arXiv subjects

Sang Bin Moon

Publications and source records attributed to Sang Bin Moon.

6 recordsLinked to original sources

arXiv2026

First-Order Softmax Weighted Switching Gradient Method for Distributed Stochastic Minimax Optimization with Stochastic Constraints

This paper addresses the distributed stochastic minimax optimization problem subject to stochastic constraints. We propose a novel first-order Softmax-Weighted Switching Gradient method tailored for federated learning. Under full client participation, our algorithm achieves the standard $\tilde{\mathcal{O}}(ε^{-4})$ oracle complexity to satisfy a unified bound $ε$ for both the optimality gap and feasibility tolerance. We extend our theoretical analysis to the practical partial participation regime by quantifying client sampling noise through a stochastic superiority assumption. Furthermore, by relaxing standard boundedness assumptions on the objective functions, we establish a strictly tighter lower bound for the softmax hyperparameter. We provide a unified error decomposition and establish a sharp $\mathcal{O}(\log\frac{1}δ)$ high-probability convergence guarantee. Ultimately, our framework demonstrates that a single-loop primal-only switching mechanism provides a stable alternative for optimizing worst-case client performance, effectively bypassing the hyperparameter sensitivity and convergence oscillations often encountered in traditional primal-dual or penalty-based approaches. We verify the efficacy of our algorithm via experiment on the Neyman-Pearson (NP) classification, fair classification, and federated safe reinforcement learning tasks.

cs.LG↗

arXiv2026

Unified High-Probability Analysis of Stochastic Variance-Reduced Estimation

Stochastic estimators are fundamental to large-scale optimization, where population quantities must be inferred from noisy oracle observations. Although influential methods such as momentum, SPIDER, STORM, and PAGE have been highly successful, their analyses are largely estimator-specific and expectation-based, obscuring the structural tradeoffs that determine reliability. In this paper, we develop a unified framework for stochastic variance-reduced estimation based on a recursion with three components: memory retention, reset probability, and a correction term for iterate movement. This framework recovers several classical estimators, motivates new second-order variants, and yields a bias-variance decomposition of estimation error. Our main result is a unified high-probability bound proved using a new dimension-free vector-valued Freedman inequality, valid for smooth normed spaces involving random sums of vector martingales. The result applies in both Euclidean and non-Euclidean settings, including the analysis of mirror-descent-based methods in Banach spaces. As applications, we obtain high-probability oracle complexities for unconstrained optimization with mirror descent, establishing the logarithmic dependence on the confidence level. We also derive the first $\tilde{\mathcal{O}}(\varepsilon^{-3})$ oracle-complexity bounds for stochastic optimization with expectation constraints, improving upon the existing $\tilde{\mathcal{O}}(\varepsilon^{-4})$ complexity by leveraging variance-reduced estimation for the first time in this setting.

cs.LG↗

arXiv2026

FedSGM: A Unified Framework for Constraint Aware, Bidirectionally Compressed, Multi-Step Federated Optimization

We introduce FedSGM, a unified framework for federated constrained optimization that addresses four major challenges in federated learning (FL): functional constraints, communication bottlenecks, local updates, and partial client participation. Building on the switching gradient method, FedSGM provides projection-free, primal-only updates, avoiding expensive dual-variable tuning or inner solvers. To handle communication limits, FedSGM incorporates bi-directional error feedback, correcting the bias introduced by compression while explicitly understanding the interaction between compression noise and multi-step local updates. We derive convergence guarantees showing that the averaged iterate achieves the canonical $\boldsymbol{\mathcal{O}}(1/\sqrt{T})$ rate, with additional high-probability bounds that decouple optimization progress from sampling noise due to partial participation. Additionally, we introduce a soft switching version of FedSGM to stabilize updates near the feasibility boundary. To our knowledge, FedSGM is the first framework to unify functional constraints, compression, multiple local updates, and partial client participation, establishing a theoretically grounded foundation for constrained federated learning. Finally, we validate the theoretical guarantees of FedSGM via experimentation on Neyman-Pearson classification and constrained Markov decision process (CMDP) tasks.

