Wavefront reconstruction is a critical component in various optical systems, including adaptive optics, interferometry, and phase contrast imaging. Traditional reconstruction methods often employ either the Cartesian (pixel) basis or the Zernike polynomial basis. While the Cartesian basis is adept at capturing high-frequency features, it is susceptible to overfitting and inefficiencies due to the high number of degrees of freedom. The Zernike basis efficiently represents common optical aberrations but struggles with complex or non-standard wavefronts such as optical vortices, Bessel beams, or wavefronts with sharp discontinuities. This paper introduces a novel approach to wavefront reconstruction using an over-complete phase dictionary combined with sparse representation techniques. By constructing a dictionary that includes a diverse set of basis functions - ranging from Zernike polynomials to specialized functions representing optical vortices and other complex modes - we enable a more flexible and efficient representation of complex wavefronts. Furthermore, a trainable affine transform is implemented to account for misalignment. Utilizing principles from compressed sensing and sparse coding, we enforce sparsity in the coefficient space to avoid overfitting and enhance robustness to noise.

Reinforcement Learning (RL) agents are able to solve a wide variety of tasks but are prone to producing unsafe behaviors. Constrained Markov Decision Processes (CMDPs) provide a popular framework for incorporating safety constraints. However, common solution methods often compromise reward maximization by being overly conservative or allow unsafe behavior during training. We propose Constrained Trust Region Policy Optimization (C-TRPO), a novel approach that modifies the geometry of the policy space based on the safety constraints and yields trust regions composed exclusively of safe policies, ensuring constraint satisfaction throughout training. We theoretically study the convergence and update properties of C-TRPO and highlight connections to TRPO, Natural Policy Gradient (NPG), and Constrained Policy Optimization (CPO). Finally, we demonstrate experimentally that C-TRPO significantly reduces constraint violations while achieving competitive reward maximization compared to state-of-theart CMDP algorithms. Reinforcement Learning (RL) has emerged as a highly successful paradigm in machine learning for solving sequential decision and control problems, with policy gradient (PG) algorithms as a popular approach (Williams, 1992; Sutton et al., 1999; Konda & Tsitsiklis, 1999).

We introduce a framework to accelerate the convergence of gradient-based methods with online learning. The framework learns to scale the gradient at each iteration through an online learning algorithm and provably accelerates gradient-based methods asymptotically. In contrast with previous literature, where convergence is established based on worst-case analysis, our framework provides a strong convergence guarantee with respect to the optimal scaling matrix for the iteration trajectory. For smooth strongly convex optimization, our results provide an $O(\kappa^\star \log(1/\varepsilon)$) complexity result, where $\kappa^\star$ is the condition number achievable by the optimal preconditioner, improving on the previous $O(\sqrt{n}\kappa^\star \log(1/\varepsilon))$ result. In particular, a variant of our method achieves superlinear convergence on convex quadratics. For smooth convex optimization, we show for the first time that the widely-used hypergradient descent heuristic improves on the convergence of gradient descent.

We study episodic linear mixture MDPs with the unknown transition and adversarial rewards under full-information feedback, employing dynamic regret as the performance measure. We start with in-depth analyses of the strengths and limitations of the two most popular methods: occupancy-measure-based and policy-based methods. We observe that while the occupancy-measure-based method is effective in addressing non-stationary environments, it encounters difficulties with the unknown transition. In contrast, the policy-based method can deal with the unknown transition effectively but faces challenges in handling non-stationary environments. Building on this, we propose a novel algorithm that combines the benefits of both methods. Specifically, it employs (i) an occupancy-measure-based global optimization with a two-layer structure to handle non-stationary environments; and (ii) a policy-based variance-aware value-targeted regression to tackle the unknown transition. We bridge these two parts by a novel conversion. Our algorithm enjoys an $\widetilde{\mathcal{O}}(d \sqrt{H^3 K} + \sqrt{HK(H + \bar{P}_K)})$ dynamic regret, where $d$ is the feature dimension, $H$ is the episode length, $K$ is the number of episodes, $\bar{P}_K$ is the non-stationarity measure. We show it is minimax optimal up to logarithmic factors by establishing a matching lower bound. To the best of our knowledge, this is the first work that achieves near-optimal dynamic regret for adversarial linear mixture MDPs with the unknown transition without prior knowledge of the non-stationarity measure.

Sequentially solving similar optimization problems under strict runtime constraints is essential for many applications, such as robot control, autonomous driving, and portfolio management. The performance of local optimization methods in these settings is sensitive to the initial solution: poor initialization can lead to slow convergence or suboptimal solutions. To address this challenge, we propose learning to predict \emph{multiple} diverse initial solutions given parameters that define the problem instance. We introduce two strategies for utilizing multiple initial solutions: (i) a single-optimizer approach, where the most promising initial solution is chosen using a selection function, and (ii) a multiple-optimizers approach, where several optimizers, potentially run in parallel, are each initialized with a different solution, with the best solution chosen afterward. We validate our method on three optimal control benchmark tasks: cart-pole, reacher, and autonomous driving, using different optimizers: DDP, MPPI, and iLQR. We find significant and consistent improvement with our method across all evaluation settings and demonstrate that it efficiently scales with the number of initial solutions required. The code is available at $\href{https://github.com/EladSharony/miso}{\tt{https://github.com/EladSharony/miso}}$.

