We present a model-agnostic framework for jointly optimizing the predictive performance and interpretability of supervised machine learning models for tabular data. Interpretability is quantified via three measures: feature sparsity, interaction sparsity of features, and sparsity of non-monotone feature effects. By treating hyperparameter optimization of a machine learning algorithm as a multi-objective optimization problem, our framework allows for generating diverse models that trade off high performance and ease of interpretability in a single optimization run. Efficient optimization is achieved via augmentation of the search space of the learning algorithm by incorporating feature selection, interaction and monotonicity constraints into the hyperparameter search space. We demonstrate that the optimization problem effectively translates to finding the Pareto optimal set of groups of selected features that are allowed to interact in a model, along with finding their optimal monotonicity constraints and optimal hyperparameters of the learning algorithm itself. We then introduce a novel evolutionary algorithm that can operate efficiently on this augmented search space. In benchmark experiments, we show that our framework is capable of finding diverse models that are highly competitive or outperform state-of-the-art XGBoost or Explainable Boosting Machine models, both with respect to performance and interpretability.

Different from conventional federated learning, personalized federated learning (PFL) is able to train a customized model for each individual client according to its unique requirement. The mainstream approach is to adopt a kind of weighted aggregation method to generate personalized models, in which weights are determined by the loss value or model parameters among different clients. However, such kinds of methods require clients to download others' models. It not only sheer increases communication traffic but also potentially infringes data privacy. In this paper, we propose a new PFL algorithm called \emph{FedDWA (Federated Learning with Dynamic Weight Adjustment)} to address the above problem, which leverages the parameter server (PS) to compute personalized aggregation weights based on collected models from clients. In this way, FedDWA can capture similarities between clients with much less communication overhead. More specifically, we formulate the PFL problem as an optimization problem by minimizing the distance between personalized models and guidance models, so as to customize aggregation weights for each client. Guidance models are obtained by the local one-step ahead adaptation on individual clients. Finally, we conduct extensive experiments using five real datasets and the results demonstrate that FedDWA can significantly reduce the communication traffic and achieve much higher model accuracy than the state-of-the-art approaches.

We propose a tuning-free dynamic SGD step size formula, which we call Distance over Gradients (DoG). The DoG step sizes depend on simple empirical quantities (distance from the initial point and norms of gradients) and have no ``learning rate'' parameter. Theoretically, we show that a slight variation of the DoG formula enjoys strong parameter-free convergence guarantees for stochastic convex optimization assuming only \emph{locally bounded} stochastic gradients. Empirically, we consider a broad range of vision and language transfer learning tasks, and show that DoG's performance is close to that of SGD with tuned learning rate. We also propose a per-layer variant of DoG that generally outperforms tuned SGD, approaching the performance of tuned Adam. A PyTorch implementation is available at https://github.com/formll/dog

On-orbit close proximity operations involve robotic spacecraft maneuvering and making decisions for a growing number of mission scenarios demanding autonomy, including on-orbit assembly, repair, and astronaut assistance. Of these scenarios, on-orbit assembly is an enabling technology that will allow large space structures to be built in-situ, using smaller building block modules. However, robotic on-orbit assembly involves a number of technical hurdles such as changing system models. For instance, grappled modules moved by a free-flying "assembler" robot can cause significant shifts in system inertial properties, which has cascading impacts on motion planning and control portions of the autonomy stack. Further, on-orbit assembly and other scenarios require collision-avoiding motion planning, particularly when operating in a "construction site" scenario of multiple assembler robots and structures. These complicating factors, relevant to many autonomous microgravity robotics use cases, are tackled in the ReSWARM flight experiments as a set of tests on the International Space Station using NASA's Astrobee robots. RElative Satellite sWarming and Robotic Maneuvering, or ReSWARM, demonstrates multiple key technologies for close proximity operations and on-orbit assembly: (1) global long-horizon planning, accomplished using offline and online sampling-based planner options that consider the system dynamics; (2) on-orbit reconfiguration model learning, using the recently-proposed RATTLE information-aware planning framework; and (3) robust control tools to provide low-level control robustness using current system knowledge. These approaches are detailed individually and in an "on-orbit assembly scenario" of multi-waypoint tracking on-orbit. Additionally, detail is provided discussing the practicalities of hardware implementation and unique aspects of working with Astrobee in microgravity.

