Symmetries and Model Minimization in Markov Decision Processes

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RUDDER: Return Decomposition for Delayed Rewards (2018, background): “unction ffrom a set Xto a set Yinduces a partition (or equivalence relation) on X, with [x] f = [x0] fif and only if f(x) = f(x0). We now can deﬁne homomorphic MDPs. Deﬁnition A1 (Ravindran and Barto [98, 99]). An MDP homomorphism hfrom an MDP P= (S;A;R;p; ) to an MDP P~ = (S~;A~;R~;p;~ ~) is a a tu”
Symmetry Detection and Exploitation for Function Approximation in Deep RL (2017, background): “The notion of symmetries in MDP can be rigorously treated using the concept of MDP homomorphisms[7].”
Symmetry Learning for Function Approximation in Reinforcement Learning (2017, background): “!R, T : S![0;1] are reward and transition functions respectively. The notion of symmetries in MDP can be rigorously treated using the concept of MDP homomorphisms(see Appendix B for some denitions). [10] dene an MDP homomorphism hfrom M= hS;A;#TAB#;T;Rito M0= hS0;A0;#TAB#0;T0;R0ias a surjection h: !”
SMDP homomorphisms: an algebraic approach to abstraction in semi-Markov decision processes (2003, unknown): “In [Ravindran and Barto, 2001] we extended the minimization framework of Dean and Givan LDean and Givan, 1997; Givan et a/.”