Many machine learning problems involve the challenge of approximating an intractable target distribution, which might only be known up to a normalization constant. Bayesian inference is a typical example, where the intractable and unnormalized target distribution is a result of the product of the prior and likelihood functions (see [11, 18, 4]). Variational Inference (VI), a widely employed across various application domains, seeks to approximate this intractable target distribution by utilizing a variational distribution (see [3, 7, 20] and references therein). VI is typically formulated as an optimization problem, with the objective of maximizing the evidence lower bound objective (ELBO), which is equivalent to minimizing the Kullback-Leiber (KL) divergence between the variational distribution and the target distribution. The conventional method for maximizing the ELBO involves the use of gradient descent, such as black-box VI (BBVI, [16]). The gradient of the ELBO can be expressed as an expectation over the variational distribution, which is typically estimated by Monte Carlo samples from this distribution.

Federated learning is a popular distributed and privacy-preserving machine learning paradigm. Meanwhile, minimax optimization, as an effective hierarchical optimization, is widely applied in machine learning. Recently, some federated optimization methods have been proposed to solve the distributed minimax problems. However, these federated minimax methods still suffer from high gradient and communication complexities. Meanwhile, few algorithm focuses on using adaptive learning rate to accelerate algorithms. To fill this gap, in the paper, we study a class of nonconvex minimax optimization, and propose an efficient adaptive federated minimax optimization algorithm (i.e., AdaFGDA) to solve these distributed minimax problems. Specifically, our AdaFGDA builds on the momentum-based variance reduced and local-SGD techniques, and it can flexibly incorporate various adaptive learning rates by using the unified adaptive matrix. Theoretically, we provide a solid convergence analysis framework for our AdaFGDA algorithm under non-i.i.d. setting. Moreover, we prove our algorithms obtain lower gradient (i.e., stochastic first-order oracle, SFO) complexity of $\tilde{O}(\epsilon^{-3})$ with lower communication complexity of $\tilde{O}(\epsilon^{-2})$ in finding $\epsilon$-stationary point of the nonconvex minimax problems. Experimentally, we conduct some experiments on the deep AUC maximization and robust neural network training tasks to verify efficiency of our algorithms.

Quantum computing (QC) is a field that has witnessed a rapid increase in interest and development over the past few decades since it was theoretically shown that quantum computers can provide an exponential speedup for certain tasks (Deutsch, Jozsa 1992; Grover 1996; Shor 1994). Translating this potential into a practically relevant quantum advantage, however, has proven to be a very challenging endeavor. Nevertheless, the emerging field is considered to have a highly disruptive potential for many domains, for example in machine learning (Schuld, Sinayskiy, Petruccione 2015), chemical simulations (Cao et al. 2019) and optimization (Li et al. 2020), the domain of this work. Due to the fact that optimization problems are of utmost importance also for industrial applications, we investigated a potential advantage of quantum and quantum-inspired technology for the so-called transport robot scheduling problem (TRSP), a real-world use-case in optimization that is derived from an industrial application of an automatized robot in a high-throughput laboratory. The optimization task is to plan a time-efficient schedule for the robot's movements as it transports chemical samples between a rack and multiple machines to conduct experiments.

Autonomous exploration is a fundamental problem for various applications of unmanned aerial vehicles(UAVs). Existing methods, however, are demonstrated to static local optima and two-dimensional exploration. To address these challenges, this paper introduces GO-FEAP (Global Optimal UAV Planner Using Frontier-Omission-Aware Exploration and Altitude-Stratified Planning), aiming to achieve efficient and complete three-dimensional exploration. Frontier-Omission-Aware Exploration module presented in this work takes into account multiple pivotal factors, encompassing frontier distance, nearby frontier count, frontier duration, and frontier categorization, for a comprehensive assessment of frontier importance. Furthermore, to tackle scenarios with substantial vertical variations, we introduce the Altitude-Stratified Planning strategy, which stratifies the three-dimensional space based on altitude, conducting global-local planning for each stratum. The objective of global planning is to identify the most optimal frontier for exploration, followed by viewpoint selection and local path optimization based on frontier type, ultimately generating dynamically feasible three-dimensional spatial exploration trajectories. We present extensive benchmark and real-world tests, in which our method completes the exploration tasks with unprecedented completeness compared to state-of-the-art approaches.

Oja's algorithm is a well known online algorithm studied mainly in the context of stochastic principal component analysis. We make a simple observation, yet to the best of our knowledge a novel one, that when applied to a any (not necessarily stochastic) sequence of symmetric matrices which share common eigenvectors, the regret of Oja's algorithm could be directly bounded in terms of the regret of the well known multiplicative weights update method for the problem of prediction with expert advice. Several applications to optimization with quadratic forms over the unit sphere in $\reals^n$ are discussed.

