Designing products to meet consumers' preferences is essential for a business's success. We propose the Gradient-based Survey (GBS), a discrete choice experiment for multiattribute product design. The experiment elicits consumer preferences through a sequence of paired comparisons for partial profiles. GBS adaptively constructs paired comparison questions based on the respondents' previous choices. Unlike the traditional random utility maximization paradigm, GBS is robust to model misspecification by not requiring a parametric utility model. Cross-pollinating the machine learning and experiment design, GBS is scalable to products with hundreds of attributes and can design personalized products for heterogeneous consumers. We demonstrate the advantage of GBS in accuracy and sample efficiency compared to the existing parametric and nonparametric methods in simulations.

Robots need to predict and react to human motions to navigate through a crowd without collisions. Many existing methods decouple prediction from planning, which does not account for the interaction between robot and human motions and can lead to the robot getting stuck. We propose SICNav, a Model Predictive Control (MPC) method that jointly solves for robot motion and predicted crowd motion in closed-loop. We model each human in the crowd to be following an Optimal Reciprocal Collision Avoidance (ORCA) scheme and embed that model as a constraint in the robot's local planner, resulting in a bilevel nonlinear MPC optimization problem. We use a KKT-reformulation to cast the bilevel problem as a single level and use a nonlinear solver to optimize. Our MPC method can influence pedestrian motion while explicitly satisfying safety constraints in a single-robot multi-human environment. We analyze the performance of SICNav in a simulation environment to demonstrate safe robot motion that can influence the surrounding humans. We also validate the trajectory forecasting performance of ORCA on a human trajectory dataset.

Data generation and analysis is a fundamental aspect of many industries and disciplines, from strategic decision making in business to research in the physical and social sciences. However, data generated using software and algorithms can be subject to biases and errors. These can be due to problems with the original software, default settings that do not align with the specific needs of the situation, or even deeper problems with the underlying theories and models. This paper proposes an advanced search and optimization framework aimed at generating and choosing optimal source code capable of correcting errors and biases from previous versions to address typical problems in software systems specializing in data analysis and generation, especially those in the corporate and data science world. Applying this framework multiple times on the same software system would incrementally improve the quality of the output results. It uses Solomonoff Induction as a sound theoretical basis, extending it with Kolmogorov Conditional Complexity, a novel adaptation, to evaluate a set of candidate programs. We propose the use of generative models for the creation of this set of programs, with special emphasis on the capabilities of Large Language Models (LLMs) to generate high quality code.

The delta-bar-delta algorithm is recognized as a learning rate adaptation technique that enhances the convergence speed of the training process in optimization by dynamically scheduling the learning rate based on the difference between the current and previous weight updates. While this algorithm has demonstrated strong competitiveness in full data optimization when compared to other state-of-the-art algorithms like Adam and SGD, it may encounter convergence issues in mini-batch optimization scenarios due to the presence of noisy gradients. In this study, we thoroughly investigate the convergence behavior of the delta-bar-delta algorithm in real-world neural network optimization. To address any potential convergence challenges, we propose a novel approach called RDBD (Regrettable Delta-Bar-Delta). Our approach allows for prompt correction of biased learning rate adjustments and ensures the convergence of the optimization process. Furthermore, we demonstrate that RDBD can be seamlessly integrated with any optimization algorithm and significantly improve the convergence speed. By conducting extensive experiments and evaluations, we validate the effectiveness and efficiency of our proposed RDBD approach. The results showcase its capability to overcome convergence issues in mini-batch optimization and its potential to enhance the convergence speed of various optimization algorithms. This research contributes to the advancement of optimization techniques in neural network training, providing practitioners with a reliable automatic learning rate scheduler for achieving faster convergence and improved optimization outcomes.

This work proposes FedLAP-DP, a novel privacy-preserving approach for federated learning. Unlike previous linear point-wise gradient-sharing schemes, such as FedAvg, our formulation enables a type of global optimization by leveraging synthetic samples received from clients. We additionally introduce an approach to measure effective approximation regions reflecting the quality of the approximation. Therefore, the server can recover an approximation of the global loss landscape and optimize the model globally. Moreover, motivated by the emerging privacy concerns, we demonstrate that our approach seamlessly works with record-level differential privacy (DP), granting theoretical privacy guarantees for every data record on the clients. Extensive results validate the efficacy of our formulation on various datasets with highly skewed distributions. Our method consistently improves over the baselines, especially considering highly skewed distributions and noisy gradients due to DP. The source code and setup will be released upon publication. Federated Learning (FL) (McMahan et al., 2017) is a distributed learning framework that allows participants to train a model collaboratively without sharing their data. Predominantly, existing works (McMahan et al., 2017; Karimireddy et al., 2020; Li et al., 2020) achieve this by training local models on clients' private datasets and sharing only the gradients with the central server. Despite extensive research over the past few years, these prevalent gradient-based methods still suffer from several challenges (Kairouz et al., 2021), such as data heterogeneity, potential risks of privacy breaches, and high communication costs.

