  This paper studies the distributed least-squares optimization problem with
differential privacy requirement of local cost functions, for which two
differentially private distributed solvers are proposed. The first is
established on the distributed gradient tracking algorithm, by appropriately
perturbing the initial values and parameters that contain the privacy-sensitive
data with Gaussian and truncated Laplacian noises, respectively. Rigorous
proofs are established to show the achievable trade-off between the
({\epsilon}, {\delta})-differential privacy and the computation accuracy. The
second solver is established on the combination of the distributed shuffling
mechanism and the average consensus algorithm, which enables each agent to
obtain a noisy version of parameters characterizing the global gradient. As a
result, the least-squares optimization problem can be eventually solved by each
agent locally in such a way that any given ({\epsilon}, {\delta})-differential
privacy requirement can be preserved while the solution may be computed with
the accuracy independent of the network size, which makes the latter more
suitable for large-scale distributed least-squares problems. Numerical
simulations are presented to show the effectiveness of both solvers.