Due to the high flexibility and remarkable performance, low-rank approximation methods has been widely studied for color image denoising. However, those methods mostly ignore either the cross-channel difference or the spatial variation of noise, which limits their capacity in real world color image denoising. To overcome those drawbacks, this paper is proposed to denoise color images with a double-weighted truncated nuclear norm minus truncated Frobenius norm minimization (DtNFM) method. Through exploiting the nonlocal self-similarity of the noisy image, the similar structures are gathered and a series of similar patch matrices are constructed. For each group, the DtNFM model is conducted for estimating its denoised version. The denoised image would be obtained by concatenating all the denoised patch matrices. The proposed DtNFM model has two merits. First, it models and utilizes both the cross-channel difference and the spatial variation of noise. This provides sufficient flexibility for handling the complex distribution of noise in real world images. Second, the proposed DtNFM model provides a close approximation to the underlying clean matrix since it can treat different rank components flexibly. To solve the problem resulted from DtNFM model, an accurate and effective algorithm is proposed by exploiting the framework of the alternating direction method of multipliers (ADMM). The generated subproblems are discussed in detail. And their global optima can be easily obtained in closed-form. Rigorous mathematical derivation proves that the solution sequences generated by the algorithm converge to a single critical point. Extensive experiments on synthetic and real noise datasets demonstrate that the proposed method outperforms many state-of-the-art color image denoising methods.

Motivated by bid recommendation in online ad auctions, this paper considers a general class of multi-level and multi-agent games, with two major characteristics: one is a large number of anonymous agents, and the other is the intricate interplay between competition and cooperation. To model such complex systems, we propose a novel and tractable bi-objective optimization formulation with mean-field approximation, called MESOB (Mean-field Equilibria & Social Optimality Balancing), as well as an associated occupation measure optimization (OMO) method called MESOB-OMO to solve it. MESOB-OMO enables obtaining approximately Pareto efficient solutions in terms of the dual objectives of competition and cooperation in MESOB, and in particular allows for Nash equilibrium selection and social equalization in an asymptotic manner. We apply MESOB-OMO to bid recommendation in a simulated pay-per-click ad auction. Experiments demonstrate its efficacy in balancing the interests of different parties and in handling the competitive nature of bidders, as well as its advantages over baselines that only consider either the competitive or the cooperative aspects.

Ensemble Kalman inversion (EKI) is a sequential Monte Carlo method used to solve inverse problems within a Bayesian framework. Unlike backpropagation, EKI is a gradient-free optimization method that only necessitates the evaluation of artificial neural networks in forward passes. In this study, we examine the effectiveness of EKI in training neural ordinary differential equations (neural ODEs) for system identification and control tasks. To apply EKI to optimal control problems, we formulate inverse problems that incorporate a Tikhonov-type regularization term. Our numerical results demonstrate that EKI is an efficient method for training neural ODEs in system identification and optimal control problems, with runtime and quality of solutions that are competitive with commonly used gradient-based optimizers.

This paper focuses on spatial time-optimal motion planning, a generalization of the exact time-optimal path following problem that allows the system to plan within a predefined space. In contrast to state-of-the-art methods, we drop the assumption that a collision-free geometric reference is given. Instead, we present a two-stage motion planning method that solely relies on a goal location and a geometric representation of the environment to compute a time-optimal trajectory that is compliant with system dynamics and constraints. To do so, the proposed scheme first computes an obstacle-free Pythagorean Hodograph parametric spline, and second solves a spatially reformulated minimum-time optimization problem. The spline obtained in the first stage is not a geometric reference, but an extension of the environment representation, and thus, time-optimality of the solution is guaranteed. The efficacy of the proposed approach is benchmarked by a known planar example and validated in a more complex spatial system, illustrating its versatility and applicability.

Online resource allocation seeks to maximize the total rewards in an online service system that is subject to resource constraints. As an exemplary model for sequential decision-making, online allocation has drawn considerable attention in recent decades. Meanwhile, it is strongly connected to other online problems such as revenue management (Talluri et al., 2004), online linear programming (Agrawal et al., 2014), and ads bidding problems (Lee et al., 2013), to name but a few. Online allocation finds applications in diverse fields, e.g., computer science and operation research. Oftentimes, online allocation problems feature resource constraints that are either hard (Mehta et al., 2007) or soft (Mahdavi et al., 2012), with different constraint capacities. The goal of a decision maker is to maximize the total rewards (revenue, utility) function by a real-time decision policy that enforces each of the resource constraints. So far, existing literature on online allocation mostly focused on additively separable objectives, i.e., the objective function only involves the total rewards that can be simply described as the cumulative rewards by time (e.g., Mehta et al. (2007); Devanur and Hayes (2009); Balseiro and Gur (2019)). While a separable objective is favorable for tracking additive total rewards, it falls short of describing globally non-separable quantities such as total resource consumption or average actions. For instance, the average action (Agrawal and Devanur, 2014) in online advertising measures the amount of underdelivery of impressions.

We present a stochastic optimization method that uses a fourth-order regularized model to find local minima of smooth and potentially non-convex objective functions with a finite-sum structure. This algorithm uses sub-sampled derivatives instead of exact quantities. The proposed approach is shown to find an $(\epsilon_1,\epsilon_2,\epsilon_3)$-third-order critical point in at most $\bigO\left(\max\left(\epsilon_1^{-4/3}, \epsilon_2^{-2}, \epsilon_3^{-4}\right)\right)$ iterations, thereby matching the rate of deterministic approaches. In order to prove this result, we derive a novel tensor concentration inequality for sums of tensors of any order that makes explicit use of the finite-sum structure of the objective function.