Geodesic
$A_\infty$-modules over $A_\infty$-algebras and Hochschild cohomology for modules over algebras
Matematičeskie zametki, Tome 79 (2006) no. 5, pp. 717-728

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For each left graded module $M$ over a graded algebra $A$, a Hochschild cochain complex $S^*(A,M)$ whose homology is responsible for the existence of nontrivial structures of $A_\infty$-modules over $A_\infty$-algebras on the given module is constructed. 
@article{MZM_2006_79_5_a7,
     author = {M. V. Ladoshkin},
     title = {$A_\infty$-modules over $A_\infty$-algebras and {Hochschild} cohomology for modules over algebras},
     journal = {Matemati\v{c}eskie zametki},
     pages = {717--728},
     publisher = {mathdoc},
     volume = {79},
     number = {5},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_79_5_a7/}
}
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M. V. Ladoshkin. $A_\infty$-modules over $A_\infty$-algebras and Hochschild cohomology for modules over algebras. Matematičeskie zametki, Tome 79 (2006) no. 5, pp. 717-728. http://geodesic.mathdoc.fr/item/MZM_2006_79_5_a7/