Data selection improves computational efficiency by choosing informative subsets of training samples. However, existing methods ignore the compute budget, treating data selection and importance evaluation independently of compute budget constraints. Yet empirical studies show no algorithm can consistently outperform others (or even random selection) across varying budgets. We therefore argue that compute budget must be integral to data-selection strategies, since different budgets impose distinct requirements on data quantity, quality, and distribution for effective training. To this end, we propose a novel Computational budget-Aware Data Selection (CADS) method and naturally formulate it into a bilevel optimization framework, where the inner loop trains the model within the constraints of the computational budget on some selected subset of training data, while the outer loop optimizes data selection based on model evaluation. Our technical contributions lie in addressing two main challenges in solving this bilevel optimization problem: the expensive Hessian matrix estimation for outer-loop gradients and the computational burden of achieving inner-loop optimality during iterations. To solve the first issue, we propose a probabilistic reparameterization strategy and compute the gradient using a Hessian-free policy gradient estimator. To address the second challenge, we transform the inner optimization problem into a penalty term in the outer objective, further discovering that we only need to estimate the minimum of a one-dimensional loss to calculate the gradient, significantly improving efficiency. Extensive experiments show that our method achieves performance gains of up to 14.42% over baselines in vision and language benchmarks.

Abstract-- We derive closed-form extensions of Riccati's recursions (both sequential [4] and parallel [7]) for solving dual-regularized LQR problems. We show how these methods can be used to solve general constrained, non-convex, discrete-time optimal control problems via a regularized interior point method, while guaranteeing that each primal step is a descent direction of an Augmented Barrier-Lagrangian merit function. We provide MIT -licensed implementations of our methods in C++ and JAX. Numerical optimal control, both real-time and offline, has found numerous application domains, ranging from trajectory optimization for robotics (e.g. for autonomous cars, unmanned aerial vehicles, legged robots) and airspace (e.g. Continuous-time optimal control problems, whose optimization variables are functions (thus infinite-dimensional) are typically converted into finite-dimensional optimization problems by either shooting (i.e.

Laser vision sensors (LVS) are critical perception modules for industrial robots, facilitating real-time acquisition of workpiece geometric data in welding applications. However, the camera communication delay will lead to a temporal desynchronization between captured images and the robot motions. Additionally, hand-eye extrinsic parameters may vary during prolonged measurement. To address these issues, we introduce a measurement model of LVS considering the effect of the camera's time-offset and propose a teaching-free spatiotemporal calibration method utilizing line constraints. This method involves a robot equipped with an LVS repeatedly scanning straight-line fillet welds using S-shaped trajectories. Regardless of the robot's orientation changes, all measured welding positions are constrained to a straight-line, represented by Plucker coordinates. Moreover, a nonlinear optimization model based on straight-line constraints is established. Subsequently, the Levenberg-Marquardt algorithm (LMA) is employed to optimize parameters, including time-offset, hand-eye extrinsic parameters, and straight-line parameters. The feasibility and accuracy of the proposed approach are quantitatively validated through experiments on curved weld scanning. We open-sourced the code, dataset, and simulation report at https://anonymous.4open.science/r/LVS_ST_CALIB-015F/README.md.

We introduce Pareto-NRPA, a new Monte-Carlo algorithm designed for multi-objective optimization problems over discrete search spaces. Extending the Nested Rollout Policy Adaptation (NRPA) algorithm originally formulated for single-objective problems, Pareto-NRPA generalizes the nested search and policy update mechanism to multi-objective optimization. The algorithm uses a set of policies to concurrently explore different regions of the solution space and maintains non-dominated fronts at each level of search. Policy adaptation is performed with respect to the diversity and isolation of sequences within the Pareto front. We benchmark Pareto-NRPA on two classes of problems: a novel bi-objective variant of the Traveling Salesman Problem with Time Windows problem (MO-TSPTW), and a neural architecture search task on well-known benchmarks. Results demonstrate that Pareto-NRPA achieves competitive performance against state-of-the-art multi-objective algorithms, both in terms of convergence and diversity of solutions. Particularly, Pareto-NRPA strongly outperforms state-of-the-art evolutionary multi-objective algorithms on constrained search spaces. To our knowledge, this work constitutes the first adaptation of NRPA to the multi-objective setting.

Distributionally Robust Optimization (DRO) provides a framework for decision-making under distributional uncertainty, yet its effectiveness can be compromised by outliers in the training data. This paper introduces a principled approach to simultaneously address both challenges. We focus on optimizing Wasserstein-1 DRO objectives for generalized linear models with convex Lipschitz loss functions, where an $ε$-fraction of the training data is adversarially corrupted. Our primary contribution lies in a novel modeling framework that integrates robustness against training data contamination with robustness against distributional shifts, alongside an efficient algorithm inspired by robust statistics to solve the resulting optimization problem. We prove that our method achieves an estimation error of $O(\sqrtε)$ for the true DRO objective value using only the contaminated data under the bounded covariance assumption. This work establishes the first rigorous guarantees, supported by efficient computation, for learning under the dual challenges of data contamination and distributional shifts.

