  We consider the problem of evaluating arbitrary multivariate polynomials over
a massive dataset containing multiple inputs, on a distributed computing system
with a master node and multiple worker nodes. Generalized Lagrange Coded
Computing (GLCC) codes are proposed to simultaneously provide resiliency
against stragglers who do not return computation results in time, security
against adversarial workers who deliberately modify results for their benefit,
and information-theoretic privacy of the dataset amidst possible collusion of
workers. GLCC codes are constructed by first partitioning the dataset into
multiple groups, then encoding the dataset using carefully designed
interpolation polynomials, and sharing multiple encoded data points to each
worker, such that interference computation results across groups can be
eliminated at the master. Particularly, GLCC codes include the state-of-the-art
Lagrange Coded Computing (LCC) codes as a special case, and exhibit a more
flexible tradeoff between communication and computation overheads in optimizing
system efficiency. Furthermore, we apply GLCC to distributed training of
machine learning models, and demonstrate that GLCC codes achieve a speedup of
up to $2.5\text{--}3.9\times$ over LCC codes in training time, across
experiments for training image classifiers on different datasets, model
architectures, and straggler patterns.
