Geometry-Aware Multi-Objective Optimization: Norm-Constrained Oracles with Entropic Weight Updates
The paper gives a general-norm version of multi-objective gradient descent with provable stationarity rates.
Chayti, Mirrokni, and Jaggi analyze a single-loop method that combines a norm-constrained linear minimization oracle with entropic task-weight updates. In deterministic settings, they prove an \(O(T^{-1/2})\) ergodic stationarity rate for any finite-dimensional norm pair. With stochastic gradients and one persistent blended-gradient momentum buffer, they show an \(O(T^{-1/4})\) rate whose leading term does not explicitly scale with the number of tasks. The work also covers inner-weighting regret and gap control, and compares oracle, weighting, and momentum choices experimentally. ArXiv · AI/CL/LG's note
Chayti, Mirrokni, and Jaggi analyze a single-loop method that combines a norm-constrained linear minimization oracle with entropic task-weight updates. In deterministic settings, they prove an \(O(T^{-1/2})\) ergodic stationarity rate for any finite-dimensional norm pair. With stochastic gradients and one persistent blended-gradient momentum buffer, they show an \(O(T^{-1/4})\) rate whose leading term does not explicitly scale with the number of tasks. The work also covers inner-weighting regret and gap control, and compares oracle, weighting, and momentum choices experimentally. ArXiv · AI/CL/LG's note
score 4