ADIANA Accelerated Distributed Nesterov Gradient Descent with Compression

An accelerated distributed optimization algorithm with unbiased communication compression (ADIANA, together with its single-node counterpart ACGD) for minimizing f(x) = (1/n) sum_{i=1}^n f_i(x) that couples three iterate sequences via x^k = theta_1 * z^k + theta_2 * w^k + (1 - theta_1 - theta_2) * y^k, where w^k is a loopless probabilistic reference point updated via w^{k+1} = y^k with probability p and w^k with probability 1 - p, and each worker i applies two independent omega-unbiased compressors C_i^k(nabla f_i(x^k) - h_i^k) and C_tilde_i^k(nabla f_i(w^k) - h_i^k) to form the global gradient estimator g^k = h^k + (1/n) sum_{i=1}^n C_i^k(nabla f_i(x^k) - h_i^k), update local shifts h_i^{k+1} = h_i^k + alpha * C_tilde_i^k(nabla f_i(w^k) - h_i^k) with alpha = 1 / (omega + 1), and perform Nesterov gradient and mirror steps y^{k+1} = x^k - eta * g^k and z^{k+1} = beta * z^k + (1 - beta) * x^k - (gamma / eta) * (x^k - y^{k+1}), achieving accelerated O((omega + sqrt(L / mu) + sqrt((omega/n + sqrt(omega/n)) * omega * L / mu)) log(1/eps)) communication rounds on L-smooth mu-strongly convex problems.