We study sequential decision making problems aimed at maximizing the expected total reward while satisfying a constraint on the expected total utility. We employ the natural policy gradient method to solve the discounted infinite-horizon optimal control problem for Constrained Markov Decision Processes (constrained MDPs). Specifically, we propose a new Natural Policy Gradient Primal-Dual (NPG-PD) method that updates the primal variable via natural policy gradient ascent and the dual variable via projected sub-gradient descent. Although the underlying maximization involves a nonconcave objective function and a nonconvex constraint set, under the softmax policy parametrization we prove that our method achieves global convergence with sublinear rates regarding both the optimality gap and the constraint violation. Such convergence is independent of the size of the state-action space, i.e., it is dimension-free. Furthermore, for log-linear and general smooth policy parametrizations, we establish sublinear convergence rates up to a function approximation error caused by restricted policy parametrization. We also provide convergence and finitesample complexity guarantees for two sample-based NPG-PD algorithms. Finally, we use computational experiments to showcase the merits and the effectiveness of our approach. Keywords: Constrained Markov decision processes; Natural policy gradient; Constrained nonconvex optimization; Method of Lagrange multipliers; Primal-dual algorithms.

We study online reinforcement learning in linear Markov decision processes with adversarial losses and bandit feedback, without prior knowledge on transitions or access to simulators. We introduce two algorithms that achieve improved regret performance compared to existing approaches. The first algorithm, although computationally inefficient, ensures a regret of $\widetilde{\mathcal{O}}\left(\sqrt{K}\right)$, where $K$ is the number of episodes. This is the first result with the optimal $K$ dependence in the considered setting. The second algorithm, which is based on the policy optimization framework, guarantees a regret of $\widetilde{\mathcal{O}}\left(K^{\frac{3}{4}} \right)$ and is computationally efficient. Both our results significantly improve over the state-of-the-art: a computationally inefficient algorithm by Kong et al. [2023] with $\widetilde{\mathcal{O}}\left(K^{\frac{4}{5}}+poly\left(\frac{1}{\lambda_{\min}}\right) \right)$ regret, for some problem-dependent constant $\lambda_{\min}$ that can be arbitrarily close to zero, and a computationally efficient algorithm by Sherman et al. [2023b] with $\widetilde{\mathcal{O}}\left(K^{\frac{6}{7}} \right)$ regret.

In this paper, we introduce two Gromov-Wasserstein-type distances on the set of Gaussian mixture models. The first one takes the form of a Gromov-Wasserstein distance between two discrete distributionson the space of Gaussian measures. This distance can be used as an alternative to Gromov-Wasserstein for applications which only require to evaluate how far the distributions are from each other but does not allow to derive directly an optimal transportation plan between clouds of points. To design a way to define such a transportation plan, we introduce another distance between measures living in incomparable spaces that turns out to be closely related to Gromov-Wasserstein. When restricting the set of admissible transportation couplings to be themselves Gaussian mixture models in this latter, this defines another distance between Gaussian mixture models that can be used as another alternative to Gromov-Wasserstein and which allows to derive an optimal assignment between points. Finally, we design a transportation plan associated with the first distance by analogy with the second, and we illustrate their practical uses on medium-to-large scale problems such as shape matching and hyperspectral image color transfer.

The advent of reconfigurable intelligent surfaces(RISs) brings along significant improvements for wireless technology on the verge of beyond-fifth-generation networks (B5G).The proven flexibility in influencing the propagation environment opens up the possibility of programmatically altering the wireless channel to the advantage of network designers, enabling the exploitation of higher-frequency bands for superior throughput overcoming the challenging electromagnetic (EM) propagation properties at these frequency bands. However, RISs are not magic bullets. Their employment comes with significant complexity, requiring ad-hoc deployments and management operations to come to fruition. In this paper, we tackle the open problem of bringing RISs to the field, focusing on areas with little or no coverage. In fact, we present a first-of-its-kind deep reinforcement learning (DRL) solution, dubbed as D-RISA, which trains a DRL agent and, in turn, obtain san optimal RIS deployment. We validate our framework in the indoor scenario of the Rennes railway station in France, assessing the performance of our algorithm against state-of-the-art (SOA) approaches. Our benchmarks showcase better coverage, i.e., 10-dB increase in minimum signal-to-noise ratio (SNR), at lower computational time (up to -25 percent) while improving scalability towards denser network deployments.

In this paper, we propose a novel data-driven approach for learning and control of quadrotor UAVs based on the Koopman operator and extended dynamic mode decomposition (EDMD). Building observables for EDMD based on conventional methods like Euler angles (to represent orientation) is known to involve singularities. To address this issue, we employ a set of physics-informed observables based on the underlying topology of the nonlinear system. We use rotation matrices to directly represent the orientation dynamics and obtain a lifted linear representation of the nonlinear quadrotor dynamics in the SE(3) manifold. This EDMD model leads to accurate prediction and can be generalized to several validation sets. Further, we design a linear model predictive controller (MPC) based on the proposed EDMD model to track agile reference trajectories. Simulation results show that the proposed MPC controller can run as fast as 100 Hz and is able to track arbitrary reference trajectories with good accuracy. Implementation details can be found in \url{https://github.com/sriram-2502/KoopmanMPC_Quadrotor}.