To understand the system-level interactions between the entities in Carbon Capture, Utilization, and Storage (CCUS), an agent-based foundational modeling tool, CCUS-Agent, is developed for a large-scale study of transportation flows and infrastructure in the United States. Key features of the tool include (i) modular design, (ii) multiple transportation modes, (iii) capabilities for extension, and (iv) testing against various system components and networks of small and large sizes. Five matching algorithms for CO2 supply agents (e.g., powerplants and industrial facilities) and demand agents (e.g., storage and utilization sites) are explored: Most Profitable First Year (MPFY), Most Profitable All Years (MPAY), Shortest Total Distance First Year (SDFY), Shortest Total Distance All Years (SDAY), and Shortest distance to long-haul transport All Years (ACAY). Before matching, the supply agent, demand agent, and route must be available, and the connection must be profitable. A profitable connection means the supply agent portion of revenue from the 45Q tax credit must cover the supply agent costs and all transportation costs, while the demand agent revenue portion must cover all demand agent costs. A case study employing over 5,500 supply and demand agents and multimodal CCUS transportation infrastructure in the contiguous United States is conducted. The results suggest that it is possible to capture over 9 billion tonnes (GT) of CO2 from 2025 to 2043, which will increase significantly to 22 GT if the capture costs are reduced by 40%. The MPFY and SDFY algorithms capture more CO2 earlier in the time horizon, while the MPAY and SDAY algorithms capture more later in the time horizon.

With its early roots in the development of calculus by Isaac Newton, Gottfried Wilhelm Leibniz, Pierre de Ferma t and others in the late 17th century, mathematical optimization has a rich his tory that involves contributions from numerous mathematicians, economists, eng ineers, and scientists. The birth of modern mathematical optimization is commonly c redited to George Dantzig, whose simplex algorithm developed in 1947 solves l inear optimization problems where ℓ is affine and X is a polyhedron ( Dantzig 1956). Subsequent milestones include the development of the rich theory of convex a nalysis ( Rockafellar 1970) as well as the discovery of polynomial-time solution metho ds for linear ( Khachiyan 1979, Karmarkar 1984) and broad classes of nonlinear convex optimization problems ( Nesterov and Nemirovskii 1994). Classical optimization problems are deterministic, that is, all problem data are assumed to be known with certainty. However, most decision pro blems encountered in practice depend on parameters that are corrupted by measu rement errors or that are revealed only after a decision must be determined and committed. A naïve approach to model uncertainty-affected decision problems a s deterministic optimization problems would be to replace all uncertain paramete rs with their expected values or with appropriate point predictions. However, it h as long been known and well-documented that decision-makers who replace an un certain parameter of an optimization problem with its mean value fall victim to th e'flaw of averages' ( Savage, Scholtes and Zweidler 2006, Savage 2012).

We present a novel methodology for convex optimization algorithm design using ideas from electric RLC circuits. Given an optimization problem, the first stage of the methodology is to design an appropriate electric circuit whose continuous-time dynamics converge to the solution of the optimization problem at hand. Then, the second stage is an automated, computer-assisted discretization of the continuous-time dynamics, yielding a provably convergent discrete-time algorithm. Our methodology recovers many classical (distributed) optimization algorithms and enables users to quickly design and explore a wide range of new algorithms with convergence guarantees.

Machine unlearning--enabling a trained model to forget specific data--is crucial for addressing biased data and adhering to privacy regulations like the General Data Protection Regulation (GDPR)'s "right to be forgotten". Recent works have paid little attention to privacy concerns, leaving the data intended for forgetting vulnerable to membership inference attacks. Moreover, they often come with high computational overhead. In this work, we propose Pseudo-Probability Unlearning (PPU), a novel method that enables models to forget data efficiently and in a privacy-preserving manner. Our method replaces the final-layer output probabilities of the neural network with pseudo-probabilities for the data to be forgotten. These pseudo-probabilities follow either a uniform distribution or align with the model's overall distribution, enhancing privacy and reducing risk of membership inference attacks. Our optimization strategy further refines the predictive probability distributions and updates the model's weights accordingly, ensuring effective forgetting with minimal impact on the model's overall performance. Through comprehensive experiments on multiple benchmarks, our method achieves over 20% improvements in forgetting error compared to the state-of-the-art. Additionally, our method enhances privacy by preventing the forgotten set from being inferred to around random guesses.

The efficacy of mathematical models heavily depends on the quality of the training data, yet collecting sufficient data is often expensive and challenging. Many modeling applications require inferring parameters only as a means to predict other quantities of interest (QoI). Because models often contain many unidentifiable (sloppy) parameters, QoIs often depend on a relatively small number of parameter combinations. Therefore, we introduce an information-matching criterion based on the Fisher Information Matrix to select the most informative training data from a candidate pool. This method ensures that the selected data contain sufficient information to learn only those parameters that are needed to constrain downstream QoIs. It is formulated as a convex optimization problem, making it scalable to large models and datasets. We demonstrate the effectiveness of this approach across various modeling problems in diverse scientific fields, including power systems and underwater acoustics. Finally, we use information-matching as a query function within an Active Learning loop for material science applications. In all these applications, we find that a relatively small set of optimal training data can provide the necessary information for achieving precise predictions. These results are encouraging for diverse future applications, particularly active learning in large machine learning models.