arXiv subjects

Shivangi Dubey Sharma

Publications and source records attributed to Shivangi Dubey Sharma.

3 recordsLinked to original sources

arXiv2026

Decentralized Stochastic Constrained Optimization via Prox-Linearization

This paper studies consensus-based decentralized stochastic optimization for minimizing possibly non-convex expected objectives with convex non-smooth regularizers and nonlinear functional inequality constraints. We reformulate the constrained problem using the exact-penalty model and develop two algorithms that require only local stochastic gradients and first-order constraint information. The first method, Decentralized Stochastic Momentum-based Prox-Linear Algorithm (D-SMPL), combines constraint linearization with a prox-linear step, resulting in a linearly constrained quadratic subproblem per iteration. Building on this approach, we propose a successive convex approximation (SCA) variant, Decentralized SCA Momentum-based Prox-Linear (D-SCAMPL), which handles additional objective structure through strongly convex surrogate subproblems while still allowing infeasible initialization. Both methods incorporate recursive momentum-based gradient estimators and a consensus mechanism requiring only two communication rounds per iteration. Under standard smoothness and regularity assumptions, both algorithms achieve an oracle complexity of $\mathcal{O}(ε^{-3/2})$, matching the optimal rate known for unconstrained centralized stochastic non-convex optimization. Numerical experiments on energy-optimal ocean trajectory planning corroborate the theory and demonstrate improved performance over existing decentralized baselines.

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arXiv2024

Analysis of Decentralized Stochastic Successive Convex Approximation for composite non-convex problems

This work considers the decentralized successive convex approximation (SCA) method for minimizing stochastic non-convex objectives subject to convex constraints, along with possibly non-smooth convex regularizers. Although SCA has been widely applied in decentralized settings, its stochastic first order (SFO) complexity is unknown, and it is thought to be slower than the centralized momentum-enhanced SCA variants. In this work, we advance the state-of-the-art for SCA methods by proposing an accelerated variant, namely the \textbf{D}ecentralized \textbf{M}omentum-based \textbf{S}tochastic \textbf{SCA} (\textbf{D-MSSCA}) and analyze its SFO complexity. The proposed algorithm entails creating a stochastic surrogate of the objective at every iteration, which is minimized at each node separately. Remarkably, the D-MSSCA achieves an SFO complexity of $\mathcal{O}(ε^{-3/2})$ to reach an $ε$-stationary point, which is at par with the SFO complexity lower bound for unconstrained stochastic non-convex optimization in centralized setting.

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arXiv2024

Optimized Gradient Tracking for Decentralized Online Learning

This work considers the problem of decentralized online learning, where the goal is to track the optimum of the sum of time-varying functions, distributed across several nodes in a network. The local availability of the functions and their gradients necessitates coordination and consensus among the nodes. We put forth the Generalized Gradient Tracking (GGT) framework that unifies a number of existing approaches, including the state-of-the-art ones. The performance of the proposed GGT algorithm is theoretically analyzed using a novel semidefinite programming-based analysis that yields the desired regret bounds under very general conditions and without requiring the gradient boundedness assumption. The results are applicable to the special cases of GGT, which include various state-of-the-art algorithms as well as new dynamic versions of various classical decentralized algorithms. To further minimize the regret, we consider a condensed version of GGT with only four free parameters. A procedure for offline tuning of these parameters using only the problem parameters is also detailed. The resulting optimized GGT (oGGT) algorithm not only achieves improved dynamic regret bounds, but also outperforms all state-of-the-art algorithms on both synthetic and real-world datasets.

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