arXiv subjects

Zhaoye Pan

Publications and source records attributed to Zhaoye Pan.

3 recordsLinked to original sources

arXiv2026

Distributed Online Convex Optimization with Nonseparable Costs and Constraints

This paper studies distributed online convex optimization with time-varying coupled constraints, motivated by distributed online control in network systems. Most prior work assumes a separability condition: the global objective and coupled constraint functions are sums of local costs and individual constraints. In contrast, we study a group of agents, networked via a communication graph, that collectively select actions to minimize a sequence of nonseparable global cost functions and to satisfy nonseparable long-term constraints based on full-information feedback and intra-agent communication. We propose a distributed online primal-dual belief consensus algorithm, where each agent maintains and updates a local belief of the global collective decisions, which are repeatedly exchanged with neighboring agents. Unlike the previous consensus primal-dual algorithms under separability that ask agents to only communicate their local decisions, our belief-sharing protocol eliminates coupling between the primal consensus disagreement and the dual constraint violation, yielding sublinear regret and cumulative constraint violation (CCV) bounds, both in $O({T}^{1/2})$, where $T$ denotes the time horizon. Such a result breaks the long-standing $O(T^{3/4})$ barrier for CCV and matches the lower bound of online constrained convex optimization, indicating the online learning efficiency at the cost of communication overhead.

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arXiv2025

Federated Learning on Riemannian Manifolds: A Gradient-Free Projection-Based Approach

Federated learning (FL) has emerged as a powerful paradigm for collaborative model training across distributed clients while preserving data privacy. However, existing FL algorithms predominantly focus on unconstrained optimization problems with exact gradient information, limiting its applicability in scenarios where only noisy function evaluations are accessible or where model parameters are constrained. To address these challenges, we propose a novel zeroth-order projection-based algorithm on Riemannian manifolds for FL. By leveraging the projection operator, we introduce a computationally efficient zeroth-order Riemannian gradient estimator. Unlike existing estimators, ours requires only a simple Euclidean random perturbation, eliminating the need to sample random vectors in the tangent space, thus reducing computational cost. Theoretically, we first prove the approximation properties of the estimator and then establish the sublinear convergence of the proposed algorithm, matching the rate of its first-order counterpart. Numerically, we first assess the efficiency of our estimator using kernel principal component analysis. Furthermore, we apply the proposed algorithm to two real-world scenarios: zeroth-order attacks on deep neural networks and low-rank neural network training to validate the theoretical findings.

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arXiv2024

Riemannian Accelerated Zeroth-order Algorithm: Improved Robustness and Lower Query Complexity

Optimization problems with access to only zeroth-order information of the objective function on Riemannian manifolds arise in various applications, spanning from statistical learning to robot learning. While various zeroth-order algorithms have been proposed in Euclidean space, they are not inherently designed to handle the challenging constraints imposed by Riemannian manifolds. The proper adaptation of zeroth-order techniques to Riemannian manifolds remained unknown until the pioneering work of \cite{li2023stochastic}. However, zeroth-order algorithms are widely observed to converge slowly and be unstable in practice. To alleviate these issues, we propose a Riemannian accelerated zeroth-order algorithm with improved robustness. Regarding efficiency, our accelerated algorithm has the function query complexity of $\mathcal{O}(ε^{-7/4}d)$ for finding an $ε$-approximate first-order stationary point. By introducing a small perturbation, it exhibits a function query complexity of $\tilde{\mathcal{O}}(ε^{-7/4}d)$ for seeking a second-order stationary point with a high probability, matching state-of-the-art result in Euclidean space. Moreover, we further establish the almost sure convergence in the asymptotic sense through the Stable Manifold Theorem. Regarding robustness, our algorithm requires larger smoothing parameters in the order of $\tilde{\mathcal{O}}(ε^{7/8}d^{-1/2})$, improving the existing result by a factor of $\tilde{\mathcal{O}}(ε^{3/4})$.

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