Communication between agents often constitutes a major computational bottleneck in distributed learning. One of the most common mitigation strategies is to compress the information exchanged, thereby reducing communication overhead. To counteract the degradation in convergence associated with compressed communication, error feedback schemes -- most notably $\mathrm{EF}$ and $\mathrm{EF}^{21}$ -- were introduced. In this work, we provide a tight analysis of both of these methods. Specifically, we find the Lyapunov function that yields the best possible convergence rate for each method -- with matching lower bounds. This principled approach yields sharp performance guarantees and enables a rigorous, apples-to-apples comparison between $\mathrm{EF}$, $\mathrm{EF}^{21}$, and compressed gradient descent. Our analysis is carried out in the simplified single-agent setting, which allows for clean theoretical insights and fair comparison of the underlying mechanisms.

The proliferation of saddle points, rather than poor local minima, is increasingly understood to be a primary obstacle in large-scale non-convex optimization for machine learning. Variable elimination algorithms, like Variable Projection (VarPro), have long been observed to exhibit superior convergence and robustness in practice, yet a principled understanding of why they so effectively navigate these complex energy landscapes has remained elusive. In this work, we provide a rigorous geometric explanation by comparing the optimization landscapes of the original and reduced formulations. Through a rigorous analysis based on Hessian inertia and the Schur complement, we prove that variable elimination fundamentally reshapes the critical point structure of the objective function, revealing that local maxima in the reduced landscape are created from, and correspond directly to, saddle points in the original formulation. Our findings are illustrated on the canonical problem of non-convex matrix factorization, visualized directly on two-parameter neural networks, and finally validated in training deep Residual Networks, where our approach yields dramatic improvements in stability and convergence to superior minima. This work goes beyond explaining an existing method; it establishes landscape simplification via saddle point transformation as a powerful principle that can guide the design of a new generation of more robust and efficient optimization algorithms.

In this paper, we propose a novel fairness framework grounded in the concept of happiness, a measure of the utility each group gains from decision outcomes. By capturing fairness through this intuitive lens, we not only offer a more human-centered approach, but also one that is mathematically rigorous: In order to compute the optimal, fair post-processing strategy, only a linear program needs to be solved. This makes our method both efficient and scalable with existing optimization tools. Furthermore, it unifies and extends several well-known fairness definitions, and our empirical results highlight its practical strengths across diverse scenarios.

We propose SLIM (Stochastic Learning and Inference in overidentified Models), a scalable stochastic approximation framework for nonlinear GMM. SLIM forms iterative updates from independent mini-batches of moments and their derivatives, producing unbiased directions that ensure almost-sure convergence. It requires neither a consistent initial estimator nor global convexity and accommodates both fixed-sample and random-sampling asymptotics. We further develop an optional second-order refinement achieving full-sample GMM efficiency and inference procedures based on random scaling and plug-in methods, including plug-in, debiased plug-in, and online versions of the Sargan--Hansen $J$-test tailored to stochastic learning. In Monte Carlo experiments based on a nonlinear demand system with 576 moment conditions, 380 parameters, and $n = 10^5$, SLIM solves the model in under 1.4 hours, whereas full-sample GMM in Stata on a powerful laptop converges only after 18 hours. The debiased plug-in $J$-test delivers satisfactory finite-sample inference, and SLIM scales smoothly to $n = 10^6$.

Finding lower and better-generalizing minima is crucial for deep learning. However, most existing optimizers stop searching the parameter space once they reach a local minimum. Given the complex geometric properties of the loss landscape, it is difficult to guarantee that such a point is the lowest or provides the best generalization. To address this, we propose an adaptor "E" for gradient-based optimizers. The adapted optimizer tends to continue exploring along landscape valleys (areas with low and nearly identical losses) in order to search for potentially better local minima even after reaching a local minimum. This approach increases the likelihood of finding a lower and flatter local minimum, which is often associated with better generalization. We also provide a proof of convergence for the adapted optimizers in both convex and non-convex scenarios for completeness. Finally, we demonstrate their effectiveness in an important but notoriously difficult training scenario, large-batch training, where Lamb is the benchmark optimizer. Our testing results show that the adapted Lamb, ALTO, increases the test accuracy (generalization) of the current state-of-the-art optimizer by an average of 2.5% across a variety of large-batch training tasks. This work potentially opens a new research direction in the design of optimization algorithms.