Decentralized Stochastic Constrained Optimization via Prox-Linearization
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915758754234368 |
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| author | Sharma, Shivangi Dubey Idrees, Basil M. Arora, Lavish Rajawat, Ketan |
| author_facet | Sharma, Shivangi Dubey Idrees, Basil M. Arora, Lavish Rajawat, Ketan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20345 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Decentralized Stochastic Constrained Optimization via Prox-Linearization Sharma, Shivangi Dubey Idrees, Basil M. Arora, Lavish Rajawat, Ketan Optimization and Control Signal Processing 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. |
| title | Decentralized Stochastic Constrained Optimization via Prox-Linearization |
| topic | Optimization and Control Signal Processing |
| url | https://arxiv.org/abs/2601.20345 |