Any family of entropy-like functions that fully characterizes the second laws of majorization must be countably infinite when the state space is sufficiently large.
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QPLEX Decision Processes embed QPLEX transient approximations into a nonlinear MDP framework and optimize policies via deterministic gradients and natural-gradient methods, demonstrated on a dynamic pricing problem with waiting costs or chance constraints.
Alternating optimization for MI-optimal density control of linear systems coincides with that for generalized Schrödinger bridges.
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Majorization requires infinitely many second laws
Any family of entropy-like functions that fully characterizes the second laws of majorization must be countably infinite when the state space is sufficiently large.