochastic Shortest Path (SSP) model by introducing a generic template that achieves minimax optimal regret, leading to two new algorithms: a model-free one that is the first of its kind and minimax optimal under strictly positive costs, and a model-based one that matches the best existing result even with zero-cost pairs, both offering highly sparse updates for computational efficiency and parameter-free operation.
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.