Generalized Lagrange Coded Computing: A Flexible Computation-Communication Tradeoff for Resilient, Secure, and Private Computation
This addresses the need for efficient, secure, and private computation in distributed computing systems, offering a flexible tradeoff for optimizing system efficiency, though it is incremental as it builds on prior Lagrange Coded Computing codes.
The paper tackles the problem of evaluating multivariate polynomials over massive datasets in distributed systems by proposing Generalized Lagrange Coded Computing (GLCC) codes, which provide resiliency, security, and privacy, and demonstrate a speedup of up to 2.5–3.9× over existing methods in distributed training experiments.
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 interpolating 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.