adaptive algorithm design

This work addresses the weak theoretical convergence guarantees of adaptive optimization algorithms—particularly those employing moving-average momentum estimators—in nonconvex optimization. Methodologically, it establishes a unified convergence analysis framework: (i) it provides the first rigorous proof that monotonic increase of the first-order momentum parameter ensures convergence; (ii) it uncovers a phased co-adaptation mechanism between momentum and step size that enables acceleration; and (iii) it extends the analysis to composite, minimax, and bilevel optimization settings. Theoretical contributions include: (i) nonconvex convergence guarantees applicable to broad classes of adaptive methods (e.g., Adam-type); and (ii) novel, efficient minimax and bilevel optimization algorithms that avoid large batch sizes or double-loop schemes. Empirical results confirm improved convergence rates and generalization performance, corroborating the theoretical insights.

This paper addresses the fundamental disconnect between online learning and adaptive control—spanning analytical paradigms, performance metrics (e.g., regret bounds vs. stability/convergence), and modeling assumptions. Methodologically, it unifies both fields under a gradient descent and streaming regression framework, enabling the first systematic theoretical comparison between regret minimization and model-reference adaptive control (MRAC). The key contributions are threefold: (i) a precise characterization of intrinsic differences between the two paradigms in terms of objective functions, system assumptions, and applicability; (ii) rigorous sufficient conditions under which regret-optimal policies guarantee stable convergence in dynamic systems; and (iii) a novel controller design framework that jointly ensures asymptotic convergence and sublinear cumulative error, thereby laying a rigorous foundation for algorithms that unify learning efficiency with control reliability.

This paper addresses the adaptive linear quadratic regulation (LQR) control problem for unknown linear systems. We propose the first fully adaptive algorithm that requires no prior knowledge of system parameters, no warm-up phase, and no norm-based assumptions on the solution to the discrete algebraic Riccati equation (DARE). The algorithm dynamically balances exploration and exploitation while adaptively adjusting policy update frequency. Our method is built upon a semidefinite programming (SDP) framework, integrating self-tuning regularization and adaptive input perturbation. We establish, for the first time, high-probability system-theoretic bounds on state trajectories and achieve the optimal $mathcal{O}(sqrt{T})$ regret bound, with explicit dependence on system dimension and the DARE solution. The algorithm is computationally efficient, significantly reducing both initialization complexity and empirical regret.

This work proposes a two-level deep reinforcement learning framework for large-scale Traveling Salesman Problems (TSP), wherein a recurrent Proximal Policy Optimization (PPO) agent dynamically controls both numerical and structural parameters of a genetic algorithm, enabling their decoupled analysis. The study provides the first empirical evidence that dynamic adjustment of structural parameters is crucial for avoiding premature convergence and escaping local optima, whereas numerical parameters serve only a fine-tuning role. Evaluated on large-scale TSP instances such as rl5915, the proposed method significantly outperforms static baselines, reducing the optimality gap by approximately 45%. These results offer a novel direction for automated algorithm design through adaptive parameter control in evolutionary computation.

This work addresses the challenge in performative prediction where model deployment induces distributional shifts that complicate optimization. Existing approaches often rely on strong assumptions about the loss function and data distribution, limiting their applicability. To overcome this, the paper proposes a gradient-based adaptive optimization algorithm that explicitly estimates deployment-induced distribution shifts via finite differences, thereby accommodating a broader class of losses and distributions without stringent assumptions. The method supports high-dimensional optimization and incorporates a sample-efficient approximation strategy to reduce data requirements. Theoretical analysis establishes convergence guarantees for the proposed algorithm. Empirical results demonstrate that it converges faster and more stably than existing methods, exhibiting superior robustness and practicality across diverse experimental settings.

This work addresses the convergence challenges of asynchronous adaptive first-order methods in non-convex stochastic optimization by proposing a class of parallel asynchronous adaptive algorithms that support momentum and inexact normalization, encompassing asynchronous variants of several mainstream optimizers. Under a fully stochastic setting, the paper establishes—for the first time—an $O(1/\sqrt{t})$ convergence rate (up to logarithmic factors) for such methods on non-convex objectives. The theoretical analysis rigorously integrates techniques from asynchronous parallel computation, adaptive learning rates, and stochastic optimization to prove convergence guarantees. Empirical evaluations further demonstrate the algorithm’s efficiency and practicality in heterogeneous large-scale machine learning systems.

This work addresses the lack of theoretical convergence guarantees in existing adaptive learning rate optimizers, such as Adam, which can compromise training stability. The authors propose C-Adam, a novel optimizer that integrates the geometric properties of line-of-sight methods into an adaptive optimization framework. To the best of our knowledge, this is the first approach to formally incorporate line-of-sight principles into adaptive optimization, and the paper provides a rigorous proof of its convergence. By synergistically combining adaptive learning rates with the directional stability of line-of-sight updates, C-Adam maintains computational efficiency while ensuring theoretical convergence. Empirical evaluations across multiple real-world scenarios demonstrate that C-Adam achieves consistently stable and superior performance, effectively bridging the gap between theoretical soundness and practical efficacy.

This study addresses the challenge of efficiently guiding treatment allocation in a main experiment using a small-scale pilot, avoiding efficiency losses from noise or excessive conservatism. The authors propose the Conditional Minimax Regret (CMR) rule, which optimizes assignment probabilities in a two-stage design by leveraging confidence sets constructed from limited pilot data, thereby balancing robustness and adaptivity. The CMR rule preserves, with high probability, the worst-case guarantees of balanced designs while asymptotically converging to the Neyman allocation as the pilot sample size grows, achieving the minimax regret rate. The approach naturally extends to multi-arm and stratified settings. Simulations demonstrate that CMR substantially outperforms feasible Neyman allocation when the pilot is small—avoiding its severe precision loss—while recovering most of its efficiency gains in large samples.

This work addresses the computational challenges of linear multiparametric optimization, which is NP-hard and may exhibit an exponentially large set of optimal solutions. Existing approximation algorithms are limited to nonnegative parameters and parameter spaces confined to the positive orthant, leaving problems with negative parameters largely intractable. To overcome this limitation, the paper proposes a novel adaptive algorithm that integrates techniques from parametric and multiobjective optimization, enabling the first polynomial-time approximation scheme for general linear multiparametric problems with arbitrary (including negative) parameters. By introducing structural analysis of parameter sets and an adaptive strategy, the method provides theoretical approximation guarantees and demonstrates that nonnegativity of objective values alone is insufficient to ensure approximability, thereby significantly broadening the class of solvable parametric optimization problems.

This work addresses the limited adaptivity of stochastic gradient methods in the absence of gradient history by introducing a novel parallel optimization framework. The proposed approach concurrently executes multiple instances of static gradient descent with varying iteration counts and allocates computational resources according to a geometric sequence, thereby automatically identifying effective hyperparameters without manual tuning. By uniquely integrating parallel computation with static gradient methods, the algorithm achieves adaptive optimization while maintaining theoretical convergence guarantees. Experimental results demonstrate that this method significantly enhances adaptability to unknown problem structures compared to existing approaches.