Working with Greedy Algorithms part1(Reinforcement Learning)

Abstract: In the present paper we identify those filtered probability spaces (Ω,F,(Fn),P) that determine already the martingale type of Banach space X. We isolate intrinsic conditions on the filtration (Fn) of purely atomic σ-algebras which determine that the upper ℓp estimates f pLp(Ω,X) Cp( Ef pX n 1 Δnf pLp(Ω,X)),f Lp(Ω,X) imply that the Banach space X is of the martingale type p. Abstract: We provide theoretical bounds on the worst case performance of the greedy algorithm in seeking to maximize a normalized, monotone, but not necessarily submodular objective function under a simple partition matroid constraint. We also provide worst case bounds on the performance of the greedy algorithm in the case that limited information is available at each planning step. We specifically consider limited information as a result of unreliable communications during distributed execution of the greedy algorithm. We utilize notions of curvature for normalized, monotone set functions to develop the bounds provided in this work.