document: Large-scale matrix factorization with distributed stochastic gradient descent We provide a novel algorithm to approximately factor large matrices with millions of rows , millions of columns , and billions of nonzero elements . Our approach rests on stochastic gradient descent ( SGD ) , an iterative stochastic optimization algorithm . We first develop a novel `` stratified '' SGD variant ( SSGD ) that applies to general loss-minimization problems in which the loss function can be expressed as a weighted sum of `` stratum losses . '' We establish sufficient conditions for convergence of SSGD using results from stochastic approximation theory and regenerative process theory . We then specialize SSGD to obtain a new matrix-factorization algorithm , called DSGD , that can be fully distributed and run on web-scale datasets using , e.g. , MapReduce . DSGD can handle a wide variety of matrix factorizations . We describe the practical techniques used to optimize performance in our DSGD implementation . Experiments suggest that DSGD converges significantly faster and has better scalability properties than alternative algorithms .
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