Stochastic shortest path games: theory and algorithms

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RUDDER: Return Decomposition for Delayed Rewards (2018, background): “ck as a strict inequality of variances as long as p(s t;a tjs t 1;a t 1) 6= 0 for some (s t 1;a t 1). The induction goes through as long as !(s t;a t) > !~(s t;a t). In Stephen Patek’s PhD thesis, [89] Lemma 5.1 on page 88-89 and proof thereafter state that if ~!(s;a) = !(s;a) , then the solution”
A Theoretical Analysis of Deep Q-Learning (2019, background): “By the von Neumann’s minimax theorem (Von Neumann and Morgenstern, 1947; Patek, 1997), there exists a minimax function of the game, Q∗ : S × A× B → R, such that Q(s, a, b) = max π min ν Q(s, a, b) = min ν max π Q(s, a, b).”
Approximate Dynamic Programming for Two-Player Zero-Sum Markov Games (2015, methodology): “Zero-sum two-player discounted SG is a subclass of SSPG. Similar algorithms exist to solve those games including PI (Patek, 1997), VI (Shapley, 1953) and MPI (called also Generalized Policy Iteration (GPI) (Patek, 1997) in the context of SSPG).”