Local MixVR: Breaking the Communication-Sample Dependence in Distributed Learning

Communication overhead is a crucial bottleneck in scalable distributed learning. While existing methods aim to efficiently utilize data points, such as Local SGD, Minibatch SGD, and their accelerated variants, they still exhibit communication-round complexity that scales with the total number of samples $N$. In this paper, we introduce Local MixVR, a distributed framework that integrates local updates with variance-reduction techniques to mitigate local noise. We show that Local MixVR is the first distributed method to eliminate the dependence of communication complexity on $N$, achieving a complexity that scales only with the number of workers $M$. In common regimes where $M<O\left(N^{1/4}\right)$, Local MixVR outperforms the state-of-the-art Minibatch Accelerated SGD baseline, bridging a long-standing gap in distributed optimization and establishing a new paradigm for communication-efficient training.

Safety in the Face of Adversity: Achieving Zero Constraint Violation in Online Learning with Slowly Changing Constraints

We present the first theoretical guarantees for zero constraint violation in Online Convex Optimization (OCO) across all rounds, addressing dynamic constraint changes. Unlike existing approaches in constrained OCO, which allow for occasional safety breaches, we provide the first approach for maintaining strict safety under the assumption of gradually evolving constraints, namely the constraints change at most by a small amount between consecutive rounds. This is achieved through a primal-dual approach and Online Gradient Ascent in the dual space. We show that employing a dichotomous learning rate enables ensuring both safety, via zero constraint violation, and sublinear regret. Our framework marks a departure from previous work by providing the first provable guarantees for maintaining absolute safety in the face of changing constraints in OCO.