Partial-monotone adaptive submodular maximization

Many AI/Machine learning problems require adaptively selecting a sequence of items, each selected item might provide some feedback that is valuable for making better selections in the future, with goal maximizing an adaptive submodular function. Most existing studies this field focus on either monotone case or non-monotone case. Specifically, if utility function and submodular, Golovin Krause (J Artif Intell Res 42:427–486, 2011) developed $$(1-1/e)$$ approximation solution subject to cardinality constraint. For cardinality-constrained case, Tang (Theor Comput Sci 850:249–261, 2021) showed random greedy policy attains ratio 1/e. In work, we generalize above mentioned results by studying partial-monotone maximization problem. To end, introduce notation monotonicity $$m\in [0,1]$$ measure degree Our main result show constraints, has m it then $$m(1-1/e)+(1-m)(1/e)$$ . Notably recovers aforementioned 1/e ratios when $$m = 1$$ 0$$ , respectively. We further extend our consider knapsack constraint develop $$(m+1)/10$$ general One important implication even function, still can attain close “close” This leads improved performance bounds many machine applications whose functions are almost monotone.