2025/11/25 by Panchajanya Sanyal, Srujan Teja Thomdapu, Sanyal, Panchajanya +3 · 1 citation
Computer Science · Decision Sciences · #Stochastic Gradient Optimization Techniques #Risk and Portfolio Optimization #Advanced Bandit Algorithms Research
paper · pdf · doi:10.48550/arxiv.2511.20178
Stochastic convex optimization problems with nonlinear functional constraints are ubiquitous in signal processing applications including constrained least-squares, set-membership adaptive filtering, and trajectory optimization under uncertain fields. The presence of non-linear functional constraints renders the traditional projected stochastic gradient descent and related projection-based methods inefficient, and motivates the use of first-order methods. However, existing first-order methods, including primal and primal--dual algorithms, typically rely on a bounded (sub-)gradient assumption, which may be too restrictive in high-dimensional settings. We propose a stochastic sequential quadratic programming (SSQP) algorithm that works entirely in the primal domain, avoids projecting onto the feasible region, obviates the need for bounded gradients, and achieves state-of-the-art oracle complexity under standard smoothness and convexity assumptions. A faster version, namely SSQP-Skip, is also proposed where the quadratic subproblems can be skipped in most iterations. Finally, we develop an accelerated variance-reduced version of SSQP (VARAS), whose oracle complexity bounds match those for solving unconstrained finite-sum convex optimization problems. The superior performance of the proposed algorithms is demonstrated via numerical experiments on real datasets.