In the context of IoT deployments, a multitude of devices concurrently require network access to transmit data over a shared communication channel. Employing symmetric strategies can effectively facilitate the collaborative use of the communication medium among these devices. By adopting such strategies, devices collectively optimize their transmission parameters, resulting in minimized collisions and enhanced overall network throughput. Our primary focus centers on the formulation of symmetric (i.e., identical) strategies for the sensors, aiming to optimize a finite horizon team objective. The imposition of symmetric strategies introduces novel facets and complexities into the team problem. To address this, we embrace the common information approach and adapt it to accommodate the use of symmetric strategies. This adaptation yields a dynamic programming framework grounded in common information, wherein each step entails the minimization of a single function mapping from an agent's private information space to the space of probability distributions over possible actions. Our proposed policy/method incurs a reduced cumulative cost compared to other methods employing symmetric strategies, a point substantiated by our simulation results.

This paper proposes a new method for differentiating through optimal trajectories arising from non-convex, constrained discrete-time optimal control (COC) problems using the implicit function theorem (IFT). Previous works solve a differential Karush-Kuhn-Tucker (KKT) system for the trajectory derivative, and achieve this efficiently by solving an auxiliary Linear Quadratic Regulator (LQR) problem. In contrast, we directly evaluate the matrix equations which arise from applying variable elimination on the Lagrange multiplier terms in the (differential) KKT system. By appropriately accounting for the structure of the terms within the resulting equations, we show that the trajectory derivatives scale linearly with the number of timesteps. Furthermore, our approach allows for easy parallelization, significantly improved scalability with model size, direct computation of vector-Jacobian products and improved numerical stability compared to prior works. As an additional contribution, we unify prior works, addressing claims that computing trajectory derivatives using IFT scales quadratically with the number of timesteps. We evaluate our method on a both synthetic benchmark and four challenging, learning from demonstration benchmarks including a 6-DoF maneuvering quadrotor and 6-DoF rocket powered landing.

We introduce an efficient optimization-based meta-learning technique for large-scale neural field training by realizing significant memory savings through automated online context point selection. This is achieved by focusing each learning step on the subset of data with the highest expected immediate improvement in model quality, resulting in the almost instantaneous modeling of global structure and subsequent refinement of high-frequency details. We further improve the quality of our meta-learned initialization by introducing a bootstrap correction resulting in the minimization of any error introduced by reduced context sets while simultaneously mitigating the well-known myopia of optimization-based meta-learning. Finally, we show how gradient re-scaling at meta-test time allows the learning of extremely high-quality neural fields in significantly shortened optimization procedures. Our framework is model-agnostic, intuitive, straightforward to implement, and shows significant reconstruction improvements for a wide range of signals. We provide an extensive empirical evaluation on nine datasets across multiple multiple modalities, demonstrating state-of-the-art results while providing additional insight through careful analysis of the algorithmic components constituting our method. Code is available at https://github.com/jihoontack/GradNCP

Classical evolutionary approaches for multiobjective optimization are quite effective but incur a lot of queries to the objectives; this can be prohibitive when objectives are expensive oracles. A sample-efficient approach to solving multiobjective optimization is via Gaussian process (GP) surrogates and Bayesian optimization (BO). Multiobjective Bayesian optimization (MOBO) involves the construction of an acquisition function which is optimized to acquire new observation candidates. This ``inner'' optimization can be hard due to various reasons: acquisition functions being nonconvex, nondifferentiable and/or unavailable in analytical form; the success of MOBO heavily relies on this inner optimization. We do away with this hard acquisition function optimization step and propose a simple, but effective, Thompson sampling based approach ($q\texttt{POTS}$) where new candidate(s) are chosen from the Pareto frontier of random GP posterior sample paths obtained by solving a much cheaper multiobjective optimization problem. To further improve computational tractability in higher dimensions we propose an automated active set of candidates selection combined with a Nystr\"{o}m approximation. Our approach applies to arbitrary GP prior assumptions and demonstrates strong empirical performance over the state of the art, both in terms of accuracy and computational efficiency, on synthetic as well as real-world experiments.

Estimating the structure of directed acyclic graphs (DAGs) from observational data remains a significant challenge in machine learning. Most research in this area concentrates on learning a single DAG for the entire population. This paper considers an alternative setting where the graph structure varies across individuals based on available "contextual" features. We tackle this contextual DAG problem via a neural network that maps the contextual features to a DAG, represented as a weighted adjacency matrix. The neural network is equipped with a novel projection layer that ensures the output matrices are sparse and satisfy a recently developed characterization of acyclicity. We devise a scalable computational framework for learning contextual DAGs and provide a convergence guarantee and an analytical gradient for backpropagating through the projection layer. Our experiments suggest that the new approach can recover the true context-specific graph where existing approaches fail.