cs.LG↗

arXiv2025

Beyond Convexity: Proximal-Perturbed Lagrangian Methods for Efficient Functional Constrained Optimization

Non-convex functional constrained optimization problems have gained substantial attention in machine learning and data science, addressing broad requirements that typically go beyond the often performance-centric objectives. An influential class of algorithms for functional constrained problems is the class of primal-dual methods which has been extensively analyzed for convex problems. Nonetheless, the investigation of their efficacy for non-convex problems is under-explored. This paper develops a primal-dual algorithmic framework for solving such non-convex problems. This framework is built upon a novel form of the Lagrangian function, termed the {\em Proximal-Perturbed Augmented Lagrangian}, which enables the development of simple first-order algorithms that converge to a stationary solution under mild conditions. Notably, we study this framework under both non-smoothness and smoothness of the constraint function and provide three key contributions: (i) a simple algorithm that does not require the continuous adjustment of the penalty parameter; (ii) a non-asymptotic iteration complexity of $\widetilde{\mathcal{O}}(1/ε^2)$; and (iii) extensive experimental results demonstrating the effectiveness of the proposed framework in terms of computational cost and performance, outperforming related approaches that use regularization (penalization) techniques and/or standard Lagrangian relaxation across diverse non-convex problems.

math.OC↗

arXiv2025

Optimization via First-Order Switching Methods: Skew-Symmetric Dynamics and Optimistic Discretization

Large-scale constrained optimization problems are at the core of many tasks in control, signal processing, and machine learning. Notably, problems with functional constraints arise when, beyond a performance{\nobreakdash-}centric goal (e.g., minimizing the empirical loss), one desires to satisfy other requirements such as robustness, fairness, etc. A simple method for such problems, which remarkably achieves optimal rates for non-smooth, convex, strongly convex, and weakly convex functions under first-order oracle, is Switching Gradient Method (SGM): in each iteration depending on a predetermined constraint violation tolerance, use the gradient of objective or the constraint as the update vector. While the performance of SGM is well-understood for non-smooth functions and in fact matches its unconstrained counterpart, i.e., Gradient Descent (GD), less is formally established about its convergence properties under the smoothness of loss and constraint functions. In this work, we aim to fill this gap. First, we show that SGM may not benefit from faster rates under smoothness, in contrast to improved rates for GD under smoothness. By taking a continuous-time limit perspective, we show the issue is fundamental to SGM's dynamics and not an artifact of our analysis. Our continuous-time limit perspective further provides insights towards alleviating SGM's shortcomings. Notably, we show that leveraging the idea of optimism, a well-explored concept in variational inequalities and min-max optimization, could lead to faster methods. This perspective further enables designing a new class of ``soft'' switching methods, for which we further analyze their iteration complexity under mild assumptions.

math.OC↗

arXiv2024

Optimistic Regret Bounds for Online Learning in Adversarial Markov Decision Processes

The Adversarial Markov Decision Process (AMDP) is a learning framework that deals with unknown and varying tasks in decision-making applications like robotics and recommendation systems. A major limitation of the AMDP formalism, however, is pessimistic regret analysis results in the sense that although the cost function can change from one episode to the next, the evolution in many settings is not adversarial. To address this, we introduce and study a new variant of AMDP, which aims to minimize regret while utilizing a set of cost predictors. For this setting, we develop a new policy search method that achieves a sublinear optimistic regret with high probability, that is a regret bound which gracefully degrades with the estimation power of the cost predictors. Establishing such optimistic regret bounds is nontrivial given that (i) as we demonstrate, the existing importance-weighted cost estimators cannot establish optimistic bounds, and (ii) the feedback model of AMDP is different (and more realistic) than the existing optimistic online learning works. Our result, in particular, hinges upon developing a novel optimistically biased cost estimator that leverages cost predictors and enables a high-probability regret analysis without imposing restrictive assumptions. We further discuss practical extensions of the proposed scheme and demonstrate its efficacy numerically.

stat